computational aspects of incrementally objective algorithms for large deformation plasticity a methodology for computationally efficient formulation of the tangent stiffness matrix consistent with incrementally objective algorithms for integrating finite deformation kinematics and with closest point projection algorithms for integrating material response is developed in the context of finite deformation plasticity numerical experiments illustrate an excellent performance of the proposed formulation in comparison with other algorithms copyright 1999 john wiley sons ltd

a return mapping algorithm for isotropic elastoplasticity a return mapping algorithm is presented for the numerical time integration of the constitutive equations for elastoplasticity with isotropic yield surfaces constructed from all three invariants of the stress tensor based on the first order backward euler difference formula bdf the governing equations for the stresses are solved in the space of the invariants and the discretized persistence parameter the stresses are recovered afterwards the solution concept is applied to a pressure independent yield function expressed in terms of the second and third invariant of the stress tensor the numerical performance of the method is demonstrated with two examples

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

an implicit consistent algorithm for the integration of thermoviscoplastic constitutive equations in adiabatic conditions and finite deformations abstract the so called viscoplastic consistency model proposed by wang sluys and de borst is extended here to the integration of a thermoviscoplastic constitutive equation for j2 plasticity and adiabatic conditions the consistency condition in this case includes not only strain rate but also the effect of temperature on the yield function using the backward euler integration scheme to integrate the constitutive equations an implicit algorithm is proposed leading to generalized expressions of the classical return mapping algorithm for j2 plasticity both for the iterative calculation of the plastic multiplier increment and for the consistent tangent operator when strain rate and temperature are considered also as state variables of the hardening equation the model was implemented in a commercial finite element code and its performance is demonstrated with the numerical simulation of four taylor impact tests

design sensitivity analysis for rate independent elastoplasticity abstract a new incremental direct differentiation method for design sensitivity analysis of structures with rate independent elastoplastic behavior is presented we formulate analytical sensitivity expressions that are consistent with numerical algorithms for elastoplasticity that use implicit methods to integrate the constitutive equations and return mappings to enforce the consistency conditions the sensitivity expressions can be evaluated with only a modest increase in computational expense beyond the cost of simulation combined with the inherent advantages of implicit integration strategies this represents a significant improvement over previous sensitivity formulations for history dependent materials first order sensitivity expressions involving the complete set of design variables including shape design variables are derived for a generic response functional the reduced form of the consistent tangent stiffness matrix obtained at the end of each time or load step in the finite element procedure is used to update the response sensitivities for that time step no iterations are needed in the sensitivity computations a numerical example demonstrates the accuracy and efficiency of the new sensitivity analysis method for an elastoplastic analysis problem explicit sensitivities from the new method are confirmed by finite difference estimates

analysis of the anisotropic viscoplastic damage response of composite laminates continuum basis and computational algorithms the mathematical structure underlying the rate equations of a recently developed constitutive model for the coupled viscoplastic damage response of anisotropic composites is critically examined in this regard a number of tensor projection operators have been identified and their properties were exploited to enable the development of a general computational framework for their numerical implementation using the euler fully implicit integration method in particular this facilitated i the derivation of explicit expressions of the consistent material tangent stiffnesses that are valid for both three dimensional as well as subspace e g plane stress formulations ii the implications of the symmetry or unsymmetry properties of these tangent operators from a thermodynamic standpoint and iii the development of an effective time step control strategy to ensure accuracy and convergence of the solution in addition the special limiting case of inviscid elastoplasticity is treated the results of several numerical simulations are given to demonstrate the effectiveness of the schemes developed

a detailed description of the gurson tvergaard needleman model within a mixed velocity pressure finite element formulation summary in an effort to implement gurson type models into a mixed velocity pressure finite element formulation with the mini element p1 p1 the algorithm proposed by aravas ijnme 1987 to integrate the pressure dependent plasticity as well as the formulations of consistent tangent moduli have been analyzed this work firstly reviews and clarifies the mathematical basis of the formulations used by aravas ijnme 1987 and demonstrates the equality of the tangent moduli formulations proposed by govindarajan and aravas cnme 1995 and zhang cmame 1995 which are widely used in the literature a unified formulation to calculate the tangent moduli is proven and its accuracy is also investigated by the finite difference method the implementation of the gurson tvergaard needleman model is then detailed for the mixed velocity pressure finite element formulation which employs the mini element p1 p1 due to the particularity of this element one needs to calculate two tangent moduli instead of one the formulas for calculating the linear tangent modulus and the bubble tangent modulus are then detailed finally comparison tests are carried out with abaqus dassault system simulia corp providence ri usa in order to validate the present implementation for both homogeneous and heterogeneous deformations copyright 2013 john wiley sons ltd

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

a new model of generalized plasticity and its numerical implementation abstract a previously proposed simple model of generalized plasticity is modified so that it allows behavior that is asymptotically perfectly plastic or strain softening initially presented in uniaxial form the model is then generalized to multiaxial stress numerical implementation is developed first through direct integration of the rate equations including special cases in which the solution may be obtained analytically and then by means of a return map algorithm which is particularly well suited to the finite element method consistent algorithmic tangent moduli are derived as well numerical examples are presented to illustrate the various approaches

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

singular monge ampere foliations this paper generalizes results of lempert and szoke on the structure of the singular set of a solution of the homogeneous monge ampere equation on a stein manifold their a priori assumption that the singular set has maximum dimension is shown to be a consequence of regularity of the solution in addition their requirement that the square of the solution be c 3 everywhere is replaced by a smoothness condition on the blowup of the singular set under these conditions the singular set is shown to inherit a finsler metric which in the real analytic case uniquely determines the solution of the monge ampere equation these results are proved using techniques from contact geometry

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

efficient and modular algorithms in modeling finite inelastic deformations objective integration parameter identification and sub stepping techniques this paper presents a general algorithmic formulation for constitutive equations describing inelastic material deformation the algorithmic representation focuses on the generality and modularity which is a key aspect within the development phase of constitutive equations it is shown explicitly how to solve the incremental constitutive equations by use of objective algorithms and an implicit integration scheme applying numerical as well as analytical derivatives although it is shown that using numerical gradients is significantly slower their application is easier especially in the development phase it is also demonstrated that having the constitutive equations modeled in the general context introduced the issue of parameter identification can be tackled by the same implementation using a driver algorithm besides parameter identification the general structure is also applied to two different fe simulations first the objectivity of different integration methods will be presented considering a simple shear loading superposed by a rigid rotation using a strain rate independent material model as example in the second example it is shown for a strain rate dependent material model how the simulation of the wire drawing process can be accelerated crucially by using sub stepping techniques

a nonsmooth newton method for elastoplastic problems in this work we reformulate the incremental small strain j2 plasticity problem with linear kinematic and nonlinear isotropic hardening as a set of unconstrained nonsmooth equations the reformul

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

on the interplay between strain rate and strain rate sensitivity on flow localization in the dynamic expansion of ductile rings abstract in this work a stability analysis on flow localization in the dynamic expansion of ductile rings is conducted within a 1 d theoretical framework the boundary value problem of a radially expanding thin ring is posed based on a previous work the equations governing the stretching process of the expanding ring are derived and solved using a linear perturbation method then three different perfectly plastic material constitutive behaviours are analysed the rate independent material the rate dependent material showing constant logarithmic rate sensitivity and the rate dependent material showing non constant and non monotonic logarithmic rate sensitivity the latter allows to investigate the interaction between inertia and strain rate sensitivity on necking formation the main feature of this work is rationally demonstrate that under certain loading conditions and material behaviours 1 decreasing rate sensitivity may not lead to more unstable material 2 increasing loading rate may not lead to more stable material this finding reveals that the relation between rate sensitivity and loading rate controls the unstable flow growth additionally a finite element model of the ring expansion problem is built in abaqus explicit the stability analysis properly reflects the results obtained from the numerical simulations both procedures perturbation analysis and numerical simulations allow for emphasizing the interplay between rate sensitivity and inertia on strain localization

volume estimates for kahler einstein metrics and rigidity of complex structures this paper extends our earlier results to higher dimensions using a different approach based on the rigidity of complex structures on certain domains we prove a low energy result in all dimensions in the sense that if normalized energy in a large ball is small enough then the normalized energy in any interior ball must also be small

a displacement like finite element model for j2 elastoplasticity variational formulation and finite step solution abstract the displacement like finite element formulation for finite step j2 elastoplasticity is revisited in this paper the classical computational strategy according to which plastic loading is tested at the gauss points of each element and an independent return mapping algorithm is performed for given incremental displacements is consistently derived from a suitably discretized version of a min max variational principle the sequence of solution phases to be performed within each load step adopting a full newton s method is illustrated in detail and the importance of a correct update of the plastic strains is emphasized it is further shown that in order to increase the rate of convergence and the stability properties of the newton s method the consistent elastoplastic tangent operator must be exploited even at the first iteration of each load step subsequent to the first yielding of the structural model this is in contrast with the traditional implementation according to which the elastic operator is used at the first iteration of each load step the effectiveness of the present approach is shown by a set of numerical examples referred to plane strain problems

implementation of cyclic plasticity models based on a general form of kinematic hardening this paper deals with implementation of cyclic plastic constitutive models in which a general form of strain hardening and dynamic recovery is employed to represent the multilinear as well as non linear evolution of back stress first in order to incorporate such a general form of kinematic hardening in finite element methods successive substitution and its convergence are discussed for implicitly integrating stress moreover a new expression of consistent tangent modulus is derived by introducing a set of fourth rank constitutive parameters into discretized kinematic hardening then the constitutive parameters introduced are specified in three cases of the general form of kinematic hardening the three cases have distinct capabilities of simulating ratcheting and cyclic stress relaxation numerical examples are given to verify the convergence in successive substitution and the new expression of consistent tangent stiffness error maps for implicitly integrating stress under non proportional as well as proportional loading are also given to show that the multilinear case of the general form provides high accuracy even if strain increment is very large copyright 2002 john wiley sons ltd

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

implicit objective integration for sensitivity analysis in non linear solid mechanics incrementally objective integration schemes are proposed for the accurate and efficient determination of design sensitivity coefficients dscs for solid mechanics problems with both material and geometrical non linearities the derivation of these schemes are based on the direct differentiation of objective schemes that are used in stress analysis for problems of this class two widely used objective stress rates the jaumann rate and the green naghdi rate are considered here within the same setting with only minor changes of the integration scheme numerical results are presented for a simple shear problem with different material constitutive laws including a hypoelastic model and a unified isotropic viscoplastic model for these two objective rates the numerical results are compared with analytical solutions or direct integration solutions the close agreement among these solutions demonstrates the accuracy and efficiency of the proposed scheme

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

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

regularity of einstein manifolds and the codimension 4 conjecture in this paper we are concerned with the regularity of noncollapsed riemannian manifolds m n g with bounded ricci curvature as well as their gromov hausdor limit spaces m n dj dgh x d where dj denotes the riemannian distance our main result is a solution to the codimension 4 conjecture namely thatx is smooth away from a closed subset of codimension 4 we combine this result with the ideas of quantitative stratication to prove a priori l q estimates on the full curvaturejrmj for all q v 0 and diam m d contains at most a nite number of dieomorphism classes a local version is used to show that noncollapsed 4 manifolds with bounded ricci curvature have a priori l 2 riemannian curvature estimates

numerical computation of algorithmic consistent tangent moduli in large strain computational inelasticity abstract an algorithm for the numerical computation of so called algorithmic or consistent tangent moduli in finite inelasticity is presented these moduli determine the sensitivity of algorithmic expressions for stresses with respect to the change in total deformation they serve as iteration operators by application of newton type solvers for the iterative solution of non linear initial boundary value problems in finite inelasticity the underlying concept of the numerical computation is a perturbation technique based on a forward difference approximation which reduces the computation of the tangent moduli to a multiple stress computation the algorithmic procedure is material independent and surprisingly simple it is outlined for a lagrangian as well as an eulerian geometric setting and applied to model problems of finite elasticity and finite elastoplasticity

viscoplasticity for instabilities due to strain softening and strain rate softening three viscoplastic approaches are examined in this paper first the overstress viscoplastic models i e the perzyna model and the duvaut lions model are outlined next a consistency viscoplastic approach is presented in the consistency model a rate dependent yield surface is employed while the standard kuhn tucker conditions for loading and unloading remain valid for this reason the yield surface can expand and shrink not only by softening or hardening e ects but also by softening hardening rate e ects a full algorithmic treatment is presented for each of the three models including the derivation of a consistent tangential sti ness matrix based on a limited numerical experience it seems that the consistency model shows a faster global convergence than the overstress approaches for softening problems all three approaches have a regularising e ect in the sense that the initial value problem remains well posed the width of the shear band is determined by the material parameters and if present by the size of an imperfection a relation between the length scales of the three models is given furthermore it is shown that the consistency model can properly simulate the so called s type instabilities which are associated with the occurrence of travelling portevin le chatelier bands 1997 john wiley sons ltd

plane strain neck propagation abstract quasi static neck propagation in polymers cold drawing is studied for the case of plane strain tension for a j 2 deformation theory material nonlinear elastic jump conditions across the neck provide a simple steady state solution for a j 2 flow theory material a finite element solution characterizes the complete development of a neck in an initially smooth specimen the numerical results include the overall load deflection curve details of deformation states and the triaxial stress distribution the solution algorithm is based on a convected coordinate description of the governing equations lagrangian in character with both newton equilibrium iterations and a stress integration algorithm to improve accuracy

geometry of nonlinear connections abstract we show that locally diffeomorphic exponential maps can be defined for any second order differential equation and give a possibly nonlinear covariant derivative for any possibly nonlinear connection we introduce vertically homogeneous connections as the natural correspondents of homogeneous second order differential equations we provide significant support for the prospect of studying nonlinear connections via certain closely associated second order differential equations one of the most important is our generalized ambrose palais singer correspondence

a unified numerical integration formula for the perfectly plastic von mises model the accuracy of numerical integration of the perfectly plastic constitutive equation of von mises is examined based on the analysis of the three existing numerical integration schemes a unified numerical integration formula unif is derived which encompasses the three existing schemes as special cases and allows one to integrate the constitutive equation more accurately according to the unif there are in fact many integration schemes depending on the direction of the trial stress the validity of the unif is verified by presenting ten contours of constant angular error calculated with the unif we then come to the conclusion that the three widely used schemes are by no means the most accurate ones some other schemes with better accuracy are thereby suggested the determination of the number of substeps is also discussed in conjunction with the unif when a multi step method is used

space of ricci flows i based on the compactness of the moduli of non collapsed calabi yau spaces with mild singularities we set up a structure theory for polarized kahler ricci flows with proper geo metric bounds our theory is a generalization of the structure theory of non collapsed kahler einstein manifolds as applications we prove the hamilton tian conjecture and the partial c 0 conjecture of tian

computational aspects of the logarithmic strain space description abstract computational aspects of the logarithmic strain space description are discussed and compared with so called updated lagrangian descriptions the shortcomings of the latter are demonstrated on an analytical example of homogeneous finite distortion kinematics the numerical implementation and algorithms of the logarithmic strain space description with respect to the reference configuration are presented simulation results of two special purpose finite element programs which are based on the logarithmic strain space description are shown

accurate stress updating algorithm based on constant strain rate assumption abstract the calculation of the stresses for path dependent materials possesses a delicate problem here the constitutive equations are reformulated using the assumption of constant strain rate within an increment this assumption allows the constitutive laws to be rewritten as ordinary differential equations and thus a large set of tools is available to solve the constitutive equations within this concept the possibility to form an algorithmic stiffness tensor is investigated and it turns out that the true tensor is expensive to calculate but it is of interest that an inexpensive well behaving approximative algorithmic stiffness tensor can be formulated to investigate the properties of the solution method both with respect to stress calculation and convergence properties in a newton raphson method an elasto plastic damage model based on von mises plasticity is considered an interesting observation is that for the usual closest point projection method the damage evolution is very sensitive to the size of load step

line search methods in general return mapping algorithms with application to porous plasticity the present paper focuses on the application of line search methods in general return mapping algorithms two inexact line search methods and an exact line search method are investigated regarding their convergence properties within an automatic time incrementation in finite element calculations as an example for the assessment of the algorithms an elastic plastic and an elastic viscoplastic version of gurson s porous plasticity model are used in simulations of the necking of a tensile bar it is shown that larger time increments are possible and therefore a smaller number of increments are required when using line search methods the exact line search method shows the best performance concerning the required number of increments but takes more cpu time to complete the simulation the application of the inexact line search methods in general lowers the number of increments along with a reduction in the cpu time as compared with the case when no line search is used copyright 2007 john wiley sons ltd

consistent integration of the constitutive equations of gurson materials under adiabatic conditions in this paper a consistent integration procedure for the thermoviscoplastic version of the complete gurson model is proposed with adiabatic conditions considered and with the use of the backward euler integration scheme a numerical algorithm implicit in all variables as well as the corresponding algorithmic operator have been developed the proposed algorithm was implemented in a finite element code and its performance is demonstrated with the numerical simulation of different examples

prediction of the mechanical behavior of nonlinear heterogeneous systems by multi level finite element modeling an accurate homogenization method that accounts for large deformations and viscoelastic material behavior on microscopic and macroscopic levels is presented this method is based on the classical homogenization theory assuming local spatial periodicity of the microstructure consequently the microstructure is identified by a representative volume element rve with conformity of opposite boundaries at any stage of the deformation process the local macroscopic stress is obtained by applying the local macroscopic deformation represented by the deformation tensor on a unique rve through imposing appropriate boundary conditions and averaging the resulting rve stress field if the assumption of local periodicity of the morphology is valid this homogenization procedure supplies a consistent objective relationship between the local macroscopic deformation and the microstructural deformation the homogenization method was implemented in a multi level finite element program with meshes on macroscopic level mesh of entire structure and microscopic level meshes of rves the performance was successfully verified by the comparison of the deformation of a perforated macroscopic sheet to the response of a homogenized sheet

on the numerical integration of a class of pressure dependent plasticity models an unconditionally stable algorithm for the numerical integration of elastoplastic pressure dependent constitutive relations is analysed in detail in this paper the application of the method to plane stress problems in which the out of plane strain component is not defined kinematically is discussed the tangent moduli resulting from this integration algorithm are obtained by consistent linearization of the elastoplastic constitutive equations the algorithm is applied to gurson s constitutive model some one dimensional problems are solved and comparisons with exact solutions are made the paper closes with a numerical study of the necking of an axi symmetric specimen using gurson s plasticity model to describe the constitutive behaviour of the material