computational plasticity for composite structures based on mathematical homogenization theory and practice abstract this paper generalizes the classical mathematical homogenization theory for heterogeneous medium to account for eigenstrains starting from the double scale asymptotic expansion for the displacement and eigenstrain fields we derive a close form expression relating arbitrary eigenstrains to the mechanical fields in the phases the overall structural response is computed using an averaging scheme by which phase concentration factors are computed in the average sense for each micro constituent and history data is updated at two points reinforcement and matrix in the microstructure one for each phase macroscopic history data is stored in the database and then subjected in the post processing stage onto the unit cell in the critical locations for numerical examples considered the cpu time obtained by means of the two point averaging scheme with variational micro history recovery with 30 seconds on sparc 10 51 as opposed to 7 hours using classical mathematical homogenization theory at the same time the maximum error in the microstress field in the critical unit cell was only 3 5 in comparison with the classical mathematical homogenization theory

two stage orthogonal least squares methods for neural network construction a number of neural networks can be formulated as the linear in the parameters models training such networks can be transformed to a model selection problem where a compact model is selected from all the candidates using subset selection algorithms forward selection methods are popular fast subset selection approaches however they may only produce suboptimal models and can be trapped into a local minimum more recently a two stage fast recursive algorithm tsfra combining forward selection and backward model refinement has been proposed to improve the compactness and generalization performance of the model this paper proposes unified two stage orthogonal least squares methods instead of the fast recursive based methods in contrast to the tsfra this paper derives a new simplified relationship between the forward and the backward stages to avoid repetitive computations using the inherent orthogonal properties of the least squares methods furthermore a new term exchanging scheme for backward model refinement is introduced to reduce computational demand finally given the error reduction ratio criterion effective and efficient forward and backward subset selection procedures are proposed extensive examples are presented to demonstrate the improved model compactness constructed by the proposed technique in comparison with some popular methods

analysis of input output clustering for determining centers of rbfn the key point in design of radial basis function networks is to specify the number and the locations of the centers several heuristic hybrid learning methods which apply a clustering algorithm for locating the centers and subsequently a linear least squares method for the linear weights have been previously suggested these hybrid methods can be put into two groups which will be called as input clustering ic and input output clustering ioc depending on whether the output vector is also involved in the clustering process the idea of concatenating the output vector to the input vector in the clustering process has independently been proposed by several papers in the literature although none of them presented a theoretical analysis on such procedures but rather demonstrated their effectiveness in several applications the main contribution of this paper is to present an approach for investigating the relationship between clustering process on input output training samples and the mean squared output error in the context of a radial basis function network rbfn we may summarize our investigations in that matter as follows 1 a weighted mean squared input output quantization error which is to be minimized by ioc yields an upper bound to the mean squared output error 2 this upper bound and consequently the output error can be made arbitrarily small zero in the limit case by decreasing the quantization error which can be accomplished through increasing the number of hidden units

formulation methods of geometric and material nonlinearity problems a concise survey of formulation methods of geometric and material nonlinearity problems is given differences between existing formulations in the literature are discussed a consistent lagrangian and updated lagrangian formulations are derived from the energy balance equation transformed to the proper reference configuration differences between the existing formulations and similar ones in the literature are found to be in specific geometric nonlinear terms in the final incremental equation as well as in the definition of the load increment vector specific forms of constitutive equations for elastic and elastoplastic materials are presented some of the forms used by other authors in application to elastoplastic materials are shown to be inconsistent sample numerical examples intended for checking some particular points in the formulation are presented

a new discrete continuous algorithm for radial basis function networks construction the construction of a radial basis function rbf network involves the determination of the model size hidden nodes and output weights least squares based subset selection methods can determine a rbf model size and its parameters simultaneously although these methods are robust they may not achieve optimal results alternatively gradient methods are widely used to optimize all the parameters the drawback is that most algorithms may converge slowly as they treat hidden nodes and output weights separately and ignore their correlations in this paper a new discrete continuous algorithm is proposed for the construction of a rbf model first the orthogonal least squares ols based forward stepwise selection constructs an initial model by selecting model terms one by one from a candidate term pool then a new levenberg marquardt lm based parameter optimization is proposed to further optimize the hidden nodes and output weights in the continuous space to speed up the convergence the proposed parameter optimization method considers the correlation between the hidden nodes and output weights which is achieved by translating the output weights to dependent parameters using the ols method the correlation is also used by the previously proposed continuous forward algorithm cfa however unlike the cfa the new method optimizes all the parameters simultaneously in addition an equivalent recursive sum of squared error is derived to reduce the computation demanding for the first derivatives used in the lm method computational complexity is given to confirm the new method is much more computationally efficient than the cfa different numerical examples are presented to illustrate the effectiveness of the proposed method further friedman statistical tests on 13 classification problems are performed and the results demonstrate that rbf networks built by the new method are very competitive in comparison with some popular classifiers

on the implementation of inelastic constitutive equations with special reference to large deformation problems abstract methods for finite element analysis of inelastic problems are reviewed problems with currently popular methods based on rate principles of virtual work are pointed out a formulation is presented based on the exact incremental virtual work equation the procedure for integration of the constitutive rate equations to obtain incremental constitutive equations is based on the assumption of a constant strain rate or straight strain path during the increment full newton raphson iteration is used to solve the resulting set of nonlinear equations the treatment of the constitutive equations in this newton raphson scheme leads to a linearized form which is substantially different from the classical rate equations the procedure is implemented in a finite element program and its effectiveness is shown in a number of examples

algorithmic issues for three invariant hyperplastic critical state models implicit stress integration and the consistent tangents are presented for critical state hyperplasticity models which include a dependence on the third invariant of stress an elliptical deviatoric yielding criterion 43 is incorporated within the family of geotechnical models first proposed by collins and hilder 8 an alternative expression for the yield function is proposed and the consequences of different forms of that function are revealed in terms of the stability and efficiency of the stress return algorithm errors associated with the integration scheme are presented it is shown how calibration of the two new material constants is achieved through examining one dimesional consolidation tests and undrained triaxial compression data material point simulations of drained triaxial compression tests are then compared with established experimental results strain probe analyses are used to demonstrate the concepts of energy dissipation and stored plastic work along with the robustness of the integration method over twenty finite element boundary value problems are then simulated these include single three dimensional element tests plane strain footing analyses and cavity expansion tests the rapid convergence of the global newton raphson procedure using the consistent tangent is demonstrated in small strain and finite deformation simulations

efficient and modular algorithms in modeling finite inelastic deformations objective integration parameter identification and sub stepping techniques this paper presents a general algorithmic formulation for constitutive equations describing inelastic material deformation the algorithmic representation focuses on the generality and modularity which is a key aspect within the development phase of constitutive equations it is shown explicitly how to solve the incremental constitutive equations by use of objective algorithms and an implicit integration scheme applying numerical as well as analytical derivatives although it is shown that using numerical gradients is significantly slower their application is easier especially in the development phase it is also demonstrated that having the constitutive equations modeled in the general context introduced the issue of parameter identification can be tackled by the same implementation using a driver algorithm besides parameter identification the general structure is also applied to two different fe simulations first the objectivity of different integration methods will be presented considering a simple shear loading superposed by a rigid rotation using a strain rate independent material model as example in the second example it is shown for a strain rate dependent material model how the simulation of the wire drawing process can be accelerated crucially by using sub stepping techniques

forward and backward least angle regression for nonlinear system identification a forward and backward least angle regression lar algorithm is proposed to construct the nonlinear autoregressive model with exogenous inputs narx that is widely used to describe a large class of nonlinear dynamic systems the main objective of this paper is to improve model sparsity and generalization performance of the original forward lar algorithm this is achieved by introducing a replacement scheme using an additional backward lar stage the backward stage replaces insignificant model terms selected by forward lar with more significant ones leading to an improved model in terms of the model compactness and performance a numerical example to construct four types of narx models namely polynomials radial basis function rbf networks neuro fuzzy and wavelet networks is presented to illustrate the effectiveness of the proposed technique in comparison with some popular methods

nonsmooth dynamics in spiking neuron models large scale studies of spiking neural networks are a key part of modern approaches to understanding the dynamics of biological neural tissue one approach in computational neuroscience has been to consider the detailed electrophysiological properties of neurons and build vast computational compartmental models an alternative has been to develop minimal models of spiking neurons with a reduction in the dimensionality of both parameter and variable space that facilitates more effective simulation studies in this latter case the single neuron model of choice is often a variant of the classic integrate and fire model which is described by a nonsmooth dynamical system in this paper we review some of the more popular spiking models of this class and describe the types of spiking pattern that they can generate ranging from tonic to burst firing we show that a number of techniques originally developed for the study of impact oscillators are directly relevant to their analysis particularly those for treating grazing bifurcations importantly we highlight one particular single neuron model capable of generating realistic spike trains that is both computationally cheap and analytically tractable this is a planar nonlinear integrate and fire model with a piecewise linear vector field and a state dependent reset upon spiking we call this the pwl if model and analyse it at both the single neuron and network level the techniques and terminology of nonsmooth dynamical systems are used to flesh out the bifurcation structure of the single neuron model as well as to develop the notion of liapunov exponents we also show how to construct the phase response curve for this system emphasising that techniques in mathematical neuroscience may also translate back to the field of nonsmooth dynamical systems the stability of periodic spiking orbits is assessed using a linear stability analysis of spiking times at the network level we consider linear coupling between voltage variables as would occur in neurobiological networks with gap junction coupling and show how to analyse the properties existence and stability of both the asynchronous and synchronous states in the former case we use a phase density technique that is valid for any large system of globally coupled limit cycle oscillators whilst in the latter we develop a novel technique that can handle the nonsmooth reset of the model upon spiking finally we discuss other aspects of neuroscience modelling that may benefit from further translation of ideas from the growing body of knowledge on nonsmooth dynamics

analysis of augmented input layer rbfnn in this paper we present and analyze a new structure for designing a radial basis function neural network rbfnn in the training phase input layer of rbfnn is augmented with desired output vector generalization phase involves the following steps 1 identify the cluster to which a previously unseen input vector belongs 2 augment the input layer with an average of the targets of the input vectors in the identified cluster and 3 use the augmented network to estimate the unknown target it is shown that under some reasonable assumptions the generalization error function admits an upper bound in terms of the quantization errors minimized when determining the centers of the proposed method over the training set and the difference between training samples and generalization samples in a deterministic setting when the difference between the training and generalization samples goes to zero the upper bound can be made arbitrarily small by increasing the number of hidden neurons computer simulations verified the effectiveness of the proposed method

comparison of different isotropic elastoplastic models at finite strains used in numerical analysis several thermodynamically consistent isotropic elastoplastic models at finite strains that are based on the multiplicative decomposition of the total deformation gradient are analyzed and compared it occurs that some of them that are often used in numerical calculations and cited in literature are completely equivalent and give the same results despite quite different structures of the final equations however not all models for isotropic elastoplasticity at finite strains that are based on the multiplicative decomposition of the total deformation gradient and the same elastic and plastic constitutive equations are equivalent because of different equations for the plastic rotation tensor comparison of some models showed their dependency on equations for the plastic spin such equations are often accepted as assumptions that help to construct an effective numerical algorithm it is shown that the assumption of a zero modified plastic spin for a thermoelastoplastic model with the thermal deformation gradient leads to a new very effective finite element procedure that is similar to the case of small strains the derivation and details of such a numerical algorithm are given a two dimensional thermoelastoplastic problem at finite strains is solved

nonlinear thin shell analysis using a curved triangular element abstract this paper describes a simple but robust curved triangular thin shell element the element has twelve degrees of freedom namely the displacement components in the corner nodes and the rotations about the element sides the element is based upon the well known facet element with constant membrane strains and constant stress couples and is augmented to take into account the influence of the changes of curvature on the membrane deformations due to the quadratic character of this influence curved geometries can be modelled in order to permit arbitrarily large rotational increments reference vectors are attached to each element side these reference vectors are updated by means of orthogonal transformations the latter are determined uniquely by the subsequent orientations of the associated element sides the changes of curvature are evaluated using these reference vectors and a corotated reference configuration to describe time independent elastoplasticity a layered shell model is applied while besseling s fraction model is adopted for each layer a number of numerical examples illustrate the performance of the element

fully implicit formulation of elastoplastic homogenization problem for two scale analysis abstract in this study using a virtual work equation a micro macro kinematic relation and a linearized constitutive relation a boundary value problem is fully implicitly formulated to determine perturbed displacement increment fields in elastoplastic unit cells for two scale analysis it is shown that this implicit homogenization problem can be iteratively solved with quadratic convergences by successively updating strain increment fields in unit cells and that the boundary value problem formulated provides a computational algorithm which is versatile for initial setting of strain increment fields the computational algorithm developed is then examined by performing a two scale analysis of a holed plate with an elastoplastic micro structure subjected to tensile loading this demonstrates that the convergence in iteratively solving the implicit homogenization problem strongly depends on the initial setting of strain increment fields in unit cells

design sensitivity analysis of elastoplastic structures an iterative and incremental algorithm is presented for the design sensitivity analysis dsa of elastoplastic structures geometrical non linearity is included in the formulation and the structure may be subjected to a cyclic loading the key concept is discussed using an elastoplastic truss it is shown that the design sensitivity coefficients dscs are path dependent and discontinuous at the time at which yielding takes place in a member yield time in the proposed algorithm the yield time is considered to be a function of the design variables in this way the discontinuity in the dscs at the material transition points can be overcome in a simple and routine way incremental response analysis and dsa are carried out simultaneously using the newton raphson type iterative procedure since the proposed algorithm is completely consistent with the analysis procedure it can be implemented into an existing code for structural analysis application to distributed parameter structures with kinematic and or isotropic hardening is discussed using the von mises yield condition and the elastic predictor radial return method dsa is carried out for a ten bar truss with a piecewise linear constitutive relation it is shown that the dscs found using the proposed method agree quite well with those calculated by the central difference method finally an alternate method without any iteration for dsa is proposed and the results from the two methods are compared

computational model for 3 d contact problems with friction based on the penalty method the friction forces are assumed to follow the coulomb law with a slip criterion treated in the context of a standard return mapping algorithm consistent linearization of the field equations is performed which leads to a fully implicit scheme with non symmetric tangent stiffness which preserves asymptotic quadratic convergence of the newton raphson method

finite deformation formulation for embedded frictional crack with the extended finite element method we reformulate an extended finite element fe framework for embedded frictional cracks in elastoplastic solids to accommodate finite deformation including finite stretching and rotation for the fe representation we consider a galerkin approximation in which both the trial and weighting functions adapt to the current contact configuration contact and frictional constraints employ two kuhn tucker conditions a contact separation constraint nesting over a stick slip constraint for the case when the crack faces are in frictional sliding mode we integrate finite deformation bulk plasticity into the formulation using the multiplicative decomposition technique of nonlinear continuum mechanics we then present plane strain simulations demonstrating various aspects of the extended fe solutions the mechanisms considered include combined opening and frictional sliding in initially straight curved and s shaped cracks with and without bulk plasticity to gain further insight into the extended fe solutions we perform mesh convergence studies focusing on both the global and the local responses of structures with cracks including the distribution of the normal component of traction on the crack faces copyright 2009 john wiley sons ltd

material growth in thermoelastic continua theory algorithmics and simulation a theoretical formulation of stress induced volumetric material growth in thermoelastic continua is developed material growth is regulated by a three surface activation criterion and corresponding flow rules a simple model is proposed based on this formulation and its algorithmic implementation including a method for solving the underlying differential algebraic equations for growth is examined in the context of an implicit finite element method selected numerical simulations are presented that showcase the predictive capacity of the model for both soft and hard biomaterials

an extended orthogonal forward regression algorithm for system identification using entropy in this paper a fast identification algorithm for non linear dynamic stochastic system identification is presented the algorithm extends the classical orthogonal forward regression ofr algorithm so that instead of using the error reduction ratio err for term selection a new optimality criterion shannon s entropy power reduction ratio eprr is introduced to deal with both gaussian and non gaussian signals it is shown that the new algorithm is both fast and reliable and examples are provided to illustrate the effectiveness of the new approach

numerical simulation of ductile fracture with the rousselier constitutive law this contribution aims at developing robust and reliable tools dedicated to predictive numerical simulation of ductile fracture description of damage mechanisms relies here on the rousselier constitutive law to achieve robustness and objectivity several points need then to be addressed reduction of the set of internal variables so as to recast the model into the framework of generalised standard materials proper expression of the normal plastic flow rule at the vertex of the yield surface finite strain formulation based on a multiplicative split of the deformation gradient fully implicit integration of the constitutive equations leading to a single scalar equation that admits a unique root use of mixed finite elements to avoid volumetric locking strain gradient based nonlocal model to control strain localisation and remedy spurious mesh dependency the capabilities of the resulting numerical formulation are demonstrated through simulating the cup cone fracture of a notched tensile specimen

internal symmetry groups for the drucker prager material model of plasticity and numerical integrating methods abstract internal symmetries for the drucker prager material model and numerical methods based on them are investigated here we first convert the non linear constitutive equations to a lie type system x a x t x where a sl 5 2 r is a lie algebra of the special orthochronous pseudo linear group sl 5 2 r the underlying space of drucker prager model in the plastic phase is a pseudo sphere in the pseudo riemann manifold which is locally a pseudo euclidean space e 7 5 2 and whose metric tensor is indefinite having signature 5 2 and also depends on the temporal component then we split the drucker prager yield condition into two sub yield conditions which together with two integrating factors idea led us to derive two lie type systems in the product space m 5 1 m 1 1 the lie algebra is the direct sum so 5 1 so 1 1 and the symmetry group is thus soo 5 1 soo 1 1 these results are essential from computational aspect based on these symmetry groups exponential mappings are developed which update stress points exactly on the yield surface at every time increment without any iteration as an example the results calculated by using the two different group preserving schemes are compared to that calculated by the runge kutta scheme together with the newton raphson iterative solution of a non linear algebraic equation which enforcing the consistency condition

computational modeling of deformation bands in granular media ii numerical simulations development of accurate mathematical models of geomaterial behavior requires a more fundamental understanding of the localization phenomena in particular the important factors responsible for the inception and development of localized deformation the objective of this paper is to implement and test the mathematical formulations presented in a companion paper to better understand the different failure processes in granular media specifically the formation of deformation bands in geomaterials our approach revolves around the use of classical bifurcation theory combined with advanced constitutive modeling and state of the art computation to capture the end members of the failures modes described in the companion paper namely simple shear pure compaction and pure dilation bands as well as the combination modes described in the geological framework the paper revisits the notion of the critical hardening modulus as it applies to the entire range of failure modes elucidates the role of the third stress invariant and finite deformation effects on the localization properties and describes some useful properties of the constitutive and algorithmic tangent operators as they relate to the capture of the onset of deformation bands in geomaterials

network amplification of local fluctuations causes high spike rate variability fractal firing patterns and oscillatory local field potentials we investigate a model for neural activity in a two dimensional sheet of leaky integrate and fire neurons with feedback connectivity consisting of local excitation and surround inhibition each neuron receives stochastic input from an external source independent in space and time as recently suggested by softky and koch 1992 1993 independent stochastic input alone cannot explain the high interspike interval variability exhibited by cortical neurons in behaving monkeys we show that high variability can be obtained due to the amplification of correlated fluctuations in a recurrent network furthermore the cross correlation functions have a dual structure with a sharp peak on top of a much broader hill this is due to the inhibitory and excitatory feedback connections which cause hotspots of neural activity to form within the network these localized patterns of excitation appear as clusters or stripes that coalesce disintegrate or fluctuate in size while simultaneously moving in a random walk constrained by the interaction with other clusters the synaptic current impinging upon a single neuron shows large fluctuations at many time scales leading to a large coefficient of variation cv for the interspike interval statistics the power spectrum associated with single units shows a 1 f decay for small frequencies and is flat at higher frequencies while the power spectrum of the spiking activity averaged over many cells equivalent to the local field potential shows no 1 f decay but a prominent peak around 40 hz in agreement with data recorded from cat and monkey cortex gray et al 1990 eckhorn et al 1993 firing rates exhibit self similarity between 20 and 800 msec resulting in 1 f like noise consistent with the fractal nature of neural spike trains teich 1992

finite deformation plasticity based on the additive split of the rate of deformation and hyperelasticity abstract finite deformation plasticity formulation based on additive split of rate of deformation and hyperelasticity is presented this approach is valid for finite elastic and plastic strains while rendering the choice and numerical integration of objective stress rates superfluous as the results are automatically objective for small elastic strains our method reduces to the classical hypoelastic corotational formulation provided that the dienes objective stress rate is employed while in the absence of inelastic deformation it coincides with the hyper elastic formulation the validity of the model has been examined on four test problems and the numerical results were found to be in good agreement with either the exact solution or experimental data

dynamics of two mutually coupled slow inhibitory neurons abstract inhibition in oscillatory networks of neurons can have apparently paradoxical effects sometimes creating dispersion of phases sometimes fostering synchrony in the network we analyze a pair of biophysically modeled neurons and show how the rates of onset and decay of inhibition interact with the timescales of the intrinsic oscillators to determine when stable synchrony is possible we show that there are two different regimes in parameter space in which different combinations of the time constants and other parameters regulate whether the synchronous state is stable we also discuss the construction and stability of nonsynchronous solutions and the implications of the analysis for larger networks the analysis uses geometric techniques of singular perturbation theory that allow one to combine estimates from slow flows and fast jumps

type i membranes phase resetting curves and synchrony type i membrane oscillators such as the connor model connor et al 1977 and the morris lecar model morris and lecar 1981 admit very low frequency oscillations near the critical applied current hansel et al 1995 have numerically shown that synchrony is difficult to achieve with these models and that the phase resetting curve is strictly positive we use singular perturbation methods and averaging to show that this is a general property of type i membrane models we show in a limited sense that so called type ii resetting occurs with models that obtain rhythmicity via a hopf bifurcation we also show the differences between synapses that act rapidly and those that act slowly and derive a canonical form for the phase interactions

implicit bem formulations for usual and sensitivity problems in elasto plasticity using the consistent tangent operator concept this paper presents boundary element method bem formulations for usual and sensitivity problems in small strain elasto plasticity using the concept of the local consistent tangent operator cto usual problems here refer to analysis of nonlinear problems in structural and solid continua for which simo and taylor first proposed the use of the cto within the context of the finite element method fem a new implicit bem scheme for such problems using the cto is presented first a formulation for sensitivity analysis follows it is shown that the sensitivity of the strain increment associated with an infinitesimal variation of some design parameter solves a linear problem which is governed by the converged value of the same global cto as the one that appears in the usual problem numerical results for both usual and sensitivity problems are shown for a one dimensional example they demonstrate the effectiveness of the present approach in particular accurate sensitivities with respect to material parameters e g exponent of the power type hardening law are obtained even with few integration cells and for large load increments

uniqueness studies in boundary value problems involving some second gradient models abstract enhanced models such as second gradient models have been mainly theoretically developed during the sixties and the seventies new attention has been paid to these models recently when it has been recognized that classical inelastic constitutive equations especially the ones not obeying a normality rule induce ill posed boundary value problems however little work has been done to study the well posedness properties of boundary value problems involving these enhanced models the aim of this paper is a partial study of this point only uniqueness of solution of numerical discretization of boundary value problems involving second gradient models is considered we extend to second gradient models a numerical search method to find non uniqueness already established for classical media in the case of loss of uniqueness for the underlying model our numerical results show clearly that in some cases uniqueness is lost for second gradient model as well it seems that second gradient extensions of classical models do not restore the uniqueness properties but only the objectivity of the numerical computation finally our numerical experiments show once more that post peak behavior is a structural effect they also suggest that some constitutive equations often used in geomaterials modeling may be questionable and may not be complete because even adding second gradient enhancement to these models yields non unique solutions

tracking time varying causality and directionality of information flow using an error reduction ratio test with applications to electroencephalography data this paper introduces an error reduction ratio causality err causality test that can be used to detect and track causal relationships between two signals in comparison to the traditional granger method one significant advantage of the new err causality test is that it can effectively detect the time varying direction of linear or nonlinear causality between two signals without fitting a complete model another important advantage is that the err causality test can detect both the direction of interactions and estimate the relative time shift between the two signals numerical examples are provided to illustrate the effectiveness of the new method together with the determination of the causality between electroencephalograph signals from different cortical sites for patients during an epileptic seizure

an integration scheme for prandtl reuss elastoplastic constitutive equations we investigate the generalized midpoint rule for the time integration of elastoplastic constitutive equations for pressure independent yield criteria the incremental equations are divided into one scalar hydrostatic pressure dilation rate equation and a stress deviator strain rate deviator tensorial equation this formulation is applied to two classical problems bulging of a tube under internal pressure and tension test on a notched specimen

uniqueness loss of ellipticity and localization for the time discretized rate dependent boundary value problem with softening the discretization in time of the initial boundary value problem for rate dependent elastic viscoplastic solid materials in presence of softening is investigated in this paper the emphasis is put on uniqueness loss of ellipticity and localization it is found that the time discretized problem resembles the incremental problem for rate independent materials and softening may lead to ill posedness loss of ellipticity if the time step is greater than a critical value it is well established that the implication of loss of ellipticity for the numerical simulations after spatial discretization is the pathological mesh dependency of the computed results we furnish a method to compute the critical time step and demonstrate its use for a simple example problem copyright 2010 john wiley sons ltd

numerical aspects in the finite element simulation of the portevin le chatelier effect abstract serrated yielding and propagation of localized bands of plastic strain rate are the apparent phenomena of the portevin le chatelier plc effect the finite element modeling of this effect is investigated using a model proposed by zhang et al 74 describing dynamic strain aging and material parameters for a nickel based superalloy at 500 c this work presents 1 an efficient implicit integration scheme of the constitutive equations in the presence of instabilities 2 a numerical tool to determine the type of plastic strain rate localization bands based on results of simulations and 3 a mesh and time discretization sensitivity analysis of the model regarding the characteristics of plc bands this analysis is carried out in 2d and 3d for axisymmetric smooth and notched specimens

theory and finite element computation of cyclic martensitic phase transformation at finite strain a generalized variational formulation including quasi convexification of energy wells for arbitrarily many martensitic variants in case of mono crystals for linearized strains was developed by govindjee and miehe comp meth appl mech eng 2001 191 3 5 215 238 and computationally extended by stein and zwickert comput mech 2006 in press this work is generalized here for finite strain kinematics with monotonous hyperelastic stress strain functions in order to account for large transformation strains that can reach up to 15 a major theoretical and numerical difficulty herein is the convexification of the finite deformation phase transformation pt problems for multiple phase variants n 2 a lower bound of the mixing energy is provided by the reuss bound in case of linear kinematics and an arbitrary number of variants shown by govindjee et al j mech phys solids 2003 51 4 i xxvi in case of finite strains a generalized representation of free energy of mixing is introduced for a quasi reuss bound which in general holds for n 2 numerical validation of the used micro macro material model is presented by comparing verified numerical results with the experimental data for cu82al14ni4 monocrystals for quasiplastic pt provided by xiangyang et al j mech phys solids 2000 48 2163 2182 the zigzag type experimental stress strain curve within pt at loading called yield tooth is approximated within the finite element analysis by a smoothly decreasing and then increasing axial stress which could not be achieved with linearized kinematics yielding a constant axial stress during pt copyright 2007 john wiley sons ltd

an iterative algorithm for simulation error based identification of polynomial input output models using multi step prediction effective identification of polynomial input output models for applications requiring long range prediction or simulation performance relies on both careful model selection and accurate parameter estimation the simulation error minimisation sem approach has been shown to provide significant advantages in the model selection phase by ruling out candidate models with good short term prediction capabilities but unsuitable long term dynamics however sem based parameter estimation has been generally avoided due to excessive computational effort this article extends to the nonlinear case a computationally efficient approach for this task that was previously developed for linear models based on the iterative estimation of predictors with increasing prediction horizon conditions for the applicability of the approach to various model classes are also discussed finally some examples are provided to show the effectiveness and computational convenience of the proposed algorithm for polynomial input output

what matters in neuronal locking exploiting local stability we show what neuronal characteristics are essential to ensure that coherent oscillations are asymptotically stable in a spatially homogeneous network of spiking neurons under standard conditions a necessary and in the limit of a large number of interacting neighbors also sufficient condition is that the postsynaptic potential is increasing in time as the neurons fire if the postsynaptic potential is decreasing oscillations are bound to be unstable this is a kind of locking theorem and boils down to a subtle interplay of axonal delays postsynaptic potentials and refractory behavior the theorem also allows for mixtures of excitatory and inhibitory interactions on the basis of the locking theorem we present a simple geometric method to verify the existence and local stability of a coherent oscillation

a modified orthogonal forward regression least squares algorithm for system modelling from noisy regressors in this paper a modified orthogonal forward regression ofr least squares algorithm is presented for system identification and modelling from noisy regressors under the assumption that the energy and signal to noise ratio snr of the signals are known or can be estimated it is shown that unbiased estimates of the error reduction ratios errs and the parameters can be obtained in each forward regression step examples are provided to illustrate the proposed approach

an identification algorithm for polynomial narx models based on simulation error minimization classical prediction error approaches for the identification of non linear polynomial narx narmax models often yield unsatisfactory results for long range prediction or simulation purposes mainly due to incorrect or redundant model structure selection the paper discusses some limitations of the standard approach and suggests two modifications namely a new index based on the simulation error is employed as the regressor selection criterion and a pruning mechanism is introduced in the model selection algorithm the resulting algorithm is shown to be effective in the identification of compact and robust models generally yielding model structures closer to the correct ones computational issues are also discussed finally the identification algorithm is tested on a long range prediction benchmark application

on constitutive relations at finite strain hypo elasticity and elasto plasticity with isotropic or kinematic hardening abstract the question of generalization to finite strains of the constitutive relations of infinitesimal strain theory of elasticity and classical elasto plasticity with isotropic and kinematic hardening is critically examined simple generalizations which lead to physically plausible material behaviour are presented the current controversies surrounding i the choice of stress rate in the above generalization and ii the anomaly of oscillatory stresses in kinematic hardening plasticity as discussed by e h lee and others are analyzed it is found that these controversies are easily resolvable

finite element procedure for solving contact thermoelastoplastic problems at large strains normal and high pressures abstract the paper presents a finite element fe procedure for solving contact thermoelastoplastic problems at large strains a rigorous derivation of the constitutive relations used and the structure of a tangent stiffness matrix and load vector at arbitrary thermomecanical loading are given the deformation model 1 2 is used which is based on the multiplicative decomposition of the total deformation gradient to an elastic temperature and plastic parts and the generalization of prandtl reuss equations to the case of large strains high pressures and temperatures a method is proposed for the generalization of the elastic law at small strains to the case of high pressures which is based on the use of the existence of an elastic potential hyperelastic material at large elastic strains the algorithms for solving thermoelastoplastic problems at large strains and contact elastic problems at small strains are considered individually and in combination for solving contact thermoelastoplastic problems at large strains an algorithm for solving thermoelastoplastic problems at large strains is based on a modified method of initial stresses allowing the use of both the constant and the variable tangent stiffness matrices an algorithm allowing for contact conditions which are described using a friction surface in the particular case the coulomb s law of friction is considered involves the simultaneous consideration of an arbitrary number of deformable bodies in contact the pairs of nodes with the same coordinates are introduced along the interface owing to transformation of the set of fem equations the contact conditions reduce to the usual boundary conditions in terms of stresses or displacement with iterative redetermination of their types adhesion slip no contact in each pair of nodes optimum variants of combinations of the iterative procedures allowing for plastic flow and contact interaction are studied particular problems are solved an attractive feature of the present approach is the simplicity of allowing for the contact conditions for an arbitrary number of deformable bodies in contact and insignificant modifications of computer program which are necessary for the change from small strains to large ones

algorithms for minimal model structure detection in nonlinear dynamic system identification the minimal model structure detection mmsd problem in nonlinear dynamic system identification is formulated as a search for the optimal orthogonalization path while an exhaustive search for a model with 20 candidate terms would involve 2 43 1018 possible paths it is shown that this can typically be reduced to 2 103 by augmenting the orthogonal estimation algorithm with genetic search procedures the mmsd algorithm provides the first practical solution for optimal structure detection in narmax modelling training neural networks and fuzzy systems modelling based on the mmsd algorithm a refined forward regression orthogonal rfro algorithm is developed the rfro algorithm initially detects a parsimonious model structure using the forward regression orthogonal algorithm and then refines the model structure by applying the mmsd algorithm to the reduced model term set the rfro algorithm cannot guarantee to find the minimal model structure but it is computationally more efficient than the mmsd algori

a formulation of the mitc4 shell element for finite strain elasto plastic analysis abstract a finite strain elasto plastic formulation is developed for the mitc4 shell element the developed formulation is based on lee s multiplicative decomposition of the deformation gradient and on the hyperelastic expression of von mises flow rule expressed in terms of hencky s strain tensor the formulation incorporates thickness stretching degrees of freedom that are condensed at the element level by imposing the classical in layer plane stress condition a symmetric and consistent tangent stiffness matrix is also developed

finite elastoplastic deformations of space curved membranes abstract under restriction of an isotropic elastic response of deformed lattice a covariant theory of finite elastoplasticity is developed in principal axes of a pair of deformation tensors in material description the tensor pair consists of the plastic deformation tensor and the total deformation cauchy green tensor the proposed theory is applied to elastoplastic membranes whose reference and current configurations can be arbitrary space curved surfaces pressure insensitive von mises yield criterion and isotropic hardening are considered as a model problem with a particular form of the strain energy function given in terms of elastic principal stretches through an explicit enforcement of the plane stress condition we arrive at a reduced two dimensional problem representation which is set in the membrane tangent plane numerical implementation details are given to show an important role of the operator split methodology in simplifying the state update computation and the computation of the consistent tangent modulus a set of numerical examples illustrates the performance of the presented theory and indicates some of the possible areas of application

a two stage algorithm for identification of nonlinear dynamic systems this paper investigates the two stage stepwise identification for a class of nonlinear dynamic systems that can be described by linear in the parameters models and the model has to be built from a very large pool of basis functions or model terms the main objective is to improve the compactness of the model that is obtained by the forward stepwise methods while retaining the computational efficiency the proposed algorithm first generates an initial model using a forward stepwise procedure the significance of each selected term is then reviewed at the second stage and all insignificant ones are replaced resulting in an optimised compact model with significantly improved performance the main contribution of this paper is that these two stages are performed within a well defined regression context leading to significantly reduced computational complexity the efficiency of the algorithm is confirmed by the computational complexity analysis and its effectiveness is demonstrated by the simulation results

design sensitivity analysis for parameters affecting geometry elastic viscoplastic material constant and boundary condition by consistent tangent operator based boundary element method abstract this paper presents a design sensitivity analysis method by the consistent tangent operator concept based boundary element implicit algorithm the design variables for sensitivity analysis include geometry parameters elastic viscoplastic material parameters and boundary condition parameters based on small strain theory perzyna s elastic viscoplastic material constitutive relation with a mixed hardening model and two flow functions is considered in the sensitivity analysis the related elastic viscoplastic radial return algorithm and the formula of elastic viscoplastic consistent tangent operator are derived and discussed based on the direct differentiation approach the incremental boundary integral equations and related algorithms for both geometric and elastic viscoplastic sensitivity analysis are developed a 2d boundary element program for geometry sensitivity elastic viscoplastic material constant sensitivity and boundary condition sensitivity has been developed comparison and discussion with the results of this paper analytical solution and finite element code ansys for four plane strain numerical examples are presented finally

relaxation oscillators with time delay coupling abstract we study networks of relaxation oscillators coupled with time delays synapses a pair of oscillators is analyzed and shown to attain loosely synchronous solutions for a wide range of initial conditions and time delays simulations of one and two dimensional oscillator networks indicate that locally coupled oscillators are also loosely synchronous desynchronous solutions are possible when system parameters are varied to characterize lossely synchronous networks we introduce a measure of synchrony the maximum time difference between any two oscillators in locally excitatory globally inhibitory oscillator networks with time delays we find that desynchronous solutions for different groups of oscillators are maintained and the number of groups that can be segregated is related to the maximum time difference within each group to examine the maximum time difference we display its histograms for oscillator networks in one and two dimensions also a range of initial conditions is given so that the maximum time difference is contained as the system evolves

multispikes and synchronization in a large neural network with temporal delays coherent rhythms in the gamma frequency range are ubiquitous in the nervous system and thought to be important in a variety of cognitive activities such rhythms are known to be able to synchronize with millisecond precision across distances with significant conduction delay it is mysterious how this can operate in a setting in which cells receive many inputs over a range of time here we analyze a version of mechanism previously proposed that the synchronization in the ca1 region of the hippocampus depends on the firing of doublets by the interneurons using a network of local circuits that are arranged in a possibly disordered lattice we determine the conditions on parameters for existence and stability of synchronous solutions in which the inhibitory interneurons fire single spikes doublets or triplets per cycle we show that the synchronous solution is only marginally stable if the interneurons fire singlets if they fire doublets the synchronous state is asymptotically stable in a larger subset of parameter space than if they fire triplets an unexpected finding is that a small amount of disorder in the lattice structure enlarges the parameter regime in which the doublet solution is stable synaptic noise reduces the regime in which the doublet configuration is stable but only weakly

mixed stabilized finite element methods in nonlinear solid mechanics part ii strain localization this paper deals with the question of strain localization associated with materials which exhibit softening due to tensile straining a standard local isotropic rankine damage model with strain softening is used as exemplary constitutive model both the irreducible and mixed forms of the problem are examined and stability and solvability conditions are discussed lack of uniqueness and convergence difficulties related to the strong material nonlinearities involved are also treated from this analysis the issue of local discretization error in the pre localization regime is deemed as the main difficulty to be overcome in the discrete problem focus is placed on low order finite elements with continuous strain and displacement fields triangular p1p1 and quadrilateral q1q1 although the presented approach is very general numerical examples show that the resulting procedure is remarkably robust it does not require the use of auxiliary tracking techniques and the results obtained do not suffer from spurious mesh bias dependence

an algorithm and a method to search bifurcation points in non linear problems this paper is devoted to a numerical method able to help the determination of the bifurcation threshold in non linear time independent continuum mechanic problems first some theoretical results about uniqueness are recalled in the framework of the large strain assumption the differences between the classical finite step problem and the rate problem are presented an iterative algorithm able to solve the rate problem is given using different initializations it is seen in some numerical experiments that it is possible with this algorithm to get different solutions when the underlying mathematical problem solved does not enjoy a uniqueness property the constitutive equations used have been chosen to be simple enough to deduce some theoretical knowledge about the corresponding uniqueness problems finally a method is given which is able in some case to give an upper bound of the bifurcation threshold copyright 2001 john wiley sons ltd

on the numerical integration of a class of pressure dependent plasticity models with mixed hardening radial return algorithms for both three dimensional and plane stress situations are developed for a class of pressure dependent plasticity models formulated in state variables with mixed hardening the consistent tangent matrix has been developed which among other advantages does not require numerical inversion the algorithms for gurson s mixed hardening model are incorporated in a finite element program to solve several simple uniaxial tension problems when compared with numerically integrated solutions the results from the finite element analysis show excellent agreement finally results of the axisymmetric necking problem using gurson s mixed hardening model are presented as an example of application

accurate stress updating algorithm based on constant strain rate assumption abstract the calculation of the stresses for path dependent materials possesses a delicate problem here the constitutive equations are reformulated using the assumption of constant strain rate within an increment this assumption allows the constitutive laws to be rewritten as ordinary differential equations and thus a large set of tools is available to solve the constitutive equations within this concept the possibility to form an algorithmic stiffness tensor is investigated and it turns out that the true tensor is expensive to calculate but it is of interest that an inexpensive well behaving approximative algorithmic stiffness tensor can be formulated to investigate the properties of the solution method both with respect to stress calculation and convergence properties in a newton raphson method an elasto plastic damage model based on von mises plasticity is considered an interesting observation is that for the usual closest point projection method the damage evolution is very sensitive to the size of load step

a direct complementarity approach for the elastoplastic analysis of plane stress and plane strain structures this paper presents a direct complementarity approach for carrying out the elastoplastic analysis of plane stress and plane strain structures founded on a traditional finite step formulation our approach however avoids the typically cumbersome implementation of iterative predictorcorrector procedures associated with the ubiquitous return mapping algorithm instead at each predefined step the governing formulationcast in its most natural mathematical programming format known as a mixed complementarity problemis directly solved by using a complementarity solver run from within a mathematical modeling system we have chosen the industry standard general algebraic modeling system path mixed complementarity problem solver that is called from within the general algebraic modeling system environment we consider both von mises and tresca materials with perfect or hardening kinematic and isotropic behaviors our numerical tests five benchmark examples of which are presented in this paper have been carried out using models constructed from the mixed finite element of capsoni and corradi comput methods appl mech eng 1997 141 6793 which beneficially offers a locking free behavior and coarse mesh accuracy the results indicate in addition to an isochoric locking free behavior good accuracy and the ability to circumvent the difficult singularity problem associated with the corners of tresca yield surfaces

a component based hybrid reduced basis finite element method for solid mechanics with local nonlinearities abstract the scrbe static condensation reduced basis element method is a component to system model order reduction approach for efficient many query and real time treatment of linear partial differential equations characterized by many spatially distributed constitutive geometry and topology parameters in this paper we incorporate the scrbe approach into a framework for analysis of problems in solid mechanics which are largely linear with the exception of local nonlinearities in particular we exploit a linear nonlinear domain decomposition to develop a hybrid formulation we consider a scrbe approximation over the assumed predominant part of the domain associated to a linear elasticity model we revert to a full finite element fe approximation over the part of the domain associated to the locally nonlinear model we adapt the scrbe port training procedures to anticipate the behavior of the field over the linear nonlinear interface and hence ensure an accurate solution over the entire domain we choose a globally conforming approximation which exploits the intrinsic port structure of the scrbe method and yields a decoupled non invasive formulation of the respective linear and nonlinear blocks of the residual vector and newton jacobian matrix we present numerical results for several local nonlinearities elastic contact with and without friction plastic contact which demonstrate substantial savings relative to standard fe approximation over the entire domain in particular in the regime in which the linear part of the domain represents the majority of the fe degrees of freedom

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

a generalized approach to formulate the consistent tangent stiffness in plasticity with application to the gld porous material model abstract it has been shown that the use of the consistent tangent moduli is crucial for preserving the quadratic convergence rate of the global newton iterations in the solution of the incremental problem in this paper we present a general method to formulate the consistent tangent stiffness for plasticity the robustness and efficiency of the proposed approach are examined by applying it to the isotropic material with j2 flow plasticity and comparing the performance and the analysis results with the original implementation in the commercial finite element program abaqus the proposed approach is then applied to an anisotropic porous plasticity model the gologanu leblond devaux model performance comparison between the consistent tangent stiffness and the conventional continuum tangent stiffness demonstrates significant improvement in convergence characteristics of the overall newton iterations caused by using the consistent tangent matrix

rbf neural network center selection based on fisher ratio class separability measure for classification applications the role of hidden layer neurons of a radial basis function rbf neural network can be interpreted as a function which maps input patterns from a nonlinear separable space to a linear separable space in the new space the responses of the hidden layer neurons form new feature vectors the discriminative power is then determined by rbf centers in the present study we propose to choose rbf centers based on fisher ratio class separability measure with the objective of achieving maximum discriminative power we implement this idea using a multistep procedure that combines fisher ratio an orthogonal transform and a forward selection search method our motivation of employing the orthogonal transform is to decouple the correlations among the responses of the hidden layer neurons so that the class separability provided by individual rbf neurons can be evaluated independently the strengths of our method are double fold first our method selects a parsimonious network architecture second this method selects centers that provide large class separation

second order accurate integration algorithms for von mises plasticity with a nonlinear kinematic hardening mechanism abstract two second order numerical schemes for von mises plasticity with a combination of linear isotropic and nonlinear kinematic hardening are presented the first scheme is the generalized midpoint integration procedure originally introduced by ortiz and popov in 1985 detailed and applied here to the case of armstrong frederick nonlinear kinematic hardening the second algorithm is based on the constitutive model exponential based reformulation and on the integration procedure previously introduced by the authors in the context of linearly hardening materials there are two main targets to the work firstly we wish to extensively test the generalized midpoint procedure since in the scientific literature no thorough numerical testing campaign has been carried out on this second order algorithm secondly we wish to extend the exponential based integration technique also to nonlinear hardening materials a wide numerical investigation is carried out in order to compare the performance of the two methods

homogenization of two phase elasto plastic composite materials and structures study of tangent operators cyclic plasticity and numerical algorithms we develop homogenization schemes and numerical algorithms for two phase elasto plastic composite materials and structures a hill type incremental formulation enables the simulation of unloading and cyclic loadings it also allows to handle any rate independent model for each phase we study the crucial issue of tangent operators elasto plastic or continuum versus algorithmic or consistent and anisotropic versus isotropic we apply two methods of extraction of isotropic tangent moduli we compare mathematically the stiffnesses of various tangent operators all rate equations are discretized in time using implicit integration we implemented two homogenization schemes mori tanaka and a double inclusion model and two plasticity models classical j 2 plasticity and chaboche s model with non linear kinematic and isotropic hardenings we consider composites with different properties and present several discriminating numerical simulations in many cases the results are validated against finite element fe or experimental data we integrated our homogenization code into the fe program abaqus using a user material interface umat a two scale procedure allows to compute realistic structures made of non linear composite materials within reasonable cpu time and memory usage examples are shown c 2002 elsevier science ltd all rights reserved

implicit algorithm for finite deformation hypoelastic viscoplasticity in fcc metals an implicit objective stress update algorithm is proposed for a hypoelastic viscoplastic model a thermal dynamic yield function which is derived based on the thermal activation analysis and dislocation interaction mechanisms is used along with the consistency approach and the framework of additive viscoplasticity in deriving the proposed model for fcc metals the corotational formulation approach is utilized in developing the proposed model in the finite deformation field for the case of the newton raphson iteration method a new expression for the consistent algorithmic tangent stiffness matrix of rate dependent metals is derived by direct linearization of the stress update algorithm finite element simulations are performed by implementing the proposed viscoplasticity constitutive models in the commercial finite element program abaqus numerical implementation for a simple tensile problem is used for validating the material parameters of the ofhc copper under low and high strain rates and temperatures the numerical results of the adiabatic true stress true strain curves compare very well with the experimental data the effectiveness of the present approach is tested by studying strain localization in a simple plane strain problem results indicate excellent performance of the present framework in describing the strain localization problem and in obtaining mesh independent results copyright 2006 john wiley sons ltd

analysis of the anisotropic viscoplastic damage response of composite laminates continuum basis and computational algorithms the mathematical structure underlying the rate equations of a recently developed constitutive model for the coupled viscoplastic damage response of anisotropic composites is critically examined in this regard a number of tensor projection operators have been identified and their properties were exploited to enable the development of a general computational framework for their numerical implementation using the euler fully implicit integration method in particular this facilitated i the derivation of explicit expressions of the consistent material tangent stiffnesses that are valid for both three dimensional as well as subspace e g plane stress formulations ii the implications of the symmetry or unsymmetry properties of these tangent operators from a thermodynamic standpoint and iii the development of an effective time step control strategy to ensure accuracy and convergence of the solution in addition the special limiting case of inviscid elastoplasticity is treated the results of several numerical simulations are given to demonstrate the effectiveness of the schemes developed

finite deformation post buckling analysis involving inelasticity and contact constraints this paper is concerned with the numerical solution of large deflection structural problems involving finite strains subject to contact constraints and unilateral boundary conditions and exhibiting inelastic constitutive response first a three dimensional finite strain beam model is summarized and its numerical implementation in the two dimensional case is discussed next a penalty formulation for the solution of contact problems is presented and the correct expression for consistent tangent matrix is developed finally basic strategies for tracing limit points are reviewed and a modification of the arc length method is proposed the good performance of the procedures discussed is illustrated by means of numerical examples

consistent derivation of the constitutive algorithm for plane stress isotropic plasticity part i theoretical formulation abstract a derivation of the projected algorithm for general isotropic three invariant plasticity models under plane stress conditions is presented it is obtained by consistently specializing the 3d formulation to the 2d subspace defined by the plane stress condition closed form intrinsic algorithm linearization and a novel expression of the consistent tangent tensor are provided these are also shown to directly emanate from the analogous quantities pertaining to the fully 3d case a detailed discussion of the proposed implementation along with a representative set of numerical examples is provided in the second part of this paper valoroso n rosati l 2008 consistent derivation of the constitutive algorithm for plane stress isotropic plasticity part ii computational issues international journal of solids and structures 46 92 124

a nonsmooth newton method for elastoplastic problems in this work we reformulate the incremental small strain j2 plasticity problem with linear kinematic and nonlinear isotropic hardening as a set of unconstrained nonsmooth equations the reformul

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

large elasto plastic finite element analysis of solids and shells with the enhanced assumed strain concept abstract a finite element simulation of arbitrarily large elasto plastic deformations of three dimensional and shell structures is described two numerical aspects originally developed by j c simo have been combined i e the multiplicative large strain plasticity and the enhanced assumed strain finite element concept the constitutive model is worked out in its algorithmic version applying projection methods and consistent linearization the enhanced strain field is added to the conventional hexahedral displacement elements avoiding volumetric locking in the plastic range in addition to solid structures the three dimensional material model without any modifications is also applied to thin walled shell structures here an extended shell formulation a so called seven parameter model is used in which the thickness strain is augmented by a linear term the applicability of the entire formulation is demonstrated by several numerical examples

brief paper structure detection and parameter estimation for narx models in a unified em framework in this paper we consider structure detection and parameter estimation of the nonlinear auto regressive with exogenous inputs narx model using the em expectation maximisation algorithm the parameter estimation step uses particle smoothing to obtain the necessary expectations in the e step and the parameters are then estimated in closed form in the m step the model structure detection is performed using an f test which makes use of the parameter information matrix inverse of the covariance matrix obtained from an augmentation of the em algorithm the steps for obtaining the information matrix are robust guaranteeing a positive semi definite information matrix to use in the structure detection step for the case of unknown model orders a method is proposed using the stochastic complexity sc information criterion for selecting between candidate models the sc is composed of the information matrix representing model complexity and a likelihood estimate representing model accuracy which are both generated as byproducts of the augmented em algorithm numerical results demonstrate that the em approach performs well in comparison to a standard alternative based on orthogonal least squares and also avoids the need to estimate a noise model for the case of measurement noise corrupted output signals

solution of the slump test using a finite deformation elasto plastic drucker prager model summary development of a finite deformation elasto plasticity model based on the multiplicative decomposition of the deformation gradient is presented and discussed in detail the formulation presented in this paper includes the derivation of the full set of equations for the drucker prager yield criterion the equations which are not available elsewhere are developed within a framework using a spectral decomposition approach further expressions for the consistent algorithmic tangent moduli in the finite strain regime are developed since the finite deformation framework employed to obtain the expressions presented here collapses to the classical infinitesimal plasticity framework when the finite strain assumption is no longer necessary the finite deformation consistent tangent moduli are compared to the consistent tangent moduli valid for use with infinitesimal plasticity validation of the implemented finite deformation elasto plastic drucker prager model is performed through the solution of the concrete slump test comparisons between an existing approximate analytical solution and experimental data are presented and results are discussed in detail

elastoplastic materials with martensitic phase transition and twinning at finite strains numerical solution with the finite element method abstract a new quasistatic problem formulation and finite element fe algorithm for martensitic phase transition pt and twinning in elastoplastic materials at large strains based on a recently proposed thermomechanical approach 1 2 are presented the instantaneous occurrence of pt in some region based on thermodynamics without introduction of volume fraction and prescribing the kinetic equations for it is considered stress history dependence during the transformation process is a characteristic feature of the pt criterion the deformation model is based on the multiplicative decomposition of the total deformation gradient into elastic transformation and plastic parts and the generalization of prandtl reuss equations to the case of large strains and pt the case of small elastic but large plastic and transformation strains is assumed for numerical simulation of pt the inverse problem is considered i e the position and size of the pt region nucleus are prescribed in advance and then the condition for pt is defined from the pt criterion such an approach includes a finite element solution of the elastoplastic problem with the prescribed transformation deformation gradient and the changing elastoplastic properties in the transforming region during pt the usage of the current configuration and the true cauchy stresses along with assumptions of small elastic strains and zero modified plastic spin allows us to use with small modifications the radial return algorithm and the consistent elastoplastic moduli for the case of small strains some modifications of the iterative algorithm related to the numerical integration of constitutive equations along with the radial return algorithm are suggested in order to improve the accuracy of solutions for large increments of external load such modifications can be used for any elastoplastic problem without phase transition as well the model problems of nucleation at shear band intersection and appearance of a single martensitic plate and a single twin are solved and analyzed

coupled plastic damaged model abstract a constitutive model that couples plasticity and damage is presented the model is thermodynamically consistent and comes from a generalization of classical plasticity theory and isotropic damage theory of kachanov coupling between plasticity and damage is achieved through a simultaneous solution of the plastic and the damage problem after a description of the model a numerical algorithm for the integration of the resulting constitutive equations is presented it is an euler backward type of algorithm that is particularly suitable to solve plain stress non linear problems with a 2d finite element program the consistent stiffness matrix is also derived the paper is completed with some application examples that show that the model presented accurately reproduces the behaviour of elastic plastic damaged materials

a finite element constitutive update scheme for anisotropic viscoelastic solids exhibiting non linearity of the schapery type this study presents a new scheme for performing integration point constitutive updates for anisotropic small strain non linear viscoelasticity within the context of implicit non linear finite element structural analysis while the basic scheme has been presented earlier by the authors for linear viscoelasticity the present work illustrates the generality of the underlying fundamentals by extending to schapery s non linear model the method features a judicious choice of state variables a stable backward euler integration step and a consistent tangent operator its greatest strength lies in ready incorporation into existing fem codes numerical examples involving homogeneous stress states such as uniaxial extension and simple shear and non uniform stress states such as a beam under tip load were carried out by incorporating the present scheme into a general purpose fem package excellent agreement with analytical results is observed copyright 1999 john wiley sons ltd

partial synchronization in populations of pulse coupled oscillators i study the long term behavior of populations of nonlinear oscillators with all to all noninstantaneous pulse coupling with fast enough excitatory coupling both the fully synchronized and the asynchronous state are unstable in this case individual units fire quasiperiodically even though the network as a whole shows a periodic firing pattern the behavior of networks with three or more units is different in this regard from that of two unit networks with inhibitory coupling the network can break up into a variable number of fully synchronized clusters for fast inhibition the number of clusters tends to be large while the number of clusters is smaller for slow inhibition textcopyright 1996 the american physical society

an inverse micro mechanical analysis toward the stochastic homogenization of nonlinear random composites abstract an inverse mean field homogenization mfh process is developed to improve the computational efficiency of non linear stochastic multiscale analyzes by relying on a micro mechanics model first full field simulations of composite stochastic volume element sve realizations are performed to characterize the homogenized stochastic behavior the uncertainties observed in the non linear homogenized response which result from the uncertainties of their micro structures are then translated to an incremental secant mfh formulation by defining the mfh input parameters as random effective properties these effective input parameters which correspond to the micro structure geometrical information and to the material phases model parameters are identified by conducting an inverse analysis from the full field homogenized responses compared to the direct finite element analyzes on sves the resulting stochastic mfh process reduces not only the computational cost but also the order of uncertain parameters in the composite micro structures leading to a stochastic mean field reduced order model mf rom a data driven stochastic model is then built in order to generate the random effective properties under the form of a random field used as entry for the stochastic mf rom embedded in a stochastic finite element method sfem the two cases of elastic unidirectional ud fibers embedded in an elasto plastic matrix and of elastic ud fibers embedded in a damage enhanced elasto plastic matrix are successively considered in order to illustrate the capabilities of the method the stochastic response of a ply is studied under transverse loading condition

time structure of the activity in neural network models several neural network models in continuous time are reconsidered in the framework of a general mean field theory which is exact in the limit of a large and fully connected network the theory assumes pointlike spikes which are generated by a renewal process the effect of spikes on a receiving neuron is described by a linear response kernel which is the dominant term in a weak coupling expansion it is shown that the resulting spike response model is the most general renewal model with linear inputs the standard integrate and fire model forms a special case in a network structure with several pools of identical spiking neurons the global states and the dynamic evolution are determined by a nonlinear integral equation which describes the effective interaction within and between different pools we derive explicit stability criteria for stationary incoherent and oscillatory coherent solutions it is shown that the stationary state of noiseless systems is almost always unstable noise suppresses fast oscillations and stabilizes the system furthermore collective oscillations are stable only if the firing occurs while the synaptic potential is increasing in particular collective oscillations in a network with delayless excitatory interaction are at most semistable inhibitory interactions with short delays or excitatory interactions with long delays lead to stable oscillations our general results allow a straightforward application to different network models with spiking neurons furthermore the theory allows an estimation of the errors introduced in firing rate or graded response models

on the representation and implicit integration of general isotropic elastoplasticity based on a set of mutually orthogonal unit basis tensors summary a simple and compact representation framework and the corresponding efficient numerical integration algorithm are developed for constitutive equations of isotropic elastoplasticity central to this work is the utilization of a set of mutually orthogonal unit tensor bases and the corresponding invariants the set of bases can be regarded equivalently as a local cylindrical coordinate system in the three dimensional coaxial tensor subspace namely the principal space the base tensors are given in the global coordinate system similar to the principal space approach the proposed method reduces the problem dimension from six to three in contrast to the conventional approach the transformation procedure between the principal space and the general space is avoided and explicit computation of the principal axes is bypassed with the proposed technique the matrices which need to be inverted during iteration take a simple form for the great majority of constitutive equations in use the tangent operator consistent with the proposed algorithm can be decomposed into the direct sum of two linear maps over the coaxial tensor subspace and the subspace orthogonal to it consequently its closed form is derived in an extremely simple manner finally numerical examples demonstrate the high quality performances of the proposed scheme copyright 2014 john wiley sons ltd

alternating and synchronous rhythms in reciprocally inhibitory model neurons we study pacemaker rhythms generated by two nonoscillatory model cells that are coupled by inhibitory synapses a minimal ionic model that exhibits postinhibitory rebound pir is presented when the post synaptic conductance depends instantaneously on presynaptic potential the classical alternating rhythm is obtained using phase plane analysis we identify two underlying mechanisms release and escape for the out of phase oscillation when the postsynaptic conductance is not instantaneous but decays slowly the two cells can oscillate synchronously with no phase difference in each case different stable activity patterns can coexist over a substantial parameter range

an analysis of metal forming processes using large deformation elastic plastic formulations a concise survey of the literature related to the large deformation elasto plasticity problems including unilateral contact and friction is presented together with an extension of the friction law for large deformation analysis starting from the principle of virtual work the so called total lagrangian and updated lagrangian formulations are derived based on some fundamental assumptions in linearizing the nonlinear equations by introducing the zaremba jaumann co rotational increment to the cauchy stress tensor the classical prandtl reuss equations are generalized for describing the elastic plastic material behavior to allow a proper consideration of the contact conditions in the incremental analysis a general friction law with an associated isotropic coulomb sliding rule is obtained by the similarity between dry friction and plasticity finite element discretizations and approximations are applied to the resulting formulation of the updated lagrangian approach four example problems are solved to test the formulations developed in this paper the emphasis is made toward the numerical accuracy of the finite element solutions

asynchronous states in networks of pulse coupled oscillators we use a mean field approach to analyze the stability of the asynchronous state in a population of all to all pulse coupled nonlinear oscillators we determine the conditions that must be satisfied by the time constants and phase dependence characterizing the coupling between the oscillators in order for the asynchronous state to be stable we also consider the effects of noise this work complements results on synchronous states in similar models and allows us to study the validity of firing rate models commonly used for neural networks

a multi variant martensitic phase transformation model formulation and numerical implementation the development of models for shape memory alloys and other materials that undergo martensitic phase transformations has been moving towards a common generalized thermodynamic framework several promising models utilizing single martensitic variants and some with multiple variants have appeared recently in this work we develop a model in a general multi variant framework for single crystals that is based upon lattice correspondence variants and the use of dissipation arguments for the generation of specialized evolution equations the evolution equations that appear are of a unique nature in that not only are the thermodynamic forces restricted in range but so are their kinematic conjugates this unusual situation complicates the discrete time integration of the evolution equations we show that the trial elastic state method that is popular in metal plasticity is inadequate in the present situation and needs to be replaced by a non linear programming problem with a simple geometric interpretation the developed integration methodology is robust and leads to symmetric tangent moduli example computations show the behavior of the model in the pseudoelastic range of particular interest is the fact that the model can predict the generation of habit plane like variants solely from the lattice correspondence variants this is demonstrated through a comparison to the experimental work of shield j mech phys solids 43 1995 869