on plastic incompressibility within time adaptive finite elements combined with projection techniques abstract this article treats the interpretation of quasi static finite elements applied to constitutive equations of evolutionary type as a solution scheme to solve globally differential algebraic equations this concept is applied to finite strain viscoplasticity based on a model with non linear kinematic hardening under the assumption of plastic incompressibility the model is based on multiple multiplicative decomposition both for the deformation gradient into an elastic and an inelastic part as well as for the inelastic part into a kinematic hardening energy storage and a dissipative part both intermediate configurations are described by inelastic right cauchy green tensors satisfying inelastic incompressibility in the theoretical context the attention in view of the numerical treatment within finite elements is focused on diagonally implicit runge kutta methods which destroy the assumption of plastic incompressibility during the time integration due to an additive structure of the integration step in combination with a multilevel newton algorithm these algorithms embed the classical strain driven radial return method to this end a concept of geometric numerical integration is applied where the plastic incompressibility condition is taken into account as an additional side condition since the literature states large integration errors if the side condition is not taken into account a particular focus lies on the application of a time adaptive procedure accordingly the article investigates i the algorithmic treatment of kinematic hardening within time adaptive finite elements ii the influence of the perzyna type viscoplasticity approach in view of an order reduction phenomenon and iii the influence of taking into account the exact fulfillment of plastic incompressibility using a projection method having the advantage of simple implementation

stress computation and consistent tangent operator using non linear kinematic hardening models one possibility of formulating the tinite element method is founded on the principle of virtual displacement in which we want to include a rate independent elastoplastic constitutive model based on the assumption of a yield surface the constitutive equations result from the assumptions of small deformations hooke s law for the elastic domain the normality rule for the evolution of plastic strains the von mises yield condition and a special kind of kinematic hardening due to armstrong and frederick 1 in which linear kinematic hardening is generalized with a saturation term we show that it is not generally recommendable to propose large load steps to this end we investigate the influences of the non linear kinematic hardening model on the stress computation and the resulting consistent elastoplastic tangent operator the main topics of this paper are 1 development of a problem optimized backward euler method with regard to the kinematic hardening model 2 study of the influence of the saturation term on the numerical accuracy through isoerror maps and 3 computation of the consistent elastoplastic tangent operator

variational and projection methods for the volume constraint in finite deformation elasto plasticity this paper focuses on the treatment of volume constraints which in the context of elasto plasticity typically arise as a result of assuming volume preserving plastic flow projection methods based on the modification of the discrete gradient operator b often proposed on an ad hoc basis are systematically obtained in the variational context furnished by a three field hu washizu principle the fully nonlinear formulation proposed here is based on a local multiplicative split of the deformation gradient into volume preserving and dilatational parts without relying on rate forms of the weak form of momentum balance this approach fits naturally in a formulation of plasticity based on the multiplicative decomposition of the deformation gradient and enables one to exactly enforce the condition of volume preserving plastic flow within the framework proposed in this paper rate forms and incrementally objective algorithms are entirely bypassed

an efficient stress algorithm with applications in viscoplasticity and plasticity this paper deals with two main topics the first one concerns the equivalence of stress algorithms based on a backward euler step applied on viscoplastic models of chaboche type and their elastoplastic counterpart generally the stress algorithm yields a system of non linear algebraic equations and the corresponding consistent tangent operator occurring in the principle of virtual displacements leads to a system of linear equations this procedure can be obtained utilizing only numerical methods the second topic concerns a special constitutive relation based on a kinematic hardening model using a sum of armstrong frederick terms which is equivalent to a multi surface plasticity model applying this model a so called problem adapted stress algorithm is derived where only one non linear equation must be solved this result is independent of the number of terms in the hardening model furthermore only the viscoplastic algorithm must be implemented since it includes the elastoplastic constitutive model as a special case 1997 by john wiley sons ltd

finite strain viscoplasticity with nonlinear kinematic hardening phenomenological modeling and time integration abstract this article deals with a viscoplastic material model of overstress type the model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part an additional multiplicative decomposition of inelastic part is used to describe a nonlinear kinematic hardening of armstrong frederick type two implicit time stepping methods are adopted for numerical integration of evolution equations such that the plastic incompressibility constraint is exactly satisfied the first method is based on the tensor exponential the second method is a modified euler backward method special numerical tests show that both approaches yield similar results even for finite inelastic increments the basic features of the material response predicted by the material model are illustrated with a series of numerical simulations

an analysis of a new class of integration algorithms for elastoplastic constitutive relations an accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors is carried out in this paper for simplicity attention is confined to infinitesimal deformations the integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations general rate independent and rate dependent behaviour with plastic hardening or softening associated or non associated flow rules and nonlinear elastic response can be efficiently treated within the present framework isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding

numerical simulation of martensitic phase transitions in shape memory alloys using an improved integration algorithm the numerical simulation of structures made of shape memory materials is of increasing interest in different fields among others the computation of pipe connectors or medical devices like endoscopic instruments and stents is a challenge in such practical applications the pseudoelastic effect as well as the one way and two way shape memory effects are utilized these material properties are caused by martensitic phase transitions between austenite and martensite in the present contribution a recently proposed constitutive theory is numerically treated in the context of the finite element method this constitutive theory is formulated in the framework of continuum thermomechanics for geometrically linear problems and is able to represent the occurring martensitic phase transitions in shape memory alloys for the numerical integration of the evolution equations the backward euler method is applied in spite of the complexity of the constitutive theory it is shown that an improved integration procedure can be formulated which merely involves the solution of three non linear equations for three scalar valued unknown variables numerical examples show the capability of the proposed model and the improved integration algorithm copyright 2006 john wiley sons ltd

an implicit integration algorithm with a projection method for viscoplastic constitutive equations robinson s viscoplastic model a representative of the so called overstress models is integrated by use of the generalized midpoint rule the solution of the non linear system of algebraic equations arising from time discretization of the constitutive equations is determined using a projection method in combination with newton s method consistent tangent moduli are calculated and the quadratic convergence of the global newton equilibrium iteration is shown the time increment size is controlled by the convergence behaviour of the equilibrium iteration and the accuracy of the numerical integration various numerical examples are considered to demonstrate the efficiency of the methods

predicting nonlinear cellular automata quickly by decomposing them into linear ones we show that a wide variety of nonlinear cellular automata cas can be decomposed into a quasidirect product of linear ones these cas can be predicted by parallel circuits of depth o log2 t using gates with binary inputs or o log t depth if sum mod p gates with an unbounded number of inputs are allowed thus these cas can be predicted by idealized parallel computers much faster than by explicit simulation even though they are nonlinear this class includes any ca whose rule when written as an algebra is a solvable group we also show that cas based on nilpotent groups can be predicted in depth o log t or o 1 by circuits with binary or sum mod p gates respectively we use these techniques to give an efficient algorithm for a ca rule which like elementary ca rule 18 has diffusing defects that annihilate in pairs this can be used to predict the motion of defects in rule 18 in o log2 t parallel time

efficient implicit integration for finite strain viscoplasticity with a nested multiplicative split abstract an efficient and reliable stress computation algorithm is presented which is based on implicit integration of the local evolution equations of multiplicative finite strain plasticity viscoplasticity the algorithm is illustrated by an example involving a combined nonlinear isotropic kinematic hardening numerous backstress tensors are employed for a better description of the material behavior the considered material model exhibits the so called weak invariance under arbitrary isochoric changes of the reference configuration and the presented algorithm retains this useful property even more the weak invariance serves as a guide in constructing this algorithm the constraint of inelastic incompressibility is exactly preserved as well the proposed method is first order accurate concerning the accuracy of the stress computation the new algorithm is comparable to the euler backward method with a subsequent correction of incompressibility ebmsc and the classical exponential method em regarding the computational efficiency the new algorithm is superior to the ebmsc and em some accuracy tests are presented using parameters of the aluminum alloy 5754 o and the 42crmo4 steel fem solutions of two boundary value problems using msc marc are presented to show the correctness of the numerical implementation

on the numerical treatment of finite deformations in elastoviscoplasticity abstract this paper deals with the generalization of a geometric linear viscoplastic model to finite strains and its numerical application we owe the original formulation of the applied model to perzyna and chaboche it includes nonlinear isotropic and kinematic hardening as well as a nonlinear rate dependence the constitutive equations are integrated numerically in the context of a finite element formulation from theoretical considerations it is known that in the case of vanishing viscosity or slow processes rate independent plasticity arises as an asymptotic limit accordingly the numerical formulation includes this property in fact the stress algorithm corresponding to viscoplasticity is reduced to the asymptotic limit in a most simple way namely by setting the viscosity parameter equal to zero furthermore it is shown that the numerical integration of the constitutive model involves the solution of only one nonlinear equation for one scalar unknown this even applies to a sum of armstrong frederick terms the algorithm incorporates the inelastic incompressibility on the level of the gau points numerical computations of examples taken from metal forming technology show the physical significance of the model and the reliability of the numerical algorithm these calculations have been carried out by means of the finite element program psu

multiplicative cellular automata on nilpotent groups structure entropy and asymptotics if mathbb m mathbb z d and mathcal b is a finite nonabelian group then mathcal b mathbb m is a compact group a multiplicative cellular automaton mca is a continuous transformation mathfrak g b mathbb m to b mathbb m which commutes with all shift maps and where nearby coordinates are combined using the multiplication operation of mathcal b we characterize when mca are group endomorphisms of mathcal b mathbb m and show that mca on mathcal b mathbb m inherit a natural structure theory from the structure of mathcal b we apply this structure theory to compute the measurable entropy of mca and to study convergence of initial measures to haar measure

on the theoretical and numerical modelling of armstrong frederick kinematic hardening in the finite strain regime abstract on the theoretical level the present paper presents a detailed comparison of recent finite strain models for armstrong frederick kinematic hardening thereby two strategies are discussed 1 chaboche type concepts considering the back stress as internal variable 2 continuum mechanical extensions of the classical rheological model using only strain like internal variables it is shown in the paper that models of the second kind can be recast in the format of anisotropic inelasticity with structure tensors second the work focuses on the algorithmic treatment of the kinematic hardening concepts presented before this problem has been tackled up to now only in the context of linearized models in contrast to isotropic finite elastoplasticity the integration cannot be carried out with respect to principal axes therefore a new integration algorithm is developed which is suitable for the anisotropic case but still retains plastic incompressibility in the case of small elastic deformation the algorithm reduces to a system of only one non linear equation and twelve linear equations in general the computational effort of the new scheme does not exceed the one of the backward euler scheme which has the disadvantage that plastic incompressibility is not fulfilled automatically several numerical examples show that the representatives of both approaches 1 and 2 yield similar results if physically reasonable material parameters are chosen

on cesaro limit distribution of a class of permutative cellular automata we study cesaro means time averages of the evolution measures of the class of permutative cellular automata over 0 1 defined by mathtype mtef 2 1 feaafiart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9lq jc9 vqaqpepm0xbba9pwe9q8fs0 yqaqpepae9pg0firpepekkfr0xfr x fr xb9adbaqaaegacigaaiaabeqaamaabaabaagcbagaaiikaiabew 9aqnaabaaaleaacawgcbaabeaakiaadihacaggpawaasbaasqaaiaa d6gaaeqaaogaeyypa0jaamieamaabaaaleaacawgubgaagjcvlaayi w7cqghrawkcaami8uaagjcvlaadkfaaeqaaogaey4kasiaeuioda1a a0baasqaaiaadqgacaami8uaagjcvlabg2da9iaayiw7caami8uaag imaaqaaiaadkfacaami8uaagjcvlabgkhitiaayiw7caami8uaagym aaaakiaayiw7caami8uaagjcvlaayiw7caami8uaagjcvlaacicaca aixagaey4kasiaamoyamaabaaaleaacawgqbaabeaakiabgucariaa dihadawgaawcbagaamobaiaayiw7caami8uaey4kasiaagjcvlaayi w7cawgqbaabeaakiaacmcaaaa 7530 varphi b x n x n kern 1pt kern 1pt kern 1pt kern 1pt r pi j kern 1pt kern 1pt kern 1pt kern 1pt 0 r kern 1pt kern 1pt kern 1pt kern 1pt 1 kern 1pt kern 1pt kern 1pt kern 1pt kern 1pt kern 1pt 1 b j x n kern 1pt kern 1pt kern 1pt kern 1pt j where b b 0 b r 1is an aperiodic block in 0 1 r and operations are taken mod 2 if the initial measure is bernoulli we prove that the limit of the cesaro mean of the first column distribution exists when r 1 and b 1 b is the mod 2 sum automaton for this automaton we show that the limit is the 1 2 1 2 bernoulli measure and if the initial measure is markov we show that the limit of cesaro mean of the one site distribution is equidistributed

quasilinear cellular automata abstract simulating a cellular automaton ca for t time steps into the future requires t 2 serial computation steps or t parallel ones however certain cas based on an abelian group such as addition mod 2 are termed linear because they obey a principle of superposition this allows them to be predicted efficiently in serial time o t robinson 1987 or o log t in parallel in this paper we generalize this by looking at cas with a variety of algebraic structures including quasigroups non abelian groups steiner systems and other structures we show that in many cases an efficient algorithm exists even though these cas are not linear in the previous sense we term them quasilinear we find examples which can be predicted in serial time proportional to t t log t t log 2 t and t for t log t log log t and log 2 t we also discuss what algebraic properties are required or implied by the existence of scaling relations and principles of superposition and exhibit several novel vector valued cas

geometric integrators for multiplicative viscoplasticity analysis of error accumulation abstract the inelastic incompressibility is a typical feature of metal plasticity viscoplasticity over the last decade there has been a great amount of research related to construction of numerical integration algorithms which exactly preserve this property in this paper we examine both numerically and mathematically the excellent accuracy and convergence characteristics of such integrators in order to simplify the considerations we consider strain driven processes without hardening effects in terms of a classical model of multiplicative viscoplasticity we illustrate the notion of exponential stability of the exact solution we show that this property enables the construction of effective and stable numerical algorithms if the incompressibility is exactly satisfied on the other hand if the incompressibility constraint is violated spurious degrees of freedom are introduced in general this results in the loss of the exponential stability and a dramatic deterioration of convergence of numerical methods

applications of ergodic theory and sofic systems to cellular automata abstract we indicate a mathematical framework for analysing the evolution of cellular automata those automata obeying an additive rule are shown to be the same as endomorphisms of a compact abelian group and therefore their statistical and dynamical behavior can be told exactly by using fourier analysis and ergodic theory those obeying certain nonlinear rules are closely tied to a finitely described object called a sofic system but the underlying statistics appear to be more complicated and interesting we conclude by formulating several conjectures about one such system

computation in finite strain viscoelasticity finite elements based on the interpretation as differential algebraic equations abstract in this article the interpretation of current non linear finite element calculations applied to constitutive equations of evolutionary type as a system of differential algebraic equations is continued p ellsiepen s hartmann int j numer methods engrg 51 2001 679 this procedure is applied to a model of finite strain viscoelasticity which incorporates a particular model of non linear rate dependence three specific topics are studied firstly we investigate a possible treatment of the interpretation in view of mixed finite elements secondly the application of stiffly accurate diagonally implicit runge kutta methods which yield on element level the same structure as a backward euler based integration step is analysed it is shown that the resulting stress algorithm is reducible to the solution of only three non linear equations at each gauss point one maxwell element lastly the effect with respect to expense and achievable accuracy of a time adaptive procedure is focused which is necessary in the case of different time scales such as relaxation or creep dominated processes

formulation and numerical solution of non smooth elasto visco plasticity models abstract in this work we describe in detail a model for small strain elasto visco plasticity with convex non smooth yield functions and associative nonlinear kinetic laws restricted to linear hardening using concepts of non smooth convex geometry numerical methods are developed to integrate the evolution equations of the model these algorithms are analyzed and shown to inherit a discrete dissipation inequality irrespective of the smoothness of the yield function the results are applied to models based on tresca s and drucker prager s yield criteria which include all possible types of non smoothness numerical examples are shown to illustrate the performance of the methods

on the modelling of non linear kinematic hardening at finite strains with application to springback comparison of time integration algorithms the paper discusses the derivation and the numerical implementation of a finite strain material model for non linear kinematic and isotropic hardening the kinematic hardening component represents a continuum extension of the classical rheological model of armstrong frederick kinematic hardening in addition a comparison between several numerical algorithms for the integration of the evolution equations is conducted in particular a new form of the exponential map that preserves the plastic volume and the symmetry of the internal variables as well as two modifications of the backward euler scheme are discussed finally the applicability of the model for springback prediction is demonstrated by performing simulations of the draw bending process and a comparison with experiments the results show an excellent agreement between simulation and experiment copyright 2007 john wiley sons ltd

a return mapping algorithm for cyclic viscoplastic constitutive models abstract this paper presents a return mapping algorithm for cyclic viscoplastic constitutive models that include material memory effects the constitutive model is based on multi component forms of kinematic and isotropic hardening variables in conjunction with von mises yield criterion armstrong frederick a f type rules are used to describe the nonlinear evolution of each of the multi component kinematic hardening variables a saturation type exponential rule is used to describe the nonlinear evolution of each of the isotropic hardening variables the concept of memory surface is used to describe the strain range dependent material memory effects that are induced by the prior strain histories in this paper the above class of cyclic viscoplastic constitutive models is formulated within a consistent thermodynamic framework that encompasses the standard generalized materials framework furthermore a complete algorithmic treatment of the above rate dependent constitutive model is also presented for any desired stress or strain constrained configuration subspace a generalized midpoint algorithm is used to integrate the rate constitutive equations the consistent tangent operator is obtained by linearizing the return mapping algorithm and is found to be unsymmetric due to the presence of nonlinear evolution rules for the kinematic hardening variables several numerical examples representing the cyclic hardening and softening behavior transient and stabilized hysteresis behavior and the non fading memory effects of the material are presented these examples demonstrate the accuracy and robustness of the present algorithmic framework for modeling the cyclic viscoplastic behavior of the material

remarks on rate constitutive equations for finite deformation problems computational implications it is explicitly shown that if the spatial elasticity tensor of an elastic material is taken as isotropic for all possible configurations then its coefficients cannot be constants they must depend nontrivially on the jacobian determinant of the deformation gradient moreover the assumption typically made for computational purposes that its coefficients remain constant for all possible configurations is incompatible with elasticity it is further shown that an assumption widely used in the computational literature in the context of finite deformation plasticity namely relating an objective stress rate to the rate of deformation tensor through a fourth rank constant isotropic tensor is also incompatible with elasticity thus furnishing an example of an hypoelastic material which is not elastic