detection of couplings in ensembles of stochastic oscillators the problem of detection and quantitative characterization of directional couplings in an ensemble of noisy oscillators from a time series is addressed we suggest estimators for the strengths of couplings which are based on modeling the observed oscillations with a set of stochastic phase oscillators and easily interpreted from a physical viewpoint moreover we present an analytic formula for a statistical significance level allowing to reveal an architecture of couplings reliably from a relatively short time series the technique applies to weakly coupled nonsynchronized oscillators it is introduced for oscillators with close basic frequencies but can be readily generalized to the case of arbitrary frequencies efficiency of the technique is demonstrated in numerical experiments

exact integration of constitutive equations in elasto plasticity a unified approach is presented for establishing exact integration of the constitutive equations in elastoplasticity assuming the total strain rate direction to be constant this unified approach includes all previous exact integration procedures as special cases and in addition some new closed form solutions are derived for combined kinematic and isotropic hardening special emphasis is laid on combined kinematic and isotropic hardening for von mises material and on isotropic hardening for mohr coulomb and tresca materials

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

testing for effects on variance in experiments with factorial treatment structure and nested errors there is increased interest in industrial experiments aimed at improving quality by reducing the variability of a product characteristic while maintaining the desired mean level of the characteristic analysis of treatment effects on variability however is more difficult than analyzing the effects on mean performance in this article we extend the results of zelen to test for treatment effects on variance when there are two sources of variability that which exists between production runs or setups and variability within runs bootstrap critical values are developed to handle possibly nonnormal errors at either level of variability

bootstrap critical values for testing homogeneity of covariance matrices abstract bartlett s modified likelihood ratio statistic a is often suggested in multivariate analysis for testing equality of covariance matrices unfortunately the 2 approximation to the null distribution of 2 log is useful only when the data is normally distributed this article presents a pooled bootstrap procedure that replaces the 2 approximation and makes bartlett s statistic a useful tool for data analysis this procedure also applies to most quadratic form test statistics

a comparative study of tests for homogeneity of variances with applications to the outer continental shelf bidding data many of the existing parametric and nonparametric tests for homogeneity of variances and some variations of these tests are examined in this paper comparisons are made under the null hypothesis for robustness and under the alternative for power monte carlo simulations of various symmetric and asymmetric distributions for various sample sizes reveal a few tests that are robust and have good power these tests are further compared using data from outer continental shelf bidding on oil and gas leases

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

a semi analytical integration method for j2 flow theory of plasticity with linear isotropic hardening abstract in this paper an exact time integration scheme is presented for von mises elastoplasticity with linear isotropic hardening at small deformations the method is based on the constant strain rate assumption which is widely accepted in displacement based finite element applications the deviatoric form of the rate equation using the method proposed by krieg and krieg in r d krieg d b krieg accuracies of numerical solution methods for the elastic perfectly plastic model j press vess technol trans asme 99 1977 510 515 is rewritten to a system of nonlinear odes with two scalar functions the radius of the mises circle and an angle obtained by using the scalar product of the stress deviator and the strain rate the time integration of these functions gives an exact solution in implicit form using the incomplete beta function in addition by the exact linearization of this new semi analytical solution a stress updating algorithm and the consistent tangent operator are derived the numerical performance and accuracy of the proposed method are illustrated on numerical examples moreover a comparison of the proposed method with the well known radial return method is included

prandtl reuss elastoplasticity on off switch and superposition formulae abstract constitutive postulates for prandtl reuss elastoplasticity are selected based on them sufficient and necessary conditions for plastic irreversibility are found to be the yield condition and the straining condition this is then analyzed and it is pointed out that prandtl reuss elastoplasticity is nothing but a two phase linear system with an on off switch which is operated in the pace of an intrinsic measure of plastic irreversibility then the temporally global concept of the switch on time t on and the switch off time t off and their determination and bound estimation is developed owing to the implicit linearity superposition formulae for the stress response are discovered as an example the exact constitutive solutions for circular paths based on the superposition formulae are obtained and t on and t off are determined

integration of plasticity equations for the case of ziegler s kinematic hardening abstract an integration scheme is presented aimed at obtaining accurate solutions of the equations of flow plasticity with general yield functions in the presence of ziegler s kinematic hardening the elastic plastic rate problem is formulated within the mathematical programming framework introduced by maier the integration algorithm consists of a sequence of variable amplitude steps each subdivided into a stable loading and a neutral loading substeps the algorithm allows the error admissible on the yield condition and flow rule satisfaction to be prescribed a priori thus incorporating an automatic criterion for subincrementation numerical results providing indications about the accuracy and effectiveness of the integration scheme are presented mostly in the error contour plot method employed by krieg and krieg

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

properties of sufficiency and statistical tests 1 in a previous paper dealing with the importance of properties of sufficiency in the statistical theory of small samples attention was mainly confined to the theory of estimation in the present paper the structure of small sample tests whether these are related to problems of estimation and fiducial distributions or are of the nature of tests of goodness of fit is considered further

synchronization between main rhythmic processes in the human cardiovascular system for the cases of spontaneous respiration and paced respiration with a fixed frequency and linearly increasing frequency we investigate synchronization between three main rhythmic processes governing the cardiovascular dynamics in humans namely the main heart rhythm respiration and the process whose fundamental frequency is close to 0 1 hz the analysis of the experimental records reveals synchronous regimes of different orders n m between all the three main rhythms the influence of the regime of breathing and the magnitude of heart rate variability on the degree of synchronization is considered

extremum convergence and stability properties of the finite increment problem in elastic plastic boundary element analysis abstract the boundary element be analysis is formulated by a symmetric galerkin weightedresidual double integration approach rather than by a traditional collocation or by a nonsymmetric galerkin approach the internal variable associative elastoplastic material model is discretized in time by a stepwise holonomic backward difference integration scheme it is then enforced in a weighted average sense over cells and reformulated in terms of cell generalized variables in the above context the following results are established under suitable constitutive hypotheses a a minimum characterization of the solution to the discretized step problem in finite increments b a convergence theorem concerning a conventional iterative algorithm for solving this problem c a proof of the stability of the marching solution method in the sense of non amplification of errors along a finite step sequence an illustrative example corroborates the theoretical results

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

bifurcations in a nonlinear model of the baroreceptor cardiac reflex abstract we investigate the dynamic properties of a nonlinear model of the human cardio baroreceptor control loop as a new feature we use a phase effectiveness curve to describe the experimentally well known phase dependency of the cardiac pacemaker s sensitivity to neural activity we show that an increase of sympathetic time delays leads via a hopf bifurcation to sustained heart rate oscillations for increasing baroreflex sensitivity or for repetitive vagal stimulation we observe period doubling toroidal oscillations chaos and entrainment between the rhythms of the heart and the control loop the bifurcations depend crucially on the involvement of the cardiac pacemaker s phase dependency we compare the model output with experimental data from electrically stimulated anesthetized dogs and discuss possible implications for cardiac arrhythmias

rapid non linear finite element analysis of continuous and discontinuous galerkin methods in matlab matlab is adept at the development of concise finite element fe routines however it is commonly perceived to be too inefficient for high fidelity analysis this paper aims to challenge this preconception by presenting two optimised fe codes for both continuous galerkin cg and discontinuous galerkin dg methods although this has previously been achieved for linear elastic problems no such optimised matlab script currently exists which includes the effects of material non linearity to incorporate these elasto plastic effects the externally applied load is split into a discrete number of loadsteps equilibrium is determined at each loadstep between the externally applied load and the arising internal forces using the newton raphson method the optimisation of the scripts is primarily achieved using vectorised blocking algorithms which minimise ram to cache overheads and maximise cache reuse the optimised codes yielded maximum speed gains of 25 7 and 10 1 when compared to the corresponding unoptimised scripts for cg and dg respectively it was identified that with increasing refinement of the mesh the solver time begins to dominate the overall simulation time this bottleneck has a greater disadvantage on the dg code predominantly due the asymmetric nature of the global stiffness matrix the implementation of an efficient solver would see further improvement to the overall run times particularly for large problems

detecting synchronization of self sustained oscillators by external driving with varying frequency we propose a method for detecting the presence of a synchronization of a self sustained oscillator by external driving with linearly varying frequency the method is based on a continuous wavelet transform of the signals of the self sustained oscillator and external force and allows one to distinguish the case of true synchronization from the case of spurious synchronization caused by linear mixing of the signals we apply the method to a driven van der pol oscillator and to experimental data of human heart rate variability and respiration

accuracy and stability of integration algorithms for elastoplastic constitutive relations an analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well known trapezoidal and midpoint rules to fit the present context other integration schemes such as the radial return mean normal and closest point procedures are particular cases of this general formulation the meaning of first and second order accuracy in the presence of the plastic consistency condition is examined in detail and the criteria derived are used to identify two second order accurate members of the proposed algorithms a general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed with the aid of this methodology the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule finally numerical examples are presented that illustrate the performance of the algorithms

distance based tests for homogeneity of multivariate dispersions the traditional likelihood based test for differences in multivariate dispersions is known to be sensitive to nonnormality it is also impossible to use when the number of variables exceeds the number of observations many biological and ecological data sets have many variables are highly skewed and are zero inflated the traditional test and even some more robust alternatives are also unreasonable in many contexts where measures of dispersion based on a non euclidean dissimilarity would be more appropriate distance based tests of homogeneity of multivariate dispersions which can be based on any dissimilarity measure of choice are proposed here they rely on the rotational invariance of either the multivariate centroid or the spatial median to obtain measures of spread using principal coordinate axes the tests are straightforward multivariate extensions of levene s test with p values obtained either using the traditional f distribution or using permutation of either least squares or lad residuals examples illustrate the utility of the approach including the analysis of stabilizing selection in sparrows biodiversity of new zealand fish assemblages and the response of indonesian reef corals to an el nino monte carlo simulations from the real data sets show that the distance based tests are robust and powerful for relevant alternative hypotheses of real differences in spread

mean phase coherence as a measure for phase synchronization and its application to the eeg of epilepsy patients abstract we apply the concept of phase synchronization of chaotic and or noisy systems and the statistical distribution of the relative instantaneous phases to electroencephalograms eegs recorded from patients with temporal lobe epilepsy using the mean phase coherence as a statistical measure for phase synchronization we observe characteristic spatial and temporal shifts in synchronization that appear to be strongly related to pathological activity in particular we observe distinct differences in the degree of synchronization between recordings from seizure free intervals and those before an impending seizure indicating an altered state of brain dynamics prior to seizure activity

from granger causality to long term causality application to climatic data quantitative characterization of interaction between processes from time series is often required in different fields of natural science including geophysics and biophysics typically one estimates short term influences e g the widely used granger causality is defined via one step ahead predictions such an approach does not reveal how strongly the long term behavior of one process under study is affected by the others to overcome this problem we introduce the concept of long term causality which extends the concept of granger causality the long term causality is estimated from data via empirical modeling and analysis of model dynamics under different conditions apart from mathematical examples we apply both approaches to find out how strongly the global surface temperature gst is affected by variations in carbon dioxide atmospheric content solar activity and volcanic activity during the last 150 years influences of all the three factors on gst are detected with the granger causality however the long term causality shows that the rise in gst during the last decades can be explained only if the anthropogenic factor co 2 is taken into account in a model

phase relationships between two or more interacting processes from one dimensional time series ii application to heart rate variability data the recently proposed approach to detect synchronization from univariate data is applied to heart rate variability hrv data from ten healthy humans the approach involves introducing angles for return times map and studying their behavior for filtered human hrv data it is demonstrated that i in many of the subjects studied interactions between different processes within the cardiovascular system can be considered as weak and the angles can be well described by the derived model ii in some of the subjects the strengths of the interactions between the processes are sufficiently large that the angles map has a distinctive structure which is not captured by our model iii synchronization between the processes involved can often be detected iv the instantaneous radii are rather disordered

regions of cardiorespiratory synchronization in humans under paced respiration cardiorespiratory synchronization under paced respiration is studied systematically as the respiration frequency is changed between 3 and 30 breaths per min we plot a one dimensional cut of the classical picture of synchronization regions along the line defining the current breathing amplitude the existence of n m synchronization regions of finite width is demonstrated for each of six subjects studied the statistics of the different types of synchronization and their stability are discussed

time scale synchronization of chaotic oscillators this paper presents the result of the investigation of chaotic oscillator synchronization a new approach to detect the synchronized behaviour of chaotic oscillators has been proposed this approach is based on the analysis of different time scales in the time series generated by the coupled chaotic oscillators this approach has been applied for the coupled rossler and lorenz systems

nurbs plasticity yield surface representation and implicit stress integration for isotropic inelasticity in numerical analysis the failure of engineering materials is controlled through specifying yield envelopes or surfaces that bound the allowable stress in the material however each surface is distinct and requires a specific equation describing the shape of the surface to be formulated in each case these equations impact on the numerical implementation specifically relating to stress integration of the models and therefore a separate algorithm must be constructed for each model this paper presents for the first time a way to construct yield surfaces using techniques from non uniform rational basis spline nurbs surfaces such that any isotropic convex yield envelope can be represented within the same framework these surfaces are combined with an implicit backward euler type stress integration algorithm to provide a flexible numerical framework for computational plasticity the algorithm is inherently stable as the iterative process starts and remains on the yield surface throughout the stress integration the performance of the algorithm is explored using both material point investigations and boundary value analyses demonstrating that the framework can be applied to a variety of plasticity models

a bootstrap comparison of genetic covariance matrices summary an important problem in evolutionary biology is how population bottlenecks affect additive genetic variance va when only additive effects are present a decrease in va is predicted whereas with many forms of nonadditive interactions an increase is predicted we present an analysis of the changes in variance that occur as a result of a bottleneck in a population of the red flour beetle tribolium castaneum in this experiment the additive genetic covariance matrix for four traits in two sexes was measured in the ancestral population the population then went through a bottleneck and the genetic covariance matrix was again measured these data were analyzed by first examining the univariate estimates for va and second examining the covariance matrices for the univariate measures the statistic we used was the change in va for the multivariate comparisons we used three measures the difference in rank the difference in the number of positive eigenvalues to test changes in the number of heritable traits a multivariate equivalent of bartlett s statistic to test changes in the size of the matrices and a modification of mantel s correlation to test for changes in the correlation structure of the matrices because the distribution of all of these measures is complex and dependent on the specifics of the particular matrices being compared we chose to use a bootstrap analysis to test for significance for females we found that following the population bottleneck va was significantly decreased and that the correlation structure of the matrix was significantly changed for males we found that following the population bottleneck va significantly increased but that the correlation structure was unchanged

symmetry preserving return mapping algorithms and incrementally extremal paths a unification of concepts in this work we seek to characterize the conditions under which an elastic plastic stress update algorithm preserves the symmetries inherent to the material response from a numerical standpoint the aim is to determine under what conditions a stress update algorithm produces symmetric consistent tangents when applied to materials obeying normality for the ideally plastic solid we show that only the fully implicit or closest point return mapping algorithm is symmetry preserving for hardening plasticity symmetry cannot be preserved in general unless suitable restrictions are imposed on the constitutive equations we show that these restrictions amount to the existence of a pseudo internal energy function acting as a joint potential for both the direction of plastic flow and the hardening moduli in view of the fact that holonomic methods based on incrementally extremal paths also result in update rules possessing a potential structure and hence in symmetric tangents we address the question of whether any connections exist between the two approaches we show that holonomic methods and the fully implicit algorithm may indeed be brought into correspondence

an incremental elastic plastic finite element solver in a workstation cluster environment part i formulations and parallel processing abstract we discuss solution schemes for the incremental elastic plastic structural problem discretized by means of the finite element method attention is focused on their formulation and implementation in a parallel computing environment defined by a cluster of workstations connected by means of a network the availability of parallel computers allows one to consider possible formulations and solution strategies so far not considered competitive with the classical newton like schemes implying the definition of an elastic plastic tangent stiffness matrix the solution strategies herein considered are based on the explicit integration of the actual elastic plastic rate problem this in turn is phrased in terms of two different formulations whose relative advantages particularly with respect to their integration in parallel are discussed a u gl displacemen plastic multiplier formulation of the structural rate theory of plasticity 1 integrated by means of an explicit element by element scheme seems to be the most promising one

bootstrap methods for testing homogeneity of variances this article describes the use of bootstrap methods for the problem of testing homogeneity of variances when means are not assumed equal or known the methods are new in this context and allow the use of normal theory test statistics such as f s 2 1 s 2 2 without the normality assumption that is crucial for validity of critical values obtained from the f distribution both asymptotic analysis and monte carlo sampling show that the new resampling procedures compare favorably with older methods in terms of test validity and power

on the edgeworth expansion and the bootstrap approximation for a studentized u statistic the asymptotic accuracy of the estimated one term edgeworth expansion and the bootstrap approximation for a studentized u statistic is investigated it is shown that both the edgeworth expansion estimate and the bootstrap approximation are asymptotically closer to the exact distribution of a studentized u statistic than the normal approximation the conditions needed to obtain these results are weak moment assumptions on the kernel h of the u statistic and a nonlattice condition for the distribution of g x1 e h xl x2 1x11 as an application improved edgeworth and bootstrap based confidence intervals for the mean of a u statistic are obtained

robust methods for testing the pattern of a single covariance matrix summary patterns for a single covariance matrix may be studied using likelihood ratio or quadratic form test statistics typically these tests have an asymptotic chi squared distribution when the data are normally distributed but the asymptotic distribution is sensitive to nonnormality this paper suggests two ways to robustify inference for patterned matrices i estimate the critical values of normal theory test statistics using a new bootstrap procedure which takes advantage of certain invariances under ho and ii modify the statistics so that an asymptotic chi squared distribution holds even under nonnormality

k statistics and dispersion effects in regression on donne deux ensembles d estimateurs sans biais pour le cas ou la reponse moyenne depend lineairement de covariables connues

generalized midpoint finite element dynamic analysis of elastoplastic systems the application of a four parameter generalized midpoint integration method to small displacement elastoplastic dynamic problems is considered the integration of the governing relations over a time step is formulated as a non linear algebraic problem finite step problem by making use of generalized variables finite element modelling uniqueness and an extremum characterization of the solution of the finite step problem are discussed sufficient conditions for convergence of various iterative algorithms including newton raphson are given the b stability of the proposed procedure is assessed

multi time step explicit implicit method for non linear structural dynamics we present a method with domain decomposition to solve time dependent non linear problems this method enables arbitrary numeric schemes of the newmark family to be coupled with different time steps in each subdomain this coupling is achieved by prescribing continuity of velocities at the interface we are more specifically interested in the coupling of implicit explicit numeric schemes taking into account material and geometric non linearities the interfaces are modelled using a dual schur formulation where the lagrange multipliers represent the interfacial forces unlike the continuous formulation the discretized formulation of the dynamic problem is unable to verify simultaneously the continuity of displacements velocities and accelerations at the interfaces we show that within the framework of the newmark family of numeric schemes continuity of velocities at the interfaces enables the definition of an algorithm which is stable for all cases envisaged to prove this stability we use an energy method i e a global method over the whole time interval in order to verify the algorithms properties then we propose to extend this to non linear situations in the following cases implicit linear explicit non linear explicit non linear explicit non linear and implicit non linear explicit non linear finally we present some examples showing the feasibility of the method copyright 2001 john wiley sons ltd

nurbs plasticity yield surface evolution and implicit stress integration for isotropic hardening this paper extends the non uniform rational basis spline nurbs plasticity framework of coombs et al 2016 to include isotropic hardening of the yield surfaces the approach allows any smooth isotropic yield envelope to be represented by a nurbs surface the key extension provided by this paper is that the yield surface can expand or contract through the movement of control points linked to the level of inelastic straining experienced by the material the model is integrated using a fully implicit backward euler algorithm that constrains the return path to the yield surface and allows the derivation of the algorithmic consistent tangent to ensure optimum convergence of the global equilibrium equations this provides a powerful framework for elasto plastic constitutive models where unlike the majority of models presented in the literature the underlying numerical algorithm and implemented code remains unchanged for different yield surfaces the performance of the algorithm is demonstrated and validated using both material point and boundary values simulations including plane stress plane strain and three dimensional examples for different yield criteria

a new exact integration method for the drucker prager elastoplastic model with linear isotropic hardening abstract this paper presents the exact stress solution of the non associative drucker prager elastoplastic model governed by linear isotropic hardening rule the stress integration is performed under constant strain rate assumption and the derived formulas are valid in the setting of small strain elastoplasticity theory based on the time continuous stress solution a complete discretized stress updating algorithm is also presented providing the solutions for the special cases when the initial stress state is located in the apex and when the increment produces a stress path through the apex explicit expression for the algorithmically consistent tangent tensor is also derived in addition a fully analytical strain solution is also derived for the stress driven case using constant stress rate assumption in order to get a deeper understanding of the features of these solutions two numerical test examples are also presented

detection of synchronization from univariate data using wavelet transform a method is proposed for detecting from univariate data the presence of synchronization of a self sustained oscillator by external driving with varying frequency the method is based on the analysis of difference between the oscillator instantaneous phases calculated using continuous wavelet transform at time moments shifted by a certain constant value relative to each other we apply our method to a driven asymmetric van der pol oscillator experimental data from a driven electronic oscillator with delayed feedback and human heartbeat time series in the latest case the analysis of the heart rate variability data reveals synchronous regimes between the respiration and slow oscillations in blood pressure

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

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 stable neutral equilibrium path for the numerical solution of elastic plastic softening problems abstract an algorithm for the numerical analysis of the behavior of brittle materials in tension is presented it describes the crack opening in terms of a cohesive crack model with a predefined stress crack opening law the decreasing branch of the constitutive law is followed by means of a sequence of two elastic perfectly plastic steps a first one is a standard step of integration of the plasticity rate equations for increasing loads the second assumes a neutral equilibrium situation constant external actions and integrates a set of nonconventional plasticity rate equations governed by a negative rate of the plastic resistance at the material point undergoing fracture a stability test indicates if the process of crack opening governed by the decrease of the plastic resistance is compatible with the fracture energy g of the material if the configuration is recognized as a limit point the algorithm operates an automatic feedback reversing the sign of the external agents until stability is recovered as shown in previous work the algorithm gives results not affected by spurious dependence on the discretization also since softening is not explicitly included in the material description such consequences of indefinite governing matrices as multiplicity or non existence of solution still existing in the mathematical background are never numerically encountered since each step of the analysis is here governed by semi definite positive matrices

on the integration schemes for drucker prager s elastoplastic models based on exponential maps rate plasticity equations for the case of drucker prager s model in small strain regime are considered by defining an augmented stress vector the formulations convert the original problem into a quasi linear differential equation system two new exponential mapping schemes for integrating model equations are proposed in addition two traditional schemes for solving the dynamical system in an explicit manner are discussed the two semi implicit schemes developed pose higher accuracy and better convergency error contours are provided for all four methods to display the accuracy of each scheme in order to compare the results these contours for the classical one step backward euler integration method are also displayed accuracy and efficiency along with the rate of convergency of the existing and the proposed methods are examined by numerical examples copyright 2007 john wiley sons ltd

convergence of the newton raphson algorithm in elastic plastic incremental analysis a spatially continuous time discrete formulation of the loading of an elastic perfectly plastic body governed by a von mises yield condition is presented it is assumed that incremental changes in strain occur along minimum work paths which is equivalent to a backward difference implicit integration algorithm or the radial return method