revisited simo algorithm for the plane stress state abstract in this paper a new numerical approach of the elasto plastic problem with mixed hardening in plane stress state is proposed within the classical constitutive framework of small deformation in the formalized problem the non zero normal component of the strain namely the component in the direction perpendicular to the plane of stress is considered to be compatible with the plane stress we eliminate the rate of strains which are developed normal to the plane and solve an appropriate plane problem in the strain setting the integration algorithm for solving the elasto plastic problem with mixed hardening realizes the coupling of radial return algorithm namely an update algorithm with the finite element method applied to the discretized equilibrium balance equation the solution of the pseudo elastic nonlinear problem is then solved by newton s method the numerical algorithm which is an incremental one consists of the radial return mapping algorithm originally proposed by simo and hughes 1998 adapted to the stress plane problem and coupled with a pseudo elastic problem we rebuild the algorithmic formula giving rise to the plastic factor in terms of the trial stress state and the algorithmic elasto plastic tangent moduli which is requested to evaluate the jacobian that is necessary to determine the displacement the proposed algorithm has been named the revisited simo algorithm and is applied to exemplify the mode of integration of the bi dimensional problem

recovery procedures in error estimation and adaptivity part ii adaptivity in nonlinear problems of elasto plasticity behaviour the first part of this paper 1 discusses in some detail the use of recovery procedures for stress strain or gradients for efficient error estimator and the methods of arriving at adaptive h refinement in this paper we extend such procedure to deal with elasto plasticity and discuss in detail some special features of such computation

elastic plastic analysis of arbitrary heterogeneous materials with the voronoi cell finite element method abstract in this paper a voronoi cell finite element method is developed to solve small deformation elastic plasticity problems for arbitrary heterogenous materials dirichlet tessellation of microstructural representative materials results in a network of arbitrary sided polygons called voronoi cells each voronoi cell encompasses one second phase heterogeneity at most these are natural elements for the microstructure representing the basic structural elements of the material in this paper formulations are developed for directly considering voronoi cells as elements in a finite element model without any further dissection furthermore a composite voronoi cell finite element method is developed to account for the presence of the second phase within each polygonal element various numerical elastic plastic examples are executed for validating the effectiveness of this formulation finally studies are conducted to understand the effect of size shape and distribution of second phase on the averaged and true local responses of representative material elements

sensitivity analysis in plane stress elasto plasticity and elasto viscoplasticity abstract development of computational models for plane stress elasto plasticity is known to make some difficulties non existent in 3d and plane strain formulations tedious derivation of plane stress algorithmic tangent matrices which cannot be directly obtained as a special case of 3d matrices may serve here as an example in this paper specific features of plane stress computations are discussed in the context of parameter sensitivity analysis elasto plastic material model with isotropic kinematic hardening as well as two viscoplastic models are considered explicit expressions for sensitivity gradients are derived instructive examples solved by fem illustrate the paper

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

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

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

consistent derivation of the constitutive algorithm for plane stress isotropic plasticity part i theoretical formulation abstract a derivation of the projected algorithm for general isotropic three invariant plasticity models under plane stress conditions is presented it is obtained by consistently specializing the 3d formulation to the 2d subspace defined by the plane stress condition closed form intrinsic algorithm linearization and a novel expression of the consistent tangent tensor are provided these are also shown to directly emanate from the analogous quantities pertaining to the fully 3d case a detailed discussion of the proposed implementation along with a representative set of numerical examples is provided in the second part of this paper valoroso n rosati l 2008 consistent derivation of the constitutive algorithm for plane stress isotropic plasticity part ii computational issues international journal of solids and structures 46 92 124

mixed stabilized finite element methods in nonlinear solid mechanics part i formulation abstract this paper exploits the concept of stabilized finite element methods to formulate stable mixed stress displacement and strain displacement finite elements for the solution of nonlinear solid mechanics problems the different assumptions and approximations used to derive the methods are exposed the proposed procedure is very general applicable to 2d and 3d problems implementation and computational aspects are also discussed showing that a robust application of the proposed formulation is feasible numerical examples show that the results obtained compare favorably with those obtained with the corresponding irreducible formulation

a return mapping algorithm for a class of cyclic plasticity models a return mapping algorithm for a class of cyclic plasticity models is presented the constitutive model includes a quadratic yield criterion and multi component formulations of non linear isotropic and kinematic hardening thus both initially isotropic and anisotropic materials can be described and a proper description of the hysteresis loops and the cyclic hardening response of materials under cyclic loading is obtained the return mapping algorithm employs the closest point projection scheme in combination with a decomposition method to obtain an efficient and robust integration of the constitutive model the consistent tangent operator is derived in closed form and is found to be unsymmetric due to the non linear evolution of the kinematic hardening terms the accuracy and robustness of the algorithm are assessed through numerical examples

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

differential operators on homogeneous spaces iii characteristic varieties of harish chandra modules and of primitive ideals letg be a semi simple complex algebraic group with lie algebra and flag varietyx g b for each primitive idealj with trivial central character in the enveloping algebrau we define a characteristic variety in the cotangent bundle ofx which projects under the springer resolution mapt x onto the closure of a nilpotent orbit we prove that this characteristic variety is theg saturation of the characteristic variety of a highest weight module with annihilatorj we conjecture that it is irreducible forg sl n our conjecture would provide a geometrical explanation for the classification of primitive ideals in terms of weyl group representations as achieved by a joseph the presentation of these ideas here is simultaneously used to some extent as an opportunity to continue our more general systematic discussion of differential operators on a complete homogeneous space and to study more generally characteristic varieties of harish chandra modules

non smooth multisurface plasticity and viscoplasticity loading unloading conditions and numerical algorithms rate independent plasticity and viscoplasticity in which the boundary of the elastic domain is defined by an arbitrary number of yield surfaces intersecting in a non smooth fashion are considered in detail it is shown that the standard kuhn tucker optimality conditions lead to the only computationally useful characterization of plastic loading on the computational side an unconditionally convergent return mapping algorithm is developed which places no restrictions aside from convexity on the functional forms of the yield condition flow rule and hardening law the proposed general purpose procedure is amenable to exact linearization leading to a closed form expression of the so called consistent algorithmic tangent moduli for viscoplasticity a closed form algorithm is developed based on the rate independent solution the methodology is applied to structural elements in which the elastic domain possesses a non smooth boundary numerical simulations are presented that illustrate the excellent performance of the algorithm

estimates for n widths of multiplier operators of multiple walsh series abstract estimates for kolmogorov and gelfand n widths of multiplier operators of multiple walsh series are obtained upper and lower bounds are established for n widths of general multiplier operators these results are applied to get upper and lower bounds for n widths of specific multiplier operators which generate sets of finitely and infinitely differentiable functions in the dyadic sense it is shown that these estimates have order sharp in various important cases

a unified stress update algorithm for explicit transient shell dynamics with combined isotropic kinematic hardening in eulerian rate type phenomenological finite elasto plasticity models abstract this paper discusses applications of the objective stress rates to a unified stress update algorithm for transient shell dynamic analysis within the context of explicit time integration we propose a unified stress update algorithm via establishing the eulerian rate type constitutive equations of hypoelastic plastic materials the constitutive equations are often given on the additive decomposition of the rate of deformation tensor under the assumption that the elastic part of the rate of deformation tensor may be characterized to be hypoelastic with grade zero i e the fourth rank constant isotropic tensor several objective stress rates are derived through the lie derivative of the cauchy or kirchhoff stress tensor those stress rates cover for instance the jaumann green naghdi truesdell oldroyd and cotter rivlin stress rates further the unified stress update algorithm is implemented along with the so called radial return method and the phenomenological plasticity theory with combined isotropic kinematic hardenings among the objective stress rates employed here we emphasize especially the stress update procedure of the green naghdi stress rate for transient shell dynamics because this algorithm developed in this work is not shown even in the representative commercial codes in the implementation of the unified stress update algorithm we applied our algorithms to the belytschko lin tsay shell theory to validate its accuracy and effectiveness moreover a slightly modified secant algorithm for the zero transverse normal stress of the shell is also developed the ultimate objectivity of this work is to provide a guideline for the best choice of an appropriate objective stress rate for phenomenological elastoplastic models several numerical examples are demonstrated including non contact transient shell dynamics examples and contact impact examples such as a ball plate impact problem by which the accuracy and effectiveness of the unified stress update algorithm developed in this work are addressed

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

geometrically non linear and elastoplastic three dimensional shear flexible beam element of von mises type hardening material a three dimensional elastoplastic beam element being capable of incorporating large displacement and large rotation is developed and examined elastoplastic constitutive equations are applied to the beam element based upon the assumption of small deformational strain leading to a material formulation which is completely objective for the application of stress update procedures the continuum type equations of plastic model of j2 mixed hardening are transformed into the beam equations by satisfying beam hypotheses an effective stress update algorithm is proposed to integrate elastoplastic rate equations by means of the so called multistep method which is a method of successive control of residuals on yield surfaces it avoids severe divergence when the displacement increments become large which is usual for the continuation methods material tangent stiffness matrix is derived by using consistent elastoplastic modulus resulting from the integration algorithm and is combined with geometric tangent stiffness matrix different from other elements the present element is shear flexible and can satisfy the plasticity condition in a pointwise fashion a great number of numerical examples are analysed and compared with the literature the proposed beam element is verified to be not only quite accurate but also very effective for the analyses of pre buckling and large deflection collapse of spatial framed structures

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

a micropolar formulation of the desai hierarchical model for elastoplastic porous media in this contribution the desai hierarchical model is extended to the case of 3d elasto plastic two phase micropolar continuum an unconditionally stable implicit euler backward algorithm for integration of the constitutive relations is developed and presented in detail the regularizing effect of the introduction of a length parameter to the classical desai model is demonstrated by means of several case studies of single phase and two phase porous media

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

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

topology and shape optimization for elastoplastic structural response abstract it is a common practice to base both material topology optimization as well as a subsequent shape optimization on linear elastic response however in order to obtain a realistic design it might be essential to base the optimization on a more realistic physical behavior i e to consider geometrically or and materially nonlinear effects in the present paper an elastoplastic von mises material model with linear isotropic hardening softening for small strains is used the objective of the design problem is to maximize the structural ductility in the elastoplastic range while the mass in the design space is prescribed with respect to the specific features of either topology or shape optimization for example the number of optimization variables or their local global influence on the structural response different methods are applied for topology optimization problems the gradient of the ductility is determined by the variational adjoint approach in shape optimization the derivatives of the state variables with respect to the optimization variables are evaluated analytically by a variational direct approach the topology optimization problem is solved by an optimality criteria oc method and the shape optimization problem by a mathematical programming mp method in topology optimization a geometrically adaptive procedure is additionally applied in order to increase the efficiency and to avoid artificial stress singularities the procedures are verified by 2d design problems under plane stress conditions

a four point integration scheme with quadratic exactness for three dimensional element free galerkin method based on variationally consistent formulation abstract the formulation of three dimensional element free galerkin efg method based on the hu washizu three field variational principle is described the orthogonality condition between stress and strain difference is satisfied by correcting the derivatives of the nodal shape functions this leads to a variationally consistent formulation which has a similar form as the formulation of standard galerkin weak form based on this formulation an integration scheme which employs only four cubature points in each background tetrahedral element cell is rationally developed for three dimensional efg with quadratic approximation the consistency of the corrected nodal derivatives and the satisfaction of patch test conditions for the developed integration scheme are theoretically proved extension of the proposed method to small strain elastoplasticity is also presented the proposed method can exactly pass quadratic patch test that is quadratic exactness is achieved and thus it is named as quadratically consistent 4 point qc4 integration method in contrast efg with standard tetrahedral cubature and the existing linearly consistent 1 point lc1 integration fail to exactly pass quadratic patch test numerical results of elastic examples demonstrate the superiority of the proposed method in accuracy convergence efficiency and stability the capability of the proposed qc4 scheme in solving elastoplastic problems is also demonstrated by numerical examples

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

elasto plastic finite element method based on incremental deformation theory and continuum based shell elements for planar anisotropic sheet materials abstract an implicit approach for the incremental analysis of planar anisotropic sheet forming processes is developed based on the incremental deformation theory the incremental deformation theory based on the minimum plastic work path enables convenient decoupling of deformation and rotation by the polar decomposition the mathematical description of a constitutive law for the incremental deformation theory is obtained from the flow theory along the minimum plastic work path the resulting constitutive law is then incorporated in an elasto plastic finite element analysis code in the elasto plastic formulation continuum based resultant cbr shell element is employed the cbr shell allows large rotation and large membrane bending strain the laminar coordinate system is taken to coincide with planar anisotropic material axes then planar anisotropic axes during deformation are updated using a newly developed algorithm based on the polar decomposition an iterative solving method based on the incremental deformation theory is also developed for an accurate and stable stress integration the planar anisotropy is incorporated into the formulation for sheet forming by introducing non quadratic barlat s yield function for verification purposes two examples have been simulated and compared with experimental results the good verification results show that the present elasto plastic formulation for planar anisotropic sheet materials can provide a good theoretical basis for more extended analyses of sheet forming processes

a mixed finite element for three dimensional nonlinear analysis of steel frames abstract this paper develops and demonstrates a mixed beam finite element that can represent the inelastic three dimensional stability behavior of frames composed of open walled cross section members the kinematics of deformation of the element include finite rotation and warping of the cross section due to torsion the material inelasticity is based on a two space model that includes the effect of shear stresses due to uniform torsion in addition to normal stresses due to axial force biaxial bending and bimoment initial geometric imperfections and residual stresses are accommodated the formulation is based on a two field displacement and generalized stress hellinger reissner hr variational principle the interpolation of the generalized stresses i e cross section stress resultants along the element length is based on the geometrically exact nonlinear governing differential equations of equilibrium this leads to significant improvements in the accuracy over conventional displacement based elements in problems involving highly nonlinear variations in the curvature along the member lengths due to geometric nonlinearity and or distributed plasticity effects several numerical examples involving two and three dimensional elastic and inelastic stability behavior are presented to illustrate the capabilities of the formulation

studies in anisotropic plasticity with reference to the hill criterion algorithms based upon the notion of return mapping have been developed for the hill yield function of anisotropic plasticity the relative accuracy of two algorithms is assessed by means of iso error maps the choice of the algorithm turns out to be much more critical for the orthotropic hill criterion than for the underlying isotropic von mises plasticity model a tangent operator that is consistent with the developed integration algorithm is formulated and its efficiency is assessed compared with the classical continuum tangent operator the model has been applied to three shell plate structures

mixed stabilized finite element methods in nonlinear solid mechanics part ii strain localization this paper deals with the question of strain localization associated with materials which exhibit softening due to tensile straining a standard local isotropic rankine damage model with strain softening is used as exemplary constitutive model both the irreducible and mixed forms of the problem are examined and stability and solvability conditions are discussed lack of uniqueness and convergence difficulties related to the strong material nonlinearities involved are also treated from this analysis the issue of local discretization error in the pre localization regime is deemed as the main difficulty to be overcome in the discrete problem focus is placed on low order finite elements with continuous strain and displacement fields triangular p1p1 and quadrilateral q1q1 although the presented approach is very general numerical examples show that the resulting procedure is remarkably robust it does not require the use of auxiliary tracking techniques and the results obtained do not suffer from spurious mesh bias dependence

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

approximation of smooth functions on compact two point homogeneous spaces estimates of kolmogorov n widths dn bpr lq and linear n widths n bpr lq 1 q of sobolev s classes bpr r 0 1 p on compact two point homogeneous spaces ctphs are established for part of p q 1 1 sharp orders of dn bpr lq or n bpr lq were obtained by bordin et al j funct anal 202 2 2003 307 in this paper we obtain the sharp orders of dn bpr lq and n bpr lq for all the remaining p q our proof is based on positive cubature formulas and marcinkiewicz zygmund type inequalities on ctphs

optimal cubature formulas on compact homogeneous manifolds abstract we find lower bounds for the rate of convergence of optimal cubature formulas on sets of differentiable functions on compact homogeneous manifolds of rank i or two point homogeneous spaces it is shown that these lower bounds are sharp in the power scale in the case of s 2 the unit sphere in r 3

on the numerical integration of a class of pressure dependent plasticity models with mixed hardening radial return algorithms for both three dimensional and plane stress situations are developed for a class of pressure dependent plasticity models formulated in state variables with mixed hardening the consistent tangent matrix has been developed which among other advantages does not require numerical inversion the algorithms for gurson s mixed hardening model are incorporated in a finite element program to solve several simple uniaxial tension problems when compared with numerically integrated solutions the results from the finite element analysis show excellent agreement finally results of the axisymmetric necking problem using gurson s mixed hardening model are presented as an example of application

on the computational significance of the strain space formulation of plasticity theory the strain space and traditional stress space formulations of plasticity theory are compared we show how plasticity theory has been implemented numerically to solve static and dynamic problems and conclude that the numerical loading criteria that have been used for two decades are identical to the strain space loading criteria proposed by naghdi and co workers

a quadrilateral mixed finite element with two enhanced strain modes summary an improved plane strain stress element is derived using a hu washizu variational formulation with bilinear displacement interpolation seven strain and stress terms and two enhanced strain modes the number of unknowns of the four node element is increased from eight to ten degrees of freedom for linear and non linear applications the two unknowns associated with the enhanced strain terms can be eliminated by static condensation so that eight displacement degrees of freedom remain for the proposed element which is denoted by qe2 the excellent performance of the proposed element is demonstrated using several linear and non linear examples

elastic viscoplastic differential equations on a manifold modelling of in plane stretching of sheet metal the computational method for large deformation plasticity called differential equations on a manifold dem has previously been shown to be effective for axisymmetric and plane strain sheet metal forming problems the method has now been formulated for in plane stretching problems incorporated into a computer code and applied to several problems the code s performance is robust and accurate as evidenced by a comparison with other published results incorporation of an automatic mesh generator significantly reduces data preparation time

estimates of n widths of sobolev s classes on compact globally symmetric spaces of rank one estimates of kolmogorov s and linear n widths of sobolev s classes on compact globally symmetric spaces of rank 1 i e on sd pd r pd c pd h p16 cay are established it is shown that these estimates have sharp orders in different important cases new estimates for the p q norms of multiplier operators k k n are given we apply our results to get sharp orders of best polynomial approximation and n widths

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

non linear b stability and symmetry preserving return mapping algorithms for plasticity and viscoplasticity a class of second order accurate return mapping algorithms is presented which lead to symmetric algorithmic tangent moduli and contain the classical backward euler return maps as a particular case more importantly it is shown that this class of return maps is contractive relative to the natural norm defined by the complementary helmholz free energy function b stability since the equations of classical plasticity and viscoplasticity are shown to be contractive relative to this natural norm the requirement of b stability furnishes the appropriate notion of unconditionally stable algorithms for plasticity and viscoplasticity the analysis that follows depends critically on the assumption of convexity in particular the models of plasticity and viscoplasticity considered obey the principle of maximum plastic dissipation the proposed algorithms obey the discrete counterpart of this classical principle

a consistent formulation for the integration of combined plasticity and creep within the context of the consistent tangent update this paper outlines a stress update algorithm for combined creep and plasticity the algorithm is implicit providing unconditional stability and utilizes local newton iteration to solve scalar forms of the coupled constitutive equations for the creep and plastic strain increments the tangent for the local iteration is obtained accurately providing quadratic convergence at the gauss point level quadratic convergence of the global iteration procedure is also maintained using an explicitly derived consistent tangent for combined plasticity and creep further combination with an automatic time stepping scheme provides an efficient stable accurate and robust computational algorithm the algorithm has been implemented in the general purpose fe package lusas1

recent advances in the alternating method for elastic and inelastic fracture analyses abstract the numerical analytical alternating method wherein finite elements or boundary elements are used for numerical analysis of an uncracked structure is a very efficient and accurate method for fracture analysis it saves both time in the computational analysis and human effort in preparing analysis models in this paper we summarize the recent developments in this method including 1 the alternating method and its convergence for mixed boundary value problems with the presence of both traction and displacement boundary conditions 2 a non iterative method to construct solutions for multiple arbitrarily located embedded cracks using the solution for a single embedded crack in an infinite body 3 the analysis of elastic plastic fracture mechanics problems 4 the analysis of crack growth in plane fracture situations and 5 an efficient and accurate algorithm for the evaluation of elastoplastic stress state in a cracked structure based on the generalized mid point radial return for 3d constitutive laws and the stress subspace method for the plane stress analysis and a study of link up of multiple cracks in a wide spread fatigue damage situation in an aircraft panel some numerical examples are also given

on the consistent tangent operator algorithm for thermo plastic problems abstract in order to solve the finite element problem of thermo elasto plasticity we consider an algorithm defined from a pseudo linearization of the implicit time discretized model this procedure extends the so called consistent tangent operator method introduced by simo and taylor in standard plasticity numerical simulations prove that the algorithm is more efficient than the well known tangent stiffness matrix method in computational plasticity which is obtained by linearizing the continuous model

a multiplier version of the bernstein inequality on the complex sphere we prove a multiplier version of the bernstein inequality on the complex sphere included in this is a new result relating a bivariate sum involving jacobi polynomials and gegenbauer polynomials which relates the sum of reproducing kernels on spaces of polynomials irreducibly invariant under the unitary group with the reproducing kernel of the sum of these spaces which is irreducibly invariant under the action of the unitary group

a direct complementarity approach for the elastoplastic analysis of plane stress and plane strain structures this paper presents a direct complementarity approach for carrying out the elastoplastic analysis of plane stress and plane strain structures founded on a traditional finite step formulation our approach however avoids the typically cumbersome implementation of iterative predictorcorrector procedures associated with the ubiquitous return mapping algorithm instead at each predefined step the governing formulationcast in its most natural mathematical programming format known as a mixed complementarity problemis directly solved by using a complementarity solver run from within a mathematical modeling system we have chosen the industry standard general algebraic modeling system path mixed complementarity problem solver that is called from within the general algebraic modeling system environment we consider both von mises and tresca materials with perfect or hardening kinematic and isotropic behaviors our numerical tests five benchmark examples of which are presented in this paper have been carried out using models constructed from the mixed finite element of capsoni and corradi comput methods appl mech eng 1997 141 6793 which beneficially offers a locking free behavior and coarse mesh accuracy the results indicate in addition to an isochoric locking free behavior good accuracy and the ability to circumvent the difficult singularity problem associated with the corners of tresca yield surfaces

on a class of constitutive equations in viscoplasticity formulation and computational issues the viscoplastic constitutive model is formulated based on the existence of the dissipation potential which embodies the notion of the gauge minkowski function of the convex set a perturbation method is used for a solution of stiff differential equations characterizing the associated problem of evolution it relies on a discrete formulation of viscoplasticity which results from the regularized version of the principle of maximum plastic dissipation the operator split methodology and the newton raphson method are used to obtain the numerical solution of the discretized equations of evolution the consistent tangent modulus is expressed in a closed form as a result of the exact linearization of the discretized evolution equations for several variants of the flow potential function including some representative stiff functional forms numerical tests of the integration algorithm based on iso error maps are provided finally a numerical example is presented to illustrate the robustness and the effectiveness of the proposed approach

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

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

second order accurate integration algorithms for von mises plasticity with a nonlinear kinematic hardening mechanism abstract two second order numerical schemes for von mises plasticity with a combination of linear isotropic and nonlinear kinematic hardening are presented the first scheme is the generalized midpoint integration procedure originally introduced by ortiz and popov in 1985 detailed and applied here to the case of armstrong frederick nonlinear kinematic hardening the second algorithm is based on the constitutive model exponential based reformulation and on the integration procedure previously introduced by the authors in the context of linearly hardening materials there are two main targets to the work firstly we wish to extensively test the generalized midpoint procedure since in the scientific literature no thorough numerical testing campaign has been carried out on this second order algorithm secondly we wish to extend the exponential based integration technique also to nonlinear hardening materials a wide numerical investigation is carried out in order to compare the performance of the two methods

a canonical form return mapping algorithm for rate independent plasticity a canonical form for the representation of elastic predictor radial return plasticity algorithms is presented which is deceptive in its simplicity iterative application of the corrector is in a form used universally in the solution of ordinary differential equations and substitution of different yield functions and state variable evolution equations is trivial the consistency condition is maintained by an additional constraint equation via what is in effect a lagrange multiplier a consistent material jacobian may be obtained automatically by applying partial elimination to the same set of equations the process is numerical and requires no additional algebraic manipulation to demonstrate the validity of such a simple technique existing apparently more complex formulations are derived through the simple expedient of static condensation as a practical example of the application of the method a standard von mises plasticity model is implemented and results are presented for two standard benchmarks that test quadratic convergence for large increments copyright 2001 john wiley sons ltd

a new approach in non linear mechanics the large time increment method a new algorithm family taking into account the entire loading process in a single large time increment is proposed to compute structures with physical non linearities and is tested on some examples in elastoplasticity the method considerably reduces the number of transfers between local and global levels hence the numerical cost of calculation is also diminished