a theoretical and computational framework for anisotropic continuum damage mechanics at large strains abstract the main objective of this work is the formulation and algorithmic treatment of anisotropic continuum damage mechanics at large strains based on the concept of a fictitious isotropic undamaged configuration an additional linear tangent map is introduced which allows the interpretation as a damage deformation gradient then the corresponding finger tensor denoted as damage metric constructs a second order internal variable due to the principle of strain energy equivalence with respect to the fictitious effective space and the standard reference configuration the free energy function can be computed via push forward operations within the nominal setting referring to the framework of standard dissipative materials associated evolution equations are constructed which substantially affect the anisotropic nature of the damage formulation the numerical integration of these ordinary differential equations is highlighted whereby two different schemes and higher order methods are taken into account finally some numerical examples demonstrate the applicability of the proposed framework

equivalent spatial and material descriptions of finite deformation elastoplasticity in principal axes abstract a spatial description of the theory of rate independent finite deformation elastoplasticity in which the stress tensor is defined through the strain energy function is discussed the main assumption of isotropic elastic response and invariance requirements under superposed rigid body motion restrict the acceptable forms of the strain energy function to those given in terms of principal values of the strain measure of elastic distortion the formulation is developed on a manifold and the corresponding material description is obtained simply by pull back of the derived spatial form by appealing to the notion of covariance the method of principal axes is systematically exploited to derive the explicit expression for the stress tensor computation for an arbitrary form of the strain energy function and the explicit form of the evolution equation for an arbitrary form of the yield function a model problem of volume preserving plastic flow is discussed in the closure

modeling and analysis of a phase field system for damage and phase separation processes in solids abstract in this work we analytically investigate a multi component system for describing phase separation and damage processes in solids the model consists of a parabolic diffusion equation of fourth order for the concentration coupled with an elliptic system with material dependent coefficients for the strain tensor and a doubly nonlinear differential inclusion for the damage function the main aim of this paper is to show existence of weak solutions for the introduced model where in contrast to existing damage models in the literature different elastic properties of damaged and undamaged material are regarded to prove existence of weak solutions for the introduced model we start with an approximation system then by passing to the limit existence results of weak solutions for the proposed model are obtained via suitable variational techniques

a gradient enhanced large deformation continuum damage model for fibre reinforced materials a non local gradient based damage formulation within a geometrically non linear setting is presented the hyperelastic constitutive response at local material point level is governed by a strain energy which is additively composed of an isotropic matrix and of an anisotropic fibre reinforced material respectively the inelastic constitutive response is governed by a scalar 1 d type damage formulation where only the anisotropic elastic part is assumed to be affected by the damage following the concept in dimitrijevic and hackl 28 the local free energy function is enhanced by a gradient term this term essentially contains the gradient of the non local damage variable which itself is introduced as an additional independent variable in order to guarantee the equivalence between the local and non local damage variable a penalisation term is incorporated within the free energy function based on the principle of minimum total potential energy a coupled system of euler lagrange equations i e the balance of linear momentum and the balance of the non local damage field is obtained and solved in weak form the resulting coupled highly non linear system of equations is symmetric and can conveniently be solved by a standard incremental iterative newton raphson type solution scheme several three dimensional displacement and force driven boundary value problems partially motivated by biomechanical application highlight the mesh objective characteristics and constitutive properties of the model and illustratively underline the capabilities of the formulation proposed

a constitutive frame of elastoplasticity at large strains based on the notion of a plastic metric abstract the article presents a constitutive framework of large strain elastoplasticity in both the lagrangian and the eulerian geometric setting which takes into account anisotropic material response in summary the key ingredients of this framework are i the introduction of a plastic metric which is assumed to describe locally the history dependent inelastic material response in the sense of an internal variable formulation ii the definition of a convex elastic domain in the space of the local stress like variable conjugate to the plastic metric denoted as the plastic force iii an equivalent lagrangian and eulerian representation of all constitutive functions as isotropic tensor functions in terms of an extended set of arguments denoted as anisotropy variables iv the set up of normality rules for the evolution of the plastic metric and the anisotropy variables yielding a canonical symmetric form of the elastoplastic tangent moduli v a geometrically exact decomposition of the set of constitutive equations into possibly decoupled volumetric and isochoric contributions applications of the constitutive framework are demonstrated by means of several conceptual model problems which cover isotropic initial anisotropic and induced anisotropic elastoplastic response

on free energy based formulations for kinematic hardening and the decomposition f fpfe within the framework of linear plasticity based on additive decomposition of the linear strain tensor kinematical hardening can be described by means of extended potentials the method is elegant and avoids the need for evolution equations the extension of small strain formulations to the finite strain case which is based on the multiplicative decomposition of the deformation gradient into elastic and inelastic parts proved not straight forward specifically the symmetry of the resulting back stress remained elusive in this paper a free energy based formulation incorporating the effect of kinematic hardening is proposed the formulation is able to reproduce symmetric expressions for the back stress while incorporating the multiplicative decomposition of the deformation gradient kinematic hardening is combined with isotropic hardening where an associative flow rule and von mises yield criterion are applied it is shown that the symmetry of the back stress is strongly related to its treatment as a truly spatial tensor where contraction operations are to be conducted using the current metric the latter depends naturally on the deformation gradient itself various numerical examples are presented

critical behavior of a kam surface i empirical results kolmogorov arnol d moser kam surfaces are studied in the context of a perturbed two dimensional twist map in particular we ask how a kam surface can disappear as the perturbation parameter is increased following greene we use cycles to numerically construct the kam curve and discover that at the critical coupling it shows structure at all length scales aspects of this structure are fitted by a scaling analysis critical indices and scaling functions are determined numerically some evidence is presented which suggests that the results are universal

frenkel kontorova model with toda interactions we have studied the frenkel kontorova fk model with toda interactions the phase diagram is found to be asymmetric due to the exponential form of the toda interaction the reflection symmetry observed in the standard fk model is broken here the singularity spectrum and the generalized dimension are calculated and their dependence on the nonlinearity parameter is discussed the critical exponents of the gap in the phonon spectrum the correlation length and the peierls nabarro barrier are found to be the same as those in the standard fk model and are independent of the nonlinearity parameter

analysis of microstructure development in shearbands by energy relaxation of incremental stress potentials large strain theory for standard dissipative solids we propose a fundamentally new approach to the treatment of shearband localizations in strain softening elastic plastic solids at finite strains based on energy minimization principles associated with microstructure developments the point of departure is a general internal variable formulation that determines the finite inelastic response as a standard dissipative medium consistent with this type of inelasticity we consider an incremental variational formulation of the local constitutive response where a quasi hyperelastic stress potential is obtained from a local constitutive minimization problem with respect to the internal variables the existence of this variational formulation allows the definition of the material stability of an inelastic solid based on weak convexity conditions of the incremental stress potential in analogy to treatments of finite elasticity furthermore localization phenomena are interpreted as microstructure developments on multiple scales associated with non convex incremental stress potentials in analogy to elastic phase decomposition problems these microstructures can be resolved by the relaxation of non convex energy functionals based on a convexification of the stress potential the relaxed problem provides a well posed formulation for a mesh objective analysis of localizations as close as possible to the non convex original problem based on an approximated rank one convexification of the incremental stress potential we develop a computational two scale procedure for a mesh objective treatment of localization problems at finite strains it constitutes a local minimization problem for a relaxed incremental stress potential with just one scalar variable representing the intensity of the microshearing of a rank one laminate aligned to the shear band this problem is sufficiently robust with regard to applications to large scale inhomogeneous deformation processes of elastic plastic solids the performance of the proposed energy relaxation method is demonstrated for a representative set of numerical simulations of straight and curved shear bands which report on the mesh independence of the results copyright 2003 john wiley sons ltd

characteristic invariant subspaces generated by a single vector abstract if f is an endomorphism of a finite dimensional vector space v over a field k then an invariant subspace x v is called hyperinvariant respectively characteristic if x is invariant under all endomorphisms respectively automorphisms that commute with f the characteristic hull of a subset w of v is defined to be the smallest characteristic subspace in v that contains w it is known that characteristic subspaces that are not hyperinvariant can only exist when k 2 in this paper we study subspaces x which are the characteristic hull of a single element in the case where k 2 we derive a necessary and sufficient condition such that x is hyperinvariant

efficient iteration schemes for anisotropic hyperelasto plasticity numerical issues arising when integrating hyperelasto plastic constitutive equations with elastic anisotropy stemming from anisotropic damage and plastic anisotropy as represented by kinematic hardening are discussed in particular solution algorithms for the corresponding non linear system of equations due to implicit integration algorithms are addressed it is shown that algorithms like staggered iteration and quasi newton techniques are superior to a pure newton technique when the cpu time is compared however the drawback of the staggered and the quasi newton technique is that rather small time steps must be taken to ensure convergence which can be of importance when applying complex constitutive models in a finite element programme copyright 2005 john wiley sons ltd

on the spatial formulation of anisotropic multiplicative elasto plasticity abstract this contribution aims at a thermodynamically consistent and modular formulation of anisotropic multiplicative elasto plasticity embedded in the well established framework of non standard dissipative materials we adopt as a key ingredient the introduction of additional symmetric arguments typically structural tensors into the relevant scalar valued isotropic tensor functions on this basis the fundamental covariance relation leads us to a formulation which allows itself to be set up directly in terms of spatial arguments and thus guarantees a convenient implementation within a finite element setting

nonanalytic twist maps and frenkel kontorova models we give a review of our recent works on a class of twist maps and frenkel kontorova fk models in which the external potential function is nonanalytic c1 and endowed with a variable degree of inflection z when z 3 recurrence of invariant curves has been observed an inverse residue criterion for the reappearance of an invariant curve complementary to the residue criterion for the disappearance of an invariant curve is introduced to make a precise determination of the reappearance point we have also studied the local and global scaling behaviors of these curves the critical exponents the singularity spectrum and the generalized dimensions are found to vary with z when 2 z 3 but remain the same for z 3 the degree of inflection thus plays a role reminiscent of that of dimensionality in phase transitions with z 2 and 3 corresponding respectively to the lower and upper critical dimensions when the same nonanalytic function is substituted for the sinusoidal external potential in the standard fk model the same conclusions are reached there exists a sequence of pinning depinning transitions and the critical exponents of the phonon gap the coherence length and the peierls nabarro barrier all show the same dependence on z

a shell finite element for large strain elastoplasticity with anisotropies part ii constitutive equations and numerical applications abstract an eight node c 0 shell element for finite elastic plastic deformations with anisotropies is developed it combines the advantages of an isoparametric description of geometry and deformation the application of tensors in cartesian components and a real and effective plane stress description with three displacement and three director degrees of freedom at each node in part i of the paper the shell theory including the kinematics the variational principle the application of lagrange multipliers with their condensation on the element level and a comparative study of various assumed strain techniques were presented and the results of convergence tests given in this paper we consider the constitutive equations for large elastic and large plastic strains accounting for initial and induced anisotropies and the corresponding thermodynamics then we investigate the return algorithm for finite strains and the implementation of the element procedure including stiffness matrix and residual force vector finally we present the results of extended numerical applications and a comparison with fe solutions published in the literature as far as such are available

characteristic subspaces and hyperinvariant frames abstract let f be an endomorphism of a finite dimensional vector space v over a field k an f invariant subspace is called hyperinvariant respectively characteristic if it is invariant under all endomorphisms respectively automorphisms that commute with f we assume k 2 since all characteristic subspaces are hyperinvariant if k 2 the hyperinvariant hull w h of a subspace w of v is defined to be the smallest hyperinvariant subspace of v that contains w the hyperinvariant kernel w h of w is the largest hyperinvariant subspace of v that is contained in w and the pair w h w h is the hyperinvariant frame of w in this paper we study hyperinvariant frames of characteristic non hyperinvariant subspaces w we show that all invariant subspaces in the interval w h w h are characteristic we use this result for the construction of characteristic non hyperinvariant subspaces

aspects of the formulation and finite element implementation of large strain isotropic elasticity the paper presents a formulation of isotropic large strain elasticity and addresses some computational aspects of its finite element implementation on the theoretical side an eulerian setting of isotropic elasticity is discussed exclusively in terms of the finger tensor as a strain measure noval aspects are a direct representation of the eulerian elastic moduli in terms of the finger tensor and their rigorous decomposition into decoupled volumetric and isochoric contributions based on a multiplicative split of the finger tensor into spherical and unimodular parts the isochoric stress response is formulated in terms of the eigenvalues of the unimodular part of the finger tensor a constitutive algorithm for the computation of the stresses and tangent moduli for plane problems is developed and applied to a model problem of rubber elasticity on the computational side the implementation of the constitutive model in three possible finite element formulations is discussed after pointing out algorithmic techniques for the treatment of incompressible elasticity several numerical simulations are presented which show the performance of the proposed constitutive algorithm and the convergence behaviour of the different finite element fomulations for compressible and incompressible elasticity

coupled thermoviscoplasticity of glassy polymers in the logarithmic strain space based on the free volume theory the paper outlines a constitutive model for finite thermo visco plastic behavior of amorphous glassy polymers and considers details of its numerical implementation in contrast to existing kinematical approaches to finite plasticity of glassy polymers the formulation applies a plastic metric theory based on an additive split of lagrangian hencky type strains into elastic and plastic parts the analogy between the proposed formulation in the logarithmic strain space and the geometrically linear theory of plasticity makes this constitutive framework very transparent and attractive with regard to its numerical formulation the characteristic strain hardening of the model is derived from a polymer network model we consider the particularly simple eight chain model but also comment on the recently developed microsphere model the viscoplastic flow rule in the logarithmic strain space uses structures of the free volume flow theory which provides a highly predictive modeling capacity at the onset of viscoplastic flow the integration of this micromechanically motivated approach into a three dimensional computational model is a key concern of this work we outline details of the numerical implementation of this model including elements such as geometric pre and post transformations to from the logarithmic strain space a thermomechanical operator split algorithm consisting of an isothermal mechanical predictor followed by a heat conduction corrector and finally the consistent linearization of the local update algorithm for the dissipative variables as well as its relationship to the global tangent operator the performance of the proposed formulation is demonstrated by means of a spectrum of numerical examples which we compare with our experimental findings

on the dual variable of the logarithmic strain tensor the dual variable of the cauchy stress tensor and related issues the paper discusses relations related to the dual variables of the cauchy stress tensor and the logarithmic strain tensor we give a new proof that the logarithmic strain is dual to the cauchy stress tensor in the isotropic hyperelastic case corresponding relations are given in the case of multiplicative finite strain elasto viscoplasticity for the material eshelby like stress tensor and the rotated material stress tensor as well the general case of anisotropic response is discussed the dual variable of the logarithmic strain tensor is derived and some new expressions are given specifically it is proven that the skew symmetric part of the eshelby tensor is determined by the commutator of the logarithmic strain tensor and its conjugate variable the question of the existence of dual variables for the cauchy stress tensor and its material counterparts is rigorously answered where it is shown that in the general case a dual variable does not exist

hencky s logarithmic strain and dual stress strain and strain stress relations in isotropic finite hyperelasticity abstract it has been known that the kirchhoff stress tensor and hencky s logarithmic strain tensor h may be useful in formulations of isotropic finite elasticity and elastoplasticity in this work a straightforward proof is presented to demonstrate that for an isotropic hyperelastic solid the just mentioned stress strain pair and h are derivable from two dual scalar potentials with respect to each other these results establish a simple explicit dual formulation of isotropic finite hyperelasticity as a result they supply a complete solution to the problem of finding out the inverted stress strain relation for isotropic hyperelastic solids raised by j a blume int j non linear mech 27 1992 413 moreover an explicit form of such an inverted hyperelastic stress strain relation is derived in terms of the powers i and 2

the stress conjugate to logarithmic strain abstract a stress s is said to be conjugate to a strain measure e if the inner product s e is the power per unit volume the logarithmic strain in u with u the right stretch tensor has been considered an interesting strain measure because of the relationship of its material time derivative ln u with the stretching tensor d in a previous article int j solids structures 22 1019 1032 1986 a formula for ln u was obtained in direct notation for the cases where the principal stretches are repeated as well as for the case where they are all distinct here the formula for ln u and the definition of conjugate stress are used to derive an explicit properly invariant expression for the stress conjugate to the logarithmic strain

orbits of invariant subspaces of algebraic linear operators abstract let e be a vector space over a field k and a an algebraic k linear operator on e we describe the orbits under the action of the commutant of a and of the group of the invertible elements of the commutant of a on the lattice of a invariant subspaces

deformation analysis for finite elastic plastic strains in a lagrangean type description abstract a general concept is presented to analyse the deformation of structures undergoing arbitrarily large elastic and arbitrarily large plastic strains based on the multiplicative decomposition of the deformation gradient into elastic and plastic contributions the kinematics of two superposed finite non coaxial deformations are investigated lagrangean type elastic and plastic stretch tensors are introduced and multiplicative decompositions of the total stretch into these elastic and plastic stretches are derived it is shown that the result is independent of any decomposition of the total rotation into an elastic and a plastic rotation for the second superposed deformation the total lagrangean logarithmic hencky strain tensor with corresponding elastic and plastic logarithmic strains is defined if in a large deformation analysis the first deformation is updated such that the second deformation is constrained to be moderately large then the total logarithmic strain tensor of the second deformation can be additively decomposed into purely elastic and purely plastic parts this enables an appropriate formulation of constitutive equations for isotropic hyperelastic material behavior with associated flow rule and evolution laws for combined isotropic kinematic hardening work conjugate to the elastic logarithmic strain tensor is a back rotated kirchhoff stress tensor the rotational change of its reference configuration during the update is given explicitly finally the principle of virtual work with corresponding equilibrium equations and static and geometric boundary conditions is given the virtual work functional is transformed to deliver the consistent tangent stiffness matrix as basis for a finite element solution algorithm

formulation of implicit finite element methods for multiplicative finite deformation plasticity some constitutive and computational aspects of finite deformation plasticity are discussed attention is restricted to multiplicative theories of plasticity in which the deformation gradients are assumed to be decomposable into elastic and plastic terms it is shown by way of consistent linearization of momentum balance that geometric terms arise which are associated with the motion of the intermediate configuration and which in general render the tangent operator non symmetric even for associated plastic flow both explicit i e no equilibrium iteration and implicit finite element formulations are considered an assumed strain formulation is used to accommodate the near incompressibility associated with fully developed isochoric plastic flow as an example of explicit integration the rate tangent modulus method is reviewed in some detail an implicit scheme is derived for which the consistent tangents resulting in quadratic convergence of the equilibrium iterations can be written out in closed form for arbitrary material models all the geometrical terms associated with the motion of the intermediate configuration and the treatment of incompressibility are given explicitly examples of application to void growth and coalescence and to crack tip blunting are developed which illustrate the performance of the implicit method

exponential map algorithm for stress updates in anisotropic multiplicative elastoplasticity for single crystals this paper presents a new stress update algorithm for large strain rate independent single crystal plasticity the theoretical frame is the well established continuum slip theory based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts a distinct feature of the present formulation is the introduction and computational exploitation of a particularly simple hyperelastic stress response function based on a further multiplicative decomposition of the elastic deformation gradient into spherical and unimodular parts resulting in a very convenient representation of the schmid resolved shear stresses on the crystallographic slip systems in terms of a simple inner product of eulerian vectors the key contribution of this paper is an algorithmic formulation of the exponential map exp sl 3 sl 3 for updating the special linear group sl 3 of unimodular plastic deformation maps this update preserves exactly the plastic incompressibility condition of the anisotropic plasticity model under consideration the resulting fully implicit stress update algorithm treats the possibly redundant constraints of single crystal plasticity by means of an active set search it exploits intrinsically the simple representation of the schmid stresses by formulating the return algorithm and the associated consistent elastoplastic moduli in terms of eulerian vectors updates the performance of the proposed algorithm is demonstrated by means of a representative numerical example

a green naghdi approach to finite anisotropic rate independent and rate dependent thermo plasticity in logarithmic lagrangean strain entropy space abstract the paper presents a phenomenological model of rate independent and rate dependent thermo plasticity in the logarithmic lagrangean strain entropy space at finite strains the formulation and computational implementation are based on an additive decomposition of the strain measure into an elastic and plastic part as proposed by green and naghdi a rate independent and rate dependent constitutive model in the logarithmic lagrangean strain entropy space is developed for the modelling of isotropic elastic and anisotropic plastic material behaviour furthermore the notion of a plastic metric as proposed by miehe an isotropic hardening variable and the notion of a plastic entropy as proposed by simo and miehe dominate the internal variable description the model keeps the classical general return mapping scheme in the implicit integration algorithm of the internal variables of associative thermo plasticity the resulting coupled thermo mechanical problem is solved staggeredly via an isentropic phase for the deformation and an iso geometrical phase for the thermal field representative numerical simulations demonstrate the performance of the proposed model

generalized frenkel kontorova models we have studied two generalized frenkel kontorova fk models in one of them the interatomic potential is changed from simple harmonic to toda in the other the external potential is changed from sinusoidal to nonanalytic their critical behaviors are found to be markedly different in the toda case the local critical exponents are the same as those in the standard fk model however the global singularity spectrum and the generalized dimension depend on the anharmonicity parameter in the nonanalytic fk model the critical exponents are found to vary with the degree of inflection z for 2 z 3 a sequence of pinning and depinning transitions reflecting the recurrence of kolmogorov arnol d moser tori has also been observed

covariance in plasticity covariance is imposed to the second law of thermodynamics and consequences are shown for elastic perfectly plastic bodies in this setting pointwise balances of standard and configurational action

on theory and numerics of large viscoplastic deformation abstract a multiplicative theory and corresponding computations of finite elastic viscoplastic deformations based on unified constitutive equations are presented basic features of theory are 1 the inelastic part of the deformation gradient is understood as a material stretch type tensor no need arises for the notion of the intermediate configuration 2 in the isotropic case the use of an elastic logarithmic strain tensor is shown to lead to the identification that the elastic strains are given by the quantity c 1 p c with c p being an inelastic cauchy green type tensor 3 in spite of the fact that the logarithmic strain measure is used closed forms of the tangent operator within an implicit time integration scheme are given circumventing very involved elaborations when the spectral decomposition is used 4 evolution equations of the bodner and partom type are employed a general formalism is developed for the application of the evolution laws of the unified type within the theoretical framework the formalism can be used to generalize any unified evolution equations formulated for infinetismal strains to the range of finite strains 5 for the axisymmetric case in addition to the displacement based 4 node and 9 node finite elements an enhanced strain 4 node element is presented it is shown anyhow that in the highly nonlinear regime the enhanced strain formulation may exhibit numerical instabilities different numerical examples of finite strain deformations are presented

extensions of jordan bases for invariant subspaces of a matrix a characterization is obtained for the matrices a with the property that every some jordan basis of every a invariant subspace can be extended to a jordan basis of a these results are based on a criterion for a jordan basis of an invariant subspace to be extendable to a jordan basis of the whole space the criterion involves two concepts the constancy property and the depth property

on the relationship between the eulerian and lagrangian descriptions of finite rigid plasticity the motivation for the present paper is to clarify certain unresolved issues pertaining to the relation between the lagrangian or referential and eulerian or spatial strain space formulations of finite plasticity for conceptual simplicity attention is confined to rigid plastic materials it is shown first that for constitutive equations in which the hardening parameter is a scalar the lagrangian and eulerian descriptions are equivalent and that additionally the choice of objective stress rate is immaterial in the light of these developments the role of objective rates is further explored in connection with more general anisotropic hardening laws which contain a shift tensor a form of the constitutive equation for the rate of the shift tensor is motivated in which the choice of objective rate is arbitrary it is then demonstrated that the structure of the constitutive equations of the theory in both the eulerian and lagrangian descriptions is form invariant under arbitrary transformations of objective rate the approach taken here contrasts with that adopted in a number of recent papers in which preference is given to one particular objective rate or another

multisurface thermoplasticity for single crystals at large strains in terms of eulerian vector updates this paper presents a formulation of large strain rate independent multisurface thermoplasticity for single crystals and addresses aspects of its numerical implementation the theoretical frame is the well established continuum slip theory based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts a key feature of the present paper is the introduction and computational exploitation of a particularly simple hyperelastic stress response function based on a further multiplicative decomposition of the elastic deformation gradient into spherical and unimodular parts resulting in a very convenient representation of the schmid resolved shear stresses on the crystallographic slip systems in terms of a simple inner product of eulerian vectors this observation is intrinsically exploited on the numerical side by formulating a new fully implicit stress update algorithm and the associated consistent elastoplastic moduli in terms of these eulerian vectors the proposed return mapping algorithm treats the possibly redundant constraints of large strain multisurface plasticity for single crystals by means of an active set search furthermore it satisfies in an algorithmically exact way the plastic incompressibility condition in situations of multislip the performance of the proposed formulation is demonstrated for two representative numerical simulations of thermoplastic deformation processes in single crystals with isotropic taylor type hardening

young measure quasi static damage evolution an existence result for the quasi static evolution of incomplete damage in elastic materials is presented the absence of gradient terms in the damage variable causes a critical lack of compactness therefore the analysis is developed in the framework of young measures where a notion of solution is defined presenting some improvements with respect to previous contributions the main new feature in the proof of the existence result regards a delicate construction of the joint recovery sequence

picturing the lattice of invariant subspaces of a nilpotent complex matrix abstract let q be a nilpotent transformation acting on a finite dimensional complex vector space a method is given by which a diagrammatic representation of lat q the lattice of invariant subspaces of q can be obtained basically the method consists of adding to the hasse diagram of hyperlat q the finite lattice of hyperinvariant subspaces of q in a specified way some applications are given

scaling exponents at the transition by breaking of analyticity for incommensurate structures abstract a wide class of solid state models support incommensurate structures they are mostly given by either an analytic function in which case they are free to slide or a discontinuous function in which case there is a non zero minimum force required for depinning and a non zero minimum phonon frequency i propose that the boundary between these two types of state is given at least in part by the stable manifold of a fixed point of a renormalisation operator this permits one to perdict scaling laws for the depinning force phonon gap elasticity effective mass and other quantities

a consistent time fe method for large strain elasto plasto dynamics in the present paper energy consistent momentum conserving time stepping schemes for geometrically nonlinear multiplicative elasto plasto dynamics referred to as ecmc cg methods are developed in this context the entire discretisation procedure of the global equations of motion is based on galerkin methods in space and time whereby special emphasis is placed on the desired conservation properties related to the approximation of time integrals to guarantee energy consistency also for higher order finite elements in time a thermodynamically motivated enhanced stress tensor which defines a non standard quadrature rule is derived for elasto plastic material behaviour concerning the integration of the local evolution equations in time exemplarily a well established first order accurate exponential update is applied and adapted according to the global time stepping scheme based on linear finite elements in time the performance of the resulting scheme is demonstrated by means of several representative numerical examples whereby it is shown that global energy consistency is guaranteed exactly within the calculation accuracy by applying the proposed concepts

geometrically non linear anisotropic inelasticity based on fictitious configurations application to the coupling of continuum damage and multiplicative elasto plasticity the objective of this contribution is the formulation and algorithmic treatment of a phenomenological framework to capture anisotropic geometrically non linear inelasticity in addition to the intermediate configuration of multiplicative elasto plasticity we further introduce two microscopic configurations of lagrangian and eulerian type which characterize the so called fictitious undamaged material this kinematical framework enables us to apply two well established postulates based on standard terminology in non linear continuum mechanics concerning the free energy function the postulate of strain energy equivalence is adopted and in view of the plastic dissipation potential the concept of effective stress is a natural outcome of the underlying kinematical assumptions finally we focus on the integration technique for the class of obtained evolution equations and present numerical examples for a prototype model to underline the applicability of the proposed framework copyright 2003 john wiley sons ltd

characteristic and hyperinvariant subspaces over the field gf 2 let f be an endomorphism of a vector space v over a field k an f invariant subspace x v is called hyperinvariant respectively characteristic if x is invariant under all endomorphisms respectively automorphisms that commute with f if k 2 then all characteristic subspaces are hyperinvariant if k 2 then there are endomorphisms f with invariant subspaces that are characteristic but not hyperinvariant in this paper we give a new proof of a theorem of shoda which provides a necessary and sufficient condition for the existence of characteristic non hyperinvariant subspaces

anisotropic additive plasticity in the logarithmic strain space modular kinematic formulation and implementation based on incremental minimization principles for standard materials the paper presents a modular formulation and computational implementation of a class of anisotropic plasticity models at finite strains based on incremental minimization principles the modular kinematic setting consists of a constitutive model in the logarithmic strain space that is framed by a purely geometric pre and postprocessing on the theoretical side the point of departure is an a priori six dimensional approach to finite plasticity based on the notion of a plastic metric in a first step a geometric preprocessor defines a total and a plastic logarithmic strain measure obtained from the current and the plastic metrics respectively in a second step these strains enter in an additive format a constitutive model of anisotropic plasticity that may have a structure identical to the geometrically linear theory the model defines the stresses and consistent tangents work conjugate to the logarithmic strain measure in a third step these objects of the logarithmic space are then mapped back to nominal lagrangian or eulerian objects by a geometric postprocessor this geometric three step approach defines a broad class of anisotropic models of finite plasticity directly related to counterparts of the geometrically linear theory it is specified to a model problem of anisotropic metal plasticity on the computational side we develop an incremental variational formulation of the above outlined constitutive structure where a quasi hyperelastic stress potential is obtained from a local constitutive minimization problem with respect to the internal variables it is shown that this minimization problem is exclusively restricted to the logarithmic strain space in a structure identical to the small strain theory the minimization problem determines the internal state of the material for finite increments of time we develop a discrete formulation in terms of just one scalar parameter for the amount of incremental flow the existence of the incremental stress potential provides a natural basis for the definition of the geometric postprocessor based on function evaluations furthermore the global initial boundary value problem of the elastic plastic solid appears in the incremental setting as an energy minimization problem numerical examples show that the results obtained are surprisingly close to those obtained by a reference framework of multiplicative plasticity