continuum approach to computational multiscale modeling of propagating fracture a new approach to two scale modeling of propagating fracture based on computational homogenization fe2 is presented the specific features of the approach are a a continuum setting for representation of the fracture at both scales based on the continuum strong discontinuity approach csda and b the use for the considered non smooth discontinuous problem of the same computational homogenization framework than for classical smooth cases as a key issue the approach retrieves a characteristic length computed at the lower scale which is exported to the upper one and used therein as a regularization parameter for a propagating strong discontinuity kinematics this guarantees the correct transfer of fracture energy between scales and the proper dissipation at the upper scale representative simulations show that the resulting formulation provides consistent results which are objective with respect to size and bias of the upper scale mesh and with respect to the size of the lower scale rve failure cell as well as the capability to model propagating cracks at the upper scale in combination with crack path field and strain injection techniques the continuum character of the approach confers to the formulation a minimal intrusive character with respect to standard procedures for multi scale computational homogenization

nilpotent and high order approximations of vector field systems this paper is concerned with the study of structurally stable properties associated with systems described by one or several real analytic vector fields via approximating systems which retain inf

averaging results and the study of uniform asymptotic stability of homogeneous differential equations that are not fast time varying within the liapunov framework a sufficient condition for uniform asymptotic stability of ordinary differential equations is proposed unlike with classical liapunov theory the time derivative of the v function taken along solutions of the system may have positive and negative values it is shown that the proposed condition is useful for the study of uniform asymptotic stability of homogeneous systems with order tau 0 in particular it is established that asymptotic stability of the averaged homogeneous system implies local uniform asymptotic stability of the original time varying homogeneous system this shows that averaging techniques play a prominent role in the study of homogeneous not necessarily fast time varying systems

discontinuous displacement approximation for capturing plastic localization it is proposed to capture localized plastic deformation via the inclusion of regularized displacement discontinuities at element boundaries interfaces of the finite element subdivision the regularization is based on a kinematic assumption for an interface that resembles that which is pertinent to the classical shear band concept as a by product of the regularization an intrinsic band width is introduced as a constitutive property rather than a geometric feature of the finite element mesh in this way the spurious mesh sensitivity which is obtained when the displacement approximation is continuous can be avoided another consequence is that the interfacial relation between the elements is derived directly from the conventional constitutive properties of the continuously deforming material an interesting feature is that the acoustic tensor will not only play a role for diagnosing discontinuous bifurcation but will also serve as the tangent stiffness tensor of the interface up to within a scalar factor an analytical investigation of the behaviour of the interface is carried out and it is shown that dilatation may indeed accompany slip within a shear band for a general plasticity model the significance of proper mesh alignment is demonstrated for a simple problem in plane strain and plane stress it is shown that a unique structural post peak response in accordance with non linear fracture mechanics can be achieved when the plastic softening modulus is properly related to the bandwidth the paper concludes with a numerical simulation of the gradual development of a shear band in a soil slope

erratum to existence and attractivity of almost periodic solutions for cellular neural networks with distributed delays and variable coefficients by combining the theory of the exponential dichotomy and liapunov function we study the existence and attractivity of almost periodic solutions for cellular neural networks cnns with distributed delays and variable coefficientsdx idt b i t x i t j 1 na i j t f j x j t j 1 nb i j t f j m j 0 k i j u x j t u du i i t we obtain some sufficient conditions to ensure that for the networks there exists a unique almost periodic solution and all its solutions converge to such an almost periodic solution an example is given to illustrate that the conditions of our results are feasible

global exponential periodicity of a class of recurrent neural networks with oscillating parameters and time varying delays in this paper we present the analytical results on the global exponential periodicity of a class of recurrent neural networks with oscillating parameters and time varying delays sufficient conditions are derived for ascertaining the existence uniqueness and global exponential periodicity of the oscillatory solution of such recurrent neural networks by using the comparison principle and mixed monotone operator method the periodicity results extend or improve existing stability results for the class of recurrent neural networks with and without time delays

a consistent characteristic length for smeared cracking models a numerical scheme for crack modelling by means of continuous displacement fields is presented in two dimensional problems a crack is modelled as a limiting case of two singular lines with continuous displacements but discontinuous displacement gradients across them which tend to coincide with each other an analysis of the energy dissipated inside the band bounded by both lines allows one to obtain an expression for the characteristic length as the ratio between the energy dissipated per unit surface area fracture energy and the energy dissipated per unit volume specific energy at a point the application of these mathematical expressions to the finite element discretized medium allow one to obtain a general spatial and directional expression for the characteristic length which guarantees the objectivity of the results with respect to the size of the finite element mesh the numerical results presented show the reliability of the proposed expressions

coupled boundary interval observer for lpv systems subject to uncertainties in input output and parameters abstract the topic of this publication is the design of interval observers for lpv systems under consideration of parameter input and output uncertainties that are described by bounded intervals in the course of the design also time varying bounds of the parameter intervals are considered representing the case when parameters are measured with an unknown but bounded measurement error in this case an existing approach is extended to handle these parameter uncertainties the effectiveness of the approach is demonstrated by two numerical examples

modeling three dimensional crack propagation a comparison of crack path tracking strategies the development of a new finite element technique for the simulation of discontinuous failure phenomena in three dimensions is the key objective of this study in contrast to the widely used extended finite element technique we apply a purely deformation based strategy based on an independent interpolation of the deformation field on both sides of the discontinuity this method has been applied successfully for two dimensional crack propagation problems in the past however when it comes to three dimensional failure phenomena it faces the same difficulties as the extended finite element method unlike in two dimensions the characterization for the three dimensional failure surface is non unique and the tracking of the discrete crack can be performed in several conceptually different ways in this work we review the four most common three dimensional crack tracking strategies we perform a systematic comparison in terms of standard algorithmic quality measures such as mesh independency efficiency robustness stability and computational cost moreover we discuss more specific issues such as crack path continuity and integratability in commercial finite element packages the features of the suggested crack tracking algorithms will be elaborated by means of characteristic benchmark problems in failure analysis copyright 2008 john wiley sons ltd

geometrically non linear and consistently linearized embedded strong discontinuity models for 3d problems with an application to the dissection analysis of soft biological tissues three different finite element formulations with embedded strong discontinuities are derived on the basis of the enhanced assumed strain method according to the work by jirasek and zimmermann int j numer methods engrg 50 2001 1269 they are referred to as statically optimal symmetric sos kinematically optimal symmetric kos and statically and kinematically optimal non symmetric skon formulations the effect of the discontinuities are characterized by additional degrees of freedom on the element level modifications to the standard kos and skon formulations are proposed in order to achieve consistency with the employed type of a three field hu washizu principle under mode i condition under this condition the formulation satisfies the internal compatibility at the discontinuity i e the relation between the stress in the bulk material and the traction across the discontinuity surface which is not the case for the classical kos formulation we propose a suitable explicit expression for a transversely isotropic traction law in form of a displacement energy function and assume that softening phenomena in the cohesive zone are modeled by a damage law which depends on the maximum gap displacement of the deformation path a linearization of all quantities which are related to the non linear problem leads to new closed form expressions in particular we focus attention on the linearization of the cohesive traction vector the associated element residua and stiffness matrices are provided standard static condensation of the internal degree of freedom leads to a generalized displacement model a comparative study of the modified formulations carried out by means of two numerical examples show the performance of the individual approach we employ constant strain tetrahedral elements with a single discontinuity embedded among the known stress locking phenomena associated with the sos formulation we recognized that the non symmetric skon formulation was not able to provide meaningful results for the dissection process of an arterial layer in three dimensions on distorted meshes for both numerical examples the symmetric kos formulation seems to be most suitable for representing the embedded discontinuities

a cartesian parametrization for the numerical analysis of material instability summary we examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor we then propose a cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition this parametrization is then used to construct a tensor akin to the acoustic tensor it is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability the performance of the cartesian parametrization is compared against the other parametrizations with the results of these comparisons showing that in general the cartesian parametrization is more robust and more numerically efficient than the others copyright 2016 john wiley sons ltd

error estimation and adaptive meshing in strongly nonlinear dynamic problems we present work aimed at developing a general framework for mesh adaption in strongly nonlinear possibly dynamic problems we begin by showing that the solutions of the incremental boundary value problem for a wide class of materials including nonlinear elastic materials compressible newtonian fluids and viscoplastic solids obey a minimum principle provided that the constitutive updates are formulated appropriately this minimum principle can be taken as a basis for asymptotic error estimation in particular we chose to monitor the error of a lower order projection of the finite element solution the optimal mesh size distribution then follows from a posteriori error indicators which are purely local i e can be computed element by element we demonstrate the robustness and versatility of the computational framework with the aid of convergence studies and selected examples of application

finite element methods for the multi scale modeling of softening hinge lines in plates at failure abstract this paper presents a multi scale framework for the modeling of softening hinge lines in inelastic plates and its finite element implementation the proposed framework considers the reissner mindlin problem of thick plates as the large scale problem with the hinge introduced locally in small neighborhoods modeling the small scales of the material response the hinges are defined as strong discontinuities of the generalized displacements describing the plate deformations the consideration of the large scale limit of vanishing small scales leads to a large scale model of these localized failures of plates involving the solution of a problem in terms of those large scale generalized displacements with the standard regularity conditions enhanced finite elements define the natural framework for the numerical implementation of these considerations the new finite elements are enhanced with the singular strain fields associated with the discontinuities or hinge lines which given their local character are statically condensed at the element level we present a general strategy for the definition of these local strain fields so the kinematics of the hinge lines are captured correctly allowing in particular their fully softened state with no stresses and hence avoiding the so called stress locking we present several particular finite elements formulated in this framework including triangular and quadrilateral finite elements several numerical simulations are presented illustrating their performance

an analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids abstract this paper presents an analysis of strong discontinuities in inelastic solids at finite strains solutions exhibiting this type of discontinuities characterized by a discontinuous displacement field are shown to make physical and mathematical sense in a classical multiplicative plasticity continuum model if the softening modulus is reinterpreted as a singular distribution physically the strainsoftening is localized along the discontinuity conditions for the appearance of strong discontinuities in the geometrically nonlinear range are characterized as it is the response of the material during localization in addition these analytical results are exploited in the design of a new class of finite element methods the proposed methods fall within the class of enhanced strain methods and lead to solutions independent of the mesh size and insensitive to mesh alignment without requiring any regularization of the solutions by numerical parameters like a characteristic length

theoretical and computational issues in modelling material failure in strong discontinuity scenarios the paper deals with several aspects related to numerical modelling of material failure in strong discontinuity settings a the onset and development of local material failure in terms of continuum constitutive models equipped with strain softening closed forms formulas for the solutions of the discontinuous material bifurcation problem are given for a class of those models b finite elements with embedded discontinuities nodal and elemental enrichments families are formulated in the continuum strong discontinuity approach csda c instability treatment a discrete viscous perturbation method at the failure surfaces is presented as a way to substantially improve the robustness of the numerical simulations

combined continuum damage embedded discontinuity model for explicit dynamic fracture analyses of quasi brittle materials summary in this paper a novel constitutive model combining continuum damage with embedded discontinuity is developed for explicit dynamic analyses of quasi brittle failure phenomena the model is capable of describing the rate dependent behavior in dynamics and the three phases in failure of quasi brittle materials the first phase is always linear elastic followed by the second phase corresponding to fracture process zone creation represented with rate dependent continuum damage with isotropic hardening formulated by utilizing consistency approach the third and final phase involving nonlinear softening is formulated by using an embedded displacement discontinuity model with constant displacement jumps both in normal and tangential directions the proposed model is capable of describing the rate dependent ductile to brittle transition typical of cohesive materials e g rocks and ice the model is implemented in the finite element setting by using the cst elements the displacement jump vector is solved for implicitly at the local finite element level along with a viscoplastic return mapping algorithm whereas the global equations of motion are solved with explicit time stepping scheme the model performance is illustrated by several numerical simulations including both material point and structural tests the final validation example concerns the dynamic brazilian disc test on rock material under plane stress assumption copyright 2014 john wiley sons ltd

on the almost periodic solution of cellular neural networks with distributed delays by exponential dichotomy about differential equations a formal almost periodic solution aps of a class of cellular neural networks cnns with distributed delays is obtained then within different normed spaces several sufficient conditions guaranteeing the existence and uniqueness of an aps are proposed using two fixed point theorems based on the continuity property and some inequality techniques two theorems insuring the global stability of the unique aps are given comparing with known literatures all conclusions are drawn with slacker restrictions e g do not require the integral of the kernel function determining the distributed delays from zero to positive infinity to be one and the activation functions to be bounded etc besides all criteria are obtained by different ways finally two illustrative examples show the validity and that all criteria are easy to check and apply

variational inequalities in critical state problems similar evolutionary variational inequalities appear as convenient formulations for continuous quasistationary models for sandpile growth formation of a network of lakes and rivers magnetization of type ii superconductors and elastoplastic deformations we outline the main steps of such models derivation and try to clarify the origin of this similarity new dual variational formulations analogous to mixed variational inequalities in plasticity are derived for sandpiles and superconductors

a computational framework of three dimensional configurational force driven brittle crack propagation abstract we consider a variational formulation of quasi static brittle fracture and develop a new finite element based computational framework for propagation of cracks in three dimensional bodies we outline a consistent thermodynamical framework for crack propagation in elastic solids and show that both the elastic equilibrium response as well as the local crack evolution follow in a natural format by exploitation of a global clausius planck inequality in the sense of coleman s method consequently the crack propagation direction associated with the classical griffith criterion is identified by the material configurational force which maximizes the local dissipation at the crack front the variational formulation is realized numerically by a standard spatial discretization with finite elements which yields a discrete formulation of the global dissipation in terms configurational nodal forces therefore the constitutive setting of crack propagation in the space discretized finite element context is naturally related to discrete nodes of a typical finite element mesh in a consistent way with the node based setting the discretization of the evolving crack discontinuity is performed by the doubling of critical nodes and interface facets of the mesh the crucial step for the success of this procedure is its embedding into an r adaptive crack facet reorientation procedure based on configurational force based indicators in conjunction with crack front constraints we propose a staggered solution procedure that results in a sequence of positive definite discrete subproblems with successively decreasing overall stiffness providing a robust algorithmic setting in the postcritical range the predictive capabilitiy of the proposed formulation is demonstrated by means of representative numerical simulations

convergence domain for time varying switched systems abstract in this paper we investigate the convergence domain for time varying switched systems we construct multiple lyapunov functions and each lyapunov function is decreasing outside a ball whose radius is time varying we give a relatively accurate convergence domain for a general time varying switched system finally a numerical example a mass spring damper system is provided to show the effectiveness of the theoretical results

quasi static small strain plasticity in the limit of vanishing hardening and its numerical approximation the quasi static rate independent evolution of the prager ziegler type model of plasticity with hardening is shown to converge to the rate independent evolution of the prandtl reuss elastic perfectly plastic model based on the concept of energetic solutions we study the convergence of the solutions in the limit for hardening coefficients converging to 0 by using the abstract method of gamma convergence for rate independent systems an unconditionally convergent numerical scheme is devised and two and three dimensional numerical experiments are presented a two sided energy inequality is a posteriori verified to document experimental convergence rates

some mathematical problems in perfect plasticity mathematical problems arising in the study of problems of perfect plasticity are reviewed and some problems of current interest are discussed in the context of the dual formulation for which the problem has been thoroughly explored the strategy of viscoplastic regularization and its application are reconsidered with a view to exploring the use of this strategy in the study of the primal problem it is argued that this approach is not without substantial difficulties and so alternatives to the study of the primal problem are sought details are given of an approach by the authors in which direct methods of the calculus of variations are applied to a sequence of time discrete problems the solution to the original problem being recovered in the limit as the time step goes to zero

global asymptotic stability of reaction diffusion cohen grossberg neural networks with continuously distributed delays this paper is concerned with the global asymptotic stability of a class of reaction diffusion cohen grossberg neural networks with continuously distributed delays under some suitable assumptions and using a matrix decomposition method we apply the linear matrix inequality lmi method to propose some new sufficient stability conditions for the reaction diffusion cohen grossberg neural networks with continuously distributed delays the obtained results are easy to check and improve upon the existing stability results some remarks are given to show the advantages of the obtained results over the previous results an example is also given to demonstrate the effectiveness of the obtained results

analysis of slip planes in three dimensional solids abstract three dimensional solids in which displacement jumps develop across planes are analysed critical to such analysis is the identification of the correct orientation of the discontinuity plane to do this strain softening continuum relationships are examined for the limit case of a strong displacement discontinuity which then yields a localisation condition for the introduction of a displacement jump a numerical procedure is proposed to correctly orientate the discontinuity plane in space for the von mises and drucker prager yield criteria traction displacement relationships are developed and implemented by embedding the slip planes in conventional solid finite elements this makes the analysis ideal for large three dimensional calculations the performance of the developed discrete constitutive models and that of the embedded discontinuity elements in three dimensions are scrutinised with special attention paid to mesh objectivity and volumetric locking

an embedded strong discontinuity model for cracking of plain concrete abstract a numerical model formulated within the framework of a nonsymmetric strong discontinuity approach for fracture simulations of plain concrete is presented the model is based on the fixed crack concept and makes use of the concept of the elements with embedded discontinuities discontinuity segments of individual elements are considered to form a c0 continuous path enforcement of continuity of the crack path across adjacent elements is established by a partial domain crack tracking algorithm orientation of individual crack segments is derived from a nonlocal strain field the capabilities of the model are shown by means of numerical examples

on stability and trajectory boundedness of lotka volterra systems with polytopic uncertainty a new approach is proposed to study the stability property of the feasible equilibrium point and the trajectory boundedness of the lotka volterra lv dynamics in the presence of polytopic uncertainties stability analysis of general lv systems is not straightforward in comparison with its cooperative counterpart it is shown that under specific conditions the trajectory of the cooperative counterpart of the lv system can be considered as an upper bound for the trajectory of the corresponding dynamics consequently the stability of the cooperative counterpart of the lv system leads to boundedness of the trajectory the obtained results are extended for the lv systems with polytopic uncertainties it is shown that under specific conditions there is a region which the trajectory of the system belongs to it as time tends to infinity also the stability of lv systems with polytopic uncertainty is investigated the obtained results are confirmed through some numerical application based examples

existence and global exponential stability of almost periodic solution for cellular neural networks with variable coefficients and time varying delays in this paper we study cellular neural networks with almost periodic variable coefficients and time varying delays by using the existence theorem of almost periodic solution for general functional differential equations introducing many real parameters and applying the lyapunov functional method and the technique of young inequality we obtain some sufficient conditions to ensure the existence uniqueness and global exponential stability of almost periodic solution the results obtained in this paper are new useful and extend and improve the existing ones in previous literature

towards a generalization of a discrete strong discontinuity approach a generalized discrete strong discontinuity approach gsda is presented in which non homogeneous jumps are embedded in parent finite elements the new formulation presents similar kinematics as for interface elements accurately simulating both rigid body motion and stretching induced by the opening of a discontinuity this generalized discrete strong discontinuity approach is built within the framework of strong embedded discontinuity formulations as a consequence it is mesh independent and avoids the progressive remeshing needed with interface elements the gsda can be viewed as a generalization of other embedded formulations for which particular assumptions are adopted regarding both the jump transmission and the variational principle structural examples including mode i mode ii and mixed mode fracture are computed and compared with other embedded formulations and experimental results

selectable and unselectable sets of neurons in recurrent neural networks with saturated piecewise linear transfer function the concepts of selectable and unselectable sets are proposed to describe some interesting dynamical properties of a class of recurrent neural networks rnns with saturated piecewise linear transfer function a set of neurons is said to be selectable if it can be co unsaturated at a stable equilibrium point by some external input a set of neurons is said to be unselectable if it is not selectable i e such set of neurons can never be co unsaturated at any stable equilibrium point regardless of what the input is the importance of such concepts is that they enable a new perspective of the memory in rnns necessary and sufficient conditions for the existence of selectable and unselectable sets of neurons are obtained as an application the problem of group selection is discussed by using such concepts it shows that under some conditions each group is a selectable set and each selectable set is contained in some group thus groups are indicated by selectable sets of the rnns and can be selected by external inputs simulations are carried out to further illustrate the theory

boundedness properties for time varying nonlinear systems a liapunov theorem guaranteeing uniform boundedness and uniform ultimate boundedness for a time varying nonlinear system dot x t f x t t has been established the study of uniform boundedness and uniform ultimate boundedness of particular classes of time varying nonlinear systems dot x t f x t t is reduced to the study of the corresponding time invariant frozen systems dot x t f x t sigma for all sigma in mathbb r this approach is illustrated for time varying homogeneous systems with a positive order for particular classes of time varying nonhomogeneous systems and for time varying lotka volterra equations

time varying exponential stabilization of a rigid spacecraft with two control torques rigid body models with two controls cannot be locally asymptotically stabilized by continuous feedbacks which are functions of the state only this impossibility no longer holds when the feedback is also a function of time and time varying asymptotically stabilizing feedbacks have already been proposed however due to the smoothness of the feedbacks the convergence rate is only polynomial in this paper exponential convergence is obtained by considering time varying feedbacks which are only continuous

brief on exponential stability of nonlinear time varying differential equations within the liapunov framework a sufficient condition for exponential stability of ordinary differential equations is proposed unlike with classical liapunov theory the time derivative of the liapunov function taken along solutions of the system may have positive and negative values verification of the conditions of the main theorem may be harder than in the classical case it is shown that the proposed conditions are useful for the investigation of the exponential stability of fast time varying systems this sets the stability study by means of averaging in a liapunov context in particular it is established that exponential stability of the averaged system implies exponential stability of the original fast time varying system a comparison of our work with results taken from the literature is included

on error estimates and adaptivity in elastoplastic solids applications to the numerical simulation of strain localization in classical and cosserat continua the a posteriori error estimates based on the post processing approach are introduced for elastoplastic solids the standard energy norm error estimate established for linear elliptic problems is generalized here to account for the presence of internal variables through the norm associated with the complementary free energy this is known to represent a natural metric for the class of elastoplastic problems of evolution in addition the intrinsic dissipation functional is utilized as a basis for a complementary a posteriori error estimates a posteriori error estimates and adaptive refinement techniques are applied to the finite element analysis of a strain localization problem as a model problem the constitutive equations describing a generalization of standard j2 elastoplasticity within the cosserat continuum are used to overcome serious limitations exhibited by classical continuum models in the post instability region the proposed a posteriori error estimates are appropriately modified to account for the cosserat continuum model and linked with adaptive techniques in order to simulate strain localization problems superior behaviour of the cosserat continuum model in comparison to the classical continuum model is demonstrated through the finite element simulation of the localization in a plane strain tensile test for an elastopiastic softening material resulting in convergent solutions with an h refinement and almost uniform error distribution in all considered error norms

convergence of approximations to the primal problem in plasticity under conditions of minimal regularity this work considers semi and fully discrete approximations to the primal problem in elastoplasticity the unknowns are displacement and internal variables and the problem takes the form of an evolution variational inequality strong convergence of time discrete as well as spatially and fully discrete approximations is established without making any assumptions of regularity over and above those established in the proof of well posedness of this problem

finite elements with displacement interpolated embedded localization lines insensitive to mesh size and distortions a new finite element formulation aimed at the solution of problems involving strain localization is presented the proposed formulation incorporates displacement interpolated embedded localization lines results are shown to converge to an exact solution when the mesh is refined and also to be quite insensitive to mesh distortions

global exponential stability and periodic solutions of cohen grossberg neural networks with continuously distributed delays abstract convergence dynamics of cohen grossberg neural networks cgnns with continuously distributed delays are discussed without assuming the differentiability and monotonicity of activation functions the differentiability of amplification functions and the symmetry of synaptic interconnection weights by skilfully constructing suitable lyapunov functionals and employing inequality technique three sets of easily verifiable delay independent criteria to guarantee the global exponential stability of a unique equilibrium point are given and moreover by constructing poincare mapping other three sets of easily verifiable delay independent criteria to assure the existence and globally exponential stability of periodic solutions are obtained six examples are given to illustrate the theoretical results

stability and robustness issues in numerical modeling of material failure with the strong discontinuity approach abstract robustness and stability of the continuum strong discontinuity approach csda to material failure are addressed after identification of lack of symmetry of the finite element formulation and material softening in the constitutive model as possible causes of loss of robustness two remedies are proposed 1 the use of an specific symmetric version of the elementary enriched e fem finite element with embedded discontinuities and 2 a new implicit explicit integration of the internal variable in the constitutive model which renders the tangent constitutive algorithmic operator positive definite and constant the combination of both developments leads to finite element formulations with constant in the time step and non singular tangent structural stiffness allowing dramatic improvements in terms of robustness and computational costs after assessing the convergence and stability properties of the new strategies three dimensional numerical simulations of failure problems illustrate the performance of the proposed procedures

a generalized norton hoff model and the prandtl reuss law of plasticity the aim of this article is to study the quasistatic evolution of a three dimensional elastic perfectly plastic solid which satisfies the prandtl reuss law the evolution of the field of stresses which solves a time dependent variational inequality and that of the field of displacements u have been described in previous works 15 26 35 36 37 but it was not shown there that and u satisfy indeed the prandtl reuss constitutive law in this article we find and u in a class of functions which are sufficiently regular for the prandtl reuss law to make sense and we prove that and u satisfy the constitutive law this result is attained by considering the elastic perfectly plastic model as the limit of a family of elastic visco plastic models like those of norton and hoff the norton hoff type models which we introduce depend on a viscosity parameter 0 we study the perturbed models i e 0 fixed and then we pass to the limit 0

numerical analysis of growing crack problems using particle discretization scheme this paper presents the particle discretization scheme pds to analyze brittle failure of solids the scheme uses characteristic functions of voronoi and delaunay tessellations to discretize a function and its derivatives respectively a discretized function has numerous discontinuities so that these discontinuities are utilized as a candidate of crack path segment in modeling propagating cracks without making any extra computation to accommodate new displacement discontinuities when the scheme is implemented to a finite element method fem the resulting stiffness matrix coincides with the one that is obtained by using linear elements the accuracy of computing a stress intensity factor at a crack tip is examined it is shown that the accuracy is better than that of a fem with linear elements when the rotational degree of freedom is included in discretizing displacement functions three three dimensional growing crack problems are solved by means of the pds and the results are presented copyright 2009 john wiley sons ltd

a comprehensive review of stability analysis of continuous time recurrent neural networks stability problems of continuous time recurrent neural networks have been extensively studied and many papers have been published in the literature the purpose of this paper is to provide a comprehensive review of the research on stability of continuous time recurrent neural networks including hopfield neural networks cohen grossberg neural networks and related models since time delay is inevitable in practice stability results of recurrent neural networks with different classes of time delays are reviewed in detail for the case of delay dependent stability the results on how to deal with the constant variable delay in recurrent neural networks are summarized the relationship among stability results in different forms such as algebraic inequality forms m matrix forms linear matrix inequality forms and lyapunov diagonal stability forms is discussed and compared some necessary and sufficient stability conditions for recurrent neural networks without time delays are also discussed concluding remarks and future directions of stability analysis of recurrent neural networks are given

stability and hopf bifurcation of a general delayed recurrent neural network in this paper stability and bifurcation of a general recurrent neural network with multiple time delays is considered where all the variables of the network can be regarded as bifurcation parameters it is found that hopf bifurcation occurs when these parameters pass through some critical values where the conditions for local asymptotical stability of the equilibrium are not satisfied by analyzing the characteristic equation and using the frequency domain method the existence of hopf bifurcation is proved the stability of bifurcating periodic solutions is determined by the harmonic balance approach nyquist criterion and graphic hopf bifurcation theorem moreover a critical condition is derived under which the stability is not guaranteed thus a necessary and sufficient condition for ensuring the local asymptotical stability is well understood and from which the essential dynamics of the delayed neural network are revealed finally numerical results are given to verify the theoretical analysis and some interesting phenomena are observed and reported

existence and global attractivity of almost periodic solution for cellular neural network with distributed delays this paper is devoted to the existence and global attractivity of almost periodic solution for a class of cellular neural network with distributed delays and variable coefficients some sufficient conditions ensuring the existence and global attractivity of almost periodic solution are derived by employing banach fixed point theory and using differential inequality technique the results allow for the consideration of all unbounded neuron signal functions but not necessarily surjective thus these conditions obtained have highly important significance in designs and applications of the networks we extend and improve previously known results an example is also worked out to demonstrate the advantages of our results

exponential stability and periodic oscillatory solution in bam networks with delays both exponential stability and periodic oscillatory solution of bidirectional associative memory bam networks with axonal signal transmission delays are considered by constructing suitable lyapunov functional and some analysis techniques some simple sufficient conditions are given ensuring the global exponential stability and the existence of periodic oscillatory solutions of bam with delays these conditions are presented in terms of system parameters and have important leading significance in the design and applications of globally exponentially stable and periodic oscillatory neural circuits for bam with delays in addition two examples are given to illustrate the results

a duality principle for homogeneous vectorfields with applications we introduce a duality principle for homogeneous vectorfields as an application of this duality principle stability and boundedness results for negative order homogeneous differential equations are obtained starting from known results for positive order homogeneous differential equations

modelling strong discontinuities in solid mechanics via strain softening constitutive equations part 2 numerical simulation on the basis of the strong discontinuity analysis of standard local stress strain constitutive equations a finite element framework for the simulation of strong discontinuities which belongs to the family of assumed enhanced strain methods is presented taking the standard linear triangle as the underlying element an additional incompatible mode leads to the formulation of an enriched strain field which is shown to be able to appropriately capture strong discontinuities the presented numerical simulations show that mesh size and mesh alignment dependencies can be completely removed

a new asymptotic stability criterion for nonlinear time variant differential equations a new sufficient condition for asymptotic stability of ordinary differential equations is proposed unlike classical lyapunov theory the time derivative along solutions of the lyapunov function may have positive and negative values the classical lyapunov approach may be regarded as an infinitesimal version of the present theorem verification in practical problems is harder than in the classical case an example is included in order to indicate how the present theorem may be applied

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 comparative study on finite elements for capturing strong discontinuities e fem vs x fem a comparative study on finite elements for capturing strong discontinuities by means of elemental e fem or nodal enrichments x fem is presented based on the same constitutive model continuum damage and linear elements triangles and tetrahedra optimized implementations of both types of enrichments in the same non linear code are tested for a representative set of 2d and 3d crack propagation examples it is shown that both methods provide the same qualitative and quantitative results for enough refined meshes for the performed tests e fem exhibited in general a higher accuracy mostly for coarse meshes whereas convergence rate with mesh refinement which is super linear showed slightly higher for x fem as for the computational costs for single crack modelling x fem showed depending on the case from 1 1 to about 2 5 times more expensive than e fem for multiple cracks the computational cost of e fem keeps constant whereas the cost associated to x fem increases linearly with the number of modelled cracks

on some necessary and sufficient conditions for a recurrent neural network model with time delays to generate oscillations in this paper the existence of oscillations for a class of recurrent neural networks with time delays between neural interconnections is investigated by using the fixed point theory and liapunov functional we prove that a recurrent neural network might have a unique equilibrium point which is unstable this particular type of instability combined with the boundedness of the solutions of the system will force the network to generate a permanent oscillation some necessary and sufficient conditions for these oscillations are obtained simple and practical criteria for fixing the range of parameters in this network are also derived typical simulation examples are presented

on strong discontinuities in anelastic solids a finite element approach taking a frame indifferent gradient of the discontinuous displacements this paper presents a two dimensional 2d large deformation analysis of strong discontinuities in anelastic solids and its numerical implementation we assume associative and ideal plasticity until localization occurs in the post localization phase discontinuous displacements develop and their material gradient is set up in a proper way one leg in the current configuration the other leg in the reference configuration to provide a frame indifferent objective description the numerical implementation via displacement based six node triangular finite elements enriched by a single displacement jump parameter t2 0 in the post localization phase te locte is described in detail the solution procedure is similar to that using assumed enhanced displacement gradient elements with the only but crucial difference that on the discontinuity surface the traction is linked to the displacement jump via a proper constitutive law finally numerical results of the shear test and of the tension test are presented copyright 2000 john wiley sons ltd