stabilized finite element formulation for elastic plastic finite deformations abstract this paper presents a stabilized finite element formulation for nearly incompressible finite deformations in hyperelastic plastic solids such as metals an updated lagrangian finite element formulation is developed where mesh dependent terms are added to enhance the stability of the mixed finite element formulation this formulation circumvents the restriction on the displacement and pressure fields due to the babuska brezzi condition and provides freedom in choosing interpolation functions in the incompressible or nearly incompressible limit typical in metal forming applications moreover it facilitates the use of low order simplex elements i e p1 p1 reducing the degrees of freedom required for the solution in the incompressible limit when stable elements are necessary linearization of the weak form is derived for implementation into a finite element code numerical experiments with p1 p1 elements show that the method is effective in incompressible conditions and can be advantageous in metal forming analysis

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

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

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

on the equivalence between the multiplicative hyper elasto plasticity and the additive hypo elasto plasticity based on the modified kinetic logarithmic stress rate abstract in two theorems presented herein we prove and subsequently demonstrate in several numerical examples involving homogeneous deformation that for isotropic materials hyper elasto plasticity models based on the multiplicative decomposition of the deformation gradient coincide with an additive hypo elasto plasticity model see section 3 2 that employs the spin tensor based on the modified kinetic logarithmic rate in the absence of strain induced anisotropy characterized by kinematic hardening herein this objective stress rate coincides with the kinetic logarithmic rate recently developed by jiao and fish 2017 we also show that other well known additive decomposition models such as those based on the jaumann and logarithmic rates may considerably deviate from the multiplicative model

finite deformation plasticity in principal axes from a manifold to the euclidean setting abstract this contribution presents a link between early developments in finite deformation plasticity where the notion of a covariant formulation is introduced and employed and more recent developments where rediscovery of a fundamental work of hill on the method of principal axes led to a very efficient implementation scheme more precisely we demonstrate how to develop a covariant theory of finite deformation plasticity in an invariant form by making use of the elastic principal stretches we also show how to implement principal axis formulation in the framework of manifold to carry out all the necessary manipulations by exploiting the lie derivative formalism and eventually to simplify the final result to the euclidean setting much of our work on numerical implementation reflects the fruitful cross fertilization of ideas with those from theoretical formulation in particular we show how the operator split method which is typically used to simplify the plastic flow computation can also be used to reduce the computational cost related to the special finite element interpolation schemes based on incompatible modes the latter proves to be an indispensable ingredient for accommodating the near incompressibility constraint arising in the finite deformation deviatoric plasticity an important advantage of the proposed formulation as opposed to alternative remedies e g b bar method is that the basic structure of the governing equations need not be modified

micropolar hyper elastoplasticity constitutive model consistent linearization and simulation of 3d scale effects summary a computational model for micropolar hyperelastic based finite elastoplasticity that incorporates isotropic hardening is developed the basic concepts of the non linear micropolar kinematic framework are reviewed and a thermodynamically consistent constitutive model that features neo hooke type elasticity and generalized von mises plasticity is described the integration of the constitutive initial value problem is carried out by means of an elastic predictor plastic corrector algorithm which retains plastic incompressibility the solution procedure is developed carefully and described in detail the consistent material tangent is derived the micropolar constitutive model is implemented in an implicit finite element framework the numerical example of a notched cylindrical bar subjected to large axial displacements and large twist angles is presented the results of the finite element simulations demonstrate i that the methodology is capable of capturing the size effect in three dimensional elastoplastic solids in the finite strain regime ii that the formulation possesses a regularizing effect in the presence of strain localization and iii that asymptotically quadratic convergence rates of the newton raphson procedure are achieved throughout this paper effort is made to present the developments as a direct extension of standard finite deformation computational plasticity copyright 2012 john wiley sons ltd

a hyperelastic based large strain elasto plastic constitutive formulation with combined isotropic kinematic hardening using the logarithmic stress and strain measures summary this paper addresses the formulation of a set of constitutive equations for finite deformation metal plasticity the combined isotropic kinematic hardening model of the infinitesimal theory of plasticity is extended to the large strain range on the basis of three main assumptions i the formulation is hyperelastic based ii the stress strain law preserves the elastic constants of the infinitesimal theory but is written in terms of the hencky strain tensor and its elastic work conjugate stress tensor and iii the multiplicative decomposition of the deformation gradient is adopted since no stress rates are present the formulation is of course numerically objective in the time integration it is shown that the model gives adequate physical behaviour and comparison is made with an equivalent constitutive model based on the additive decomposition of the strain tensor

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

the computation of the exponential and logarithmic mappings and their first and second linearizations we describe two simple methods for the evaluation of the exponential and logarithmic mappings and their first and second linearizations based on the taylor expansion and the spectral representation we also provide guidelines for switching between those representations on the basis of the size of the argument the first and second linearizations of the exponential and logarithmic mappings provided here are based directly on the exponential formula for the solutions of systems of linear ordinary differential equations this representation does not require the use of perturbation formulae for eigenvalues and eigenvectors our approach leads to workable and straightforward expressions for the first and second linearizations of the exponential and logarithmic mappings regardless of degeneracies in the spectral decomposition of the argument

the effective stress function algorithm for thermo elasto plasticity and creep an algorithm for stable and accurate computations of stresses in finite element thermo elastic plastic and creep analysis of metals is presented the effective stress function algorithm solves the governing equations of the inelastic constitutive behaviour by calculating the zero of the appropriate effective stress function a functional relationship which involves as unknown only the effective stress the derivation of the effective stress function for thermo elasto plasticity conditions including creep for 2 d and 3 d analysis is presented and the algorithmic steps of the stress solution are discussed for use in the stiffness matrix a tangent material stress strain relationship is evaluated consistent with the effective stress function algorithm the solution of some demonstrative problems shows the effectiveness of the solution procedure

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

a model of finite strain viscoplasticity based on unified constitutive equations theoretical and computational considerations with applications to shells abstract a model of multiplicative finite strain viscoplasticity is developed hereby the elastic internal potential is assumed to depend quadratically on the elastic strain measure ce by means of corresponding invariants hence possible extension of the model to take anisotropy into account is straightforward the evolution equation of the unified type due to bodner and partom asme j appl mech 42 1975 385 are modified so as to fit into the framework adopted the numerical treatment of the problem is fully developed specifically the algorithmic aspects of the resulting non additive structure are intensively discussed hereby the treatment of the exponential map of a non symmetric argument is of a central importance two consistent methods are developed various applications to shell problems are considered hereby a shell theory with seven degrees of freedom together with a 4 node enhanced strain finite element formulation are used a central feature of the shell formulation is its eligibility to the application of a three dimensional constitutive law

an extension of 3 d procedure to large strain analysis of shells abstract a numerical stress integration procedure for general 3 d large strain problems in inelasticity based on the total formulation and the governing parameter method gpm is extended to shell analysis the multiplicative decomposition of the deformation gradient is adopted with the evaluation of the deformation gradient practically in the same way as in a general 3 d material deformation the calculated trial elastic logarithmic strains are transformed to the local shell cartesian coordinate system and the stress integration is performed according to the gpm developed for small strain conditions the consistent tangent matrix is calculated as in case of small strain deformation and then transformed to the global coordinate system a specific step in the proposed procedure is the updating of the left elastic green lagrangian deformation tensor namely after the stresses are computed the principal elastic strains and the principal vectors corresponding to the stresses at the end of time step are determined in this way the shell conditions are taken into account appropriately for the next step some details are given for the stress integration in case of thermoplastic and creep material model numerical examples include bulging of plate plastic thermoplastic and creep models for metal and necking of a thin sheet comparison of solutions with those available in the literature and with solutions using other type of finite elements demonstrates applicability efficiency and accuracy of the proposed procedure

on the performance of two tangent operators for finite element analysis of large deformation inelastic problems an important step in the solution of non linear deformation problems using a newton raphson type of iterative scheme is the calculation of a tangent operator the so called jacobian by linearizing the involved field equations in this paper full linearization of the virtual work equation is performed in an updated lagrangian framework together with a calculation of the consistent linearized material moduli to update the material state a material frame indifferent two parameter integration scheme introduced earlier by the authors is used in general the reference configuration is updated after each iteration to coincide instantaneously with the present guess of the unknown equilibrium configuration another approach is to use the previous equilibrium state at the beginning of a time step as the reference configuration until the new equilibrium configuration at the end of the time step is found the present paper explores the performance of two different jacobians based on the above two approaches with emphasis on their accuracy and convergence characteristics when large incremental steps are used finally some details of their finite element implementation are given and results for several numerical tests including upset forging and extrusion of an axisymmetric billet are presented and discussed

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

a framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition part ii computational aspects computational aspects of the formulation of elastoplasticity proposed in part i of this work employing a multiplicative decomposition and based on the principle of maximum plastic dissipation are examined in detail in particular the implementation of the proposed hyperelastic j2 flow theory is shown to reduce to a trivial modification of the classical radial return algorithm which is amenable to exact linearization this results in a closed form expression for the consistent elastoplastic tangent moduli the algorithmic treatment of the general case is considered subsequently it is emphasized that objective rates and incrementally objective algorithms play no role in the present approach a number of numerical experiments are presented that illustrate the excellent performance of the proposed formulation

a total lagrangian framework for simulation of powder compaction process based on a smooth three surface cap model and a mesh free method this paper presents a detailed framework for simulation of cold powder compaction process this framework consists of the following main assumptions the total lagrangian description is employed the powder is assumed to be isotropic and it is modeled by a complete smooth three surface cap model the constitutive formulation is based on the multiplicative decomposition of the deformation gradient and on stress strain pair formed by the hencky logarithmic strain and the rotated kirchhoff stress tensor the elastic constitutive relationship considers that some parameters are dependent upon the relative density of the powder the contact formulation is based on the signorini condition and the friction is modeled by using a regularized coulomb model and the spatial discretization is made by the element free galerkin method where the essential boundary conditions are enforced via an augmented lagrangian method details concerning the discretization and the linearization of the weak form are presented and a master algorithm is proposed some key examples already investigated by other authors but with somewhat different approaches are revisited in this paper in order to investigate the adequacy of the proposed model and attest the performance of the proposed numerical scheme copyright 2008 john wiley sons ltd

maximum margin bayesian network classifiers we present a maximum margin parameter learning algorithm for bayesian network classifiers using a conjugate gradient cg method for optimization in contrast to previous approaches we maintain the normalization constraints on the parameters of the bayesian network during optimization i e the probabilistic interpretation of the model is not lost this enables us to handle missing features in discriminatively optimized bayesian networks in experiments we compare the classification performance of maximum margin parameter learning to conditional likelihood and maximum likelihood learning approaches discriminative parameter learning significantly outperforms generative maximum likelihood estimation for naive bayes and tree augmented naive bayes structures on all considered data sets furthermore maximizing the margin dominates the conditional likelihood approach in terms of classification performance in most cases we provide results for a recently proposed maximum margin optimization approach based on convex relaxation 1 while the classification results are highly similar our cg based optimization is computationally up to orders of magnitude faster margin optimized bayesian network classifiers achieve classification performance comparable to support vector machines svms using fewer parameters moreover we show that unanticipated missing feature values during classification can be easily processed by discriminatively optimized bayesian network classifiers a case where discriminative classifiers usually require mechanisms to complete unknown feature values in the data first

l functions with large analytic rank and abelian varieties with large algebraic rank over function fields the goal of this paper is to explain how a simple but apparently new fact of linear algebra together with the cohomological interpretation of l functions allows one to produce many examples of l functions over function fields vanishing to high order at the center point of their functional equation conjectures of birch and swinnerton dyer bloch and beilinson relate the orders of vanishing of some of these l functions to mordell weil groups and other groups of algebraic cycles for certain abelian varieties of high analytic rank we are also able to prove the conjecture of birch and swinnerton dyer thus establishing the existence of large mordell weil groups in those cases in the rest of this section we state the main results of the paper

finite strain logarithmic hyperelasto plasticity with softening a strongly non local implicit gradient framework this paper addresses the extension of a eulerian logarithmic finite strain hyperelasto plasticity model in order to incorporate an isotropic plastic damage variable that leads to softening and failure of the plastic material it is shown that a logarithmic elasto plastic model with a strongly non local degrading yield stress exactly preserves the structure of its infinitesimal counterpart the strongly non local nature of the model makes it an attractive framework for the numerical solution of softening plasticity problems consistent constitutive tangent operators are derived for the particular case of hyperelasto j2 plasticity which are exactly equal to the corresponding infinitesimal tangent operators the finite element implementation along with the geometrically nonlinear contributions and the incremental solution strategy is outlined a benchmark example is solved illustrating the main differences between the purely elasto plastic case and the case with plastic damage finally the main model characteristics and its practical use are emphasized

a field boundary element formulation for material nonlinear problems at finite strains abstract a boundary element formulation for geometrical nonlinear problems is presented which is applicable for arbitrary constitutive equations based on the concept of hyperelastic response relative to an intermediate configuration this includes purely hyperelastic problems at large elastic strains in contrast to other formulations the total lagrange framework employed in this work significantly increases the numerical efficiency as the system matrices remain constant during the incremental solution and have to be computed only once a nonlinear set of equations with an identical structure for both boundary and internal unknowns is derived the basic unknowns are displacement gradients which are calculated via integral equations and not by differentiation of the shape functions the formulation can be consistently linearised to allow for the implementation of efficient iteration schemes using gradients e g the newton raphson scheme

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

objectivity of incremental constitutive relations over finite time steps in computational finite deformation analyses abstract computational techniques which preserve the objectivity of incremental constitutive relations for finite elastic or inelastic materials for finite time steps during which the material elements may undergo finite rotations are presented these techniques are useful in finite deformation finite rotations and finite strain computational analysis of two as well as three dimensional solids and structures

volume preserving energy momentum schemes for isochoric multiplicative plasticity abstract this paper presents a new energy dissipative momentum conserving algorithm for multiplicative finite strain plasticity f f e f p that also preserves exactly the plastic volume for isochoric plastic models the new algorithm exhibits exactly the conservation laws of linear and angular momentum of the underlying physical problem as well as its energy evolution a strictly positive energy dissipation in fact the exact energy dissipation is obtained by design during plastic steps while enforcing the plastic consistency i e the yield condition on the final stress appearing in the equations of motion exact energy conservation is attained in particular during elastic steps the aforementioned preservation of the plastic volume is obtained by a new treatment of the geometric structure behind the considered multiplicative models of finite strain plasticity namely we present a new approximation of the reference and elastic metrics whose contractions with the incremental total and elastic strains lead exactly to the increment of the total and elastic natural volumetric strains respectively the elastic metric is defined in the intermediate configuration defined itself by the proper discrete approximation in time of the plastic deformation gradient f p the new algorithm extends to the plastic range existing energy momentum conserving schemes for nonlinear elastic problems but incorporating a new modified elastic stress formula consistent with this new geometric setting the inherited conservation laws of momenta and especially the non negative character of the energy dissipation leads to an improved performance over existing more classical schemes showing numerical instabilities in the considered highly nonlinear geometric setting of large deformations and strains several numerical simulations are presented illustrating these properties

the special linear update an application of differential manifold theory to the update of isochoric plasticity flow rules the evolution of plastic deformations in metals governed by incompressible flow rules has been traditionally solved using the exponential mapping however the accurate calculation of the exponential mapping and its tangents may result in computationally demanding schemes in some cases while common low order approximations may lead to poor behavior of the constitutive update because of violation of the incompressibility condition here we introduce the special linear sl update for isochoric plasticity a flow rule integration scheme based on differential manifolds concepts the proposed update exactly enforces the plastic incompressibility condition while being first order accurate and consistent with the flow rule thus bearing all the desirable properties of the now standard exponential mapping update in contrast to the exponential mapping update we demonstrate that the sl update can drastically reduce the computing time reaching one order of magnitude speed ups in the calculation of the update tangents we demonstrate the applicability of the update by way of simulation of single crystal plasticity uniaxial loading tests we anticipate that the sl update will open the way to efficient constitutive updates for the solution of complex multiscale material models thus making it a very promising tool for large scale simulations

a finite strain finite element model for the pseudoelastic behavior of shape memory alloys this paper presents a finite deformation finite element model for the pseudoelastic response of shape memory alloys under stress loading unloading conditions at constant temperature a local multiplicative decomposition of the deformation gradient into volumetricelastic and isochori inelastic components is assumed where the inelastic component is associated with phase transformation and defines an additional intermediate configuration strain measure defined on the intermediate configuration is the hencky strain the constitutive equations are cast in the framework of generalized plasticity and the two way phase transformation is modeled via a kuhn tucker type transformation criteria for the rate independent shape memory behavior these equations are able to predict the stress induced phase transformations during complete loading unloading cycles and can also predict the correct material behavior when incomplete transformations take place the resulting nonlinear system of equations is solved for updated stress variables via the radial return algorithm embedded in the newton raphson iteration scheme numerical results are presented to show the performance of the model

on a numerical implementation of a formulation of anisotropic continuum elastoplasticity at finite strains in a recent theoretical study see c sansour i karsaj j soric a formulation of anisotropic continuum elastoplasticity at finite strains part i modelling international journal of plasticity 22 2006 2346 2365 a constitutive model for anisotropic elastoplasticity at finite strains has been developed the model is based on the multiplicative decomposition of the deformation gradient the stored energy function as well as the flow rule has been considered as quadratic functions of their arguments in both cases the list of arguments is extended to include structural tensors which describe the anisotropy of the material response at hand non linear isotropic hardening is considered as well in this paper the integration of the constitutive law is presented the associative flow rule is integrated using the exponential map which preserves the plastic incompressibility condition the numerical treatment of the problem is fully developed and expressions related to the local iteration and the consistent tangent operator are considered in detail it is shown that while the consistent linearisation of the model is quite complicated it still can be achieved if various intriguing implicit dependencies are identified and correctly dealt with various numerical examples of three dimensional deformations of whole structural components are presented the examples clearly illustrate the influence of anisotropy on finite elastoplastic deformations

on the robustness and efficiency of integration algorithms for a 3d finite strain phenomenological sma constitutive model summary most devices based on shape memory alloys experience large rotations and moderate or finite strains this motivates the development of finite strain constitutive models together with the appropriate computational counterparts to this end in the present paper a three dimensional finite strain phenomenological constitutive model is investigated and a robust and efficient integration algorithm is proposed properly defining the variables extensively used regularization schemes are avoided and a nucleation completion criterion is defined moreover introducing a logarithmic mapping a new form of time discrete equations is proposed the solution algorithm as well as a suitable initial guess for the resultant nonlinear equations are also deeply discussed extensive numerical tests are performed to show robustness as well as efficiency of the proposed integration algorithm implementation of the integration algorithm within a user defined subroutine umat in the commercial nonlinear finite element software abaqus standard makes also possible the solution of a variety of boundary value problems the obtained results show the efficiency and robustness of the proposed approach and confirm the improved efficiency in terms of solution cpu time when a nucleation completion criterion is used instead of regularization schemes as well as when a logarithmic mapping is used for the time discrete evolution equation instead of an exponential mapping copyright 2010 john wiley sons ltd

the variational formulation of viscoplastic constitutive updates we present a class of constitutive updates for general viscoplastic solids including such aspects of material behavior as finite elastic and plastic deformations non newtonian viscosity rate sensitivity and arbitrary flow and hardening rules the distinguishing characteristic of the proposed constitutive updates is that by construction the corresponding incremental stress strain relations derive from a pseudo elastic strain energy density this in turn confers the incremental boundary value problem a variational structure in particular the incremental deformation mapping follows from a minimum principle this minimum principle may conveniently be taken as a basis for error estimation and mesh adaption the accuracy and robustness of the variational constitutive updates is demonstrated with the aid of convergence tests involving the finitely deforming mises solid and ductile single crystals the ability of the updates to resolve the complex patterns of slip activity which arise in the latter application is particularly noteworthy

the logarithmic strain space description abstract the ingredients of a plasticity description in the logarithmic strain space with respect to the reference configuration are discussed within the framework of the finite deformation theory especially the features of logarithmic strain and the transformations between its time derivative the rate of deformation tensor and the work conjugate stresses the logarithmic strain space description is then illustrated using three analytical examples of homogeneous finite deformation fields

a new computational model for tresca plasticity at finite strains with an optimal parametrization in the principal space abstract a new computational model for the rate independent elasto plastic solids characterized by yield surfaces containing singularities and general nonlinear isotropic hardening is presented within the context of fully implicit return mapping algorithms a numerical scheme for integration of the constitutive equations is formulated in the space of principal stresses as a direct consequence of the principal stress approach the representation of a yield surface is cast in terms of optimal parameterization which for the tresca yield criterion takes a simple linear form the associated return mapping equations then reduce to a remarkably simple format in addition due to assumed isotropy of the models the associated algorithmic incremental constitutive functionals can be identified as particular members of a class of isotropic tensor functions of one tensor in which the function eigenvalues are expressed in terms of the eigenvalues of the argument this observation leads to a simple closed form derivation of the consistent tangent moduli associated with the described integration algorithms the extension of the present model to finite strains is carried out following standard multiplicative plasticity described in terms of logarithmic stretches and exponential approximation to the flow rule the efficiency and robustness of the computational model are illustrated on a range of numerical examples

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