homogenization of two phase elasto plastic composite materials and structures study of tangent operators cyclic plasticity and numerical algorithms we develop homogenization schemes and numerical algorithms for two phase elasto plastic composite materials and structures a hill type incremental formulation enables the simulation of unloading and cyclic loadings it also allows to handle any rate independent model for each phase we study the crucial issue of tangent operators elasto plastic or continuum versus algorithmic or consistent and anisotropic versus isotropic we apply two methods of extraction of isotropic tangent moduli we compare mathematically the stiffnesses of various tangent operators all rate equations are discretized in time using implicit integration we implemented two homogenization schemes mori tanaka and a double inclusion model and two plasticity models classical j 2 plasticity and chaboche s model with non linear kinematic and isotropic hardenings we consider composites with different properties and present several discriminating numerical simulations in many cases the results are validated against finite element fe or experimental data we integrated our homogenization code into the fe program abaqus using a user material interface umat a two scale procedure allows to compute realistic structures made of non linear composite materials within reasonable cpu time and memory usage examples are shown c 2002 elsevier science ltd all rights reserved

harmonic analysis on nilpotent groups and singular integrals ii singular kernels supported on submanifolds on etudie des operateurs de convolution singuliers sur des groupes de lie nilpotents generaux et plus specifiquement des operateurs dont les noyaux ont pour supports des varietes de faible dimension et qui peuvent aussi contenir des facteurs polynomiaux exponentiels oscillatoires

implicit algorithm for finite deformation hypoelastic viscoplasticity in fcc metals an implicit objective stress update algorithm is proposed for a hypoelastic viscoplastic model a thermal dynamic yield function which is derived based on the thermal activation analysis and dislocation interaction mechanisms is used along with the consistency approach and the framework of additive viscoplasticity in deriving the proposed model for fcc metals the corotational formulation approach is utilized in developing the proposed model in the finite deformation field for the case of the newton raphson iteration method a new expression for the consistent algorithmic tangent stiffness matrix of rate dependent metals is derived by direct linearization of the stress update algorithm finite element simulations are performed by implementing the proposed viscoplasticity constitutive models in the commercial finite element program abaqus numerical implementation for a simple tensile problem is used for validating the material parameters of the ofhc copper under low and high strain rates and temperatures the numerical results of the adiabatic true stress true strain curves compare very well with the experimental data the effectiveness of the present approach is tested by studying strain localization in a simple plane strain problem results indicate excellent performance of the present framework in describing the strain localization problem and in obtaining mesh independent results copyright 2006 john wiley sons ltd

the geometry of turbo decoding dynamics the spectacular performance offered by turbo codes sparked intense interest in them a considerable amount of research has simplified formalized and extended the ideas inherent in the original turbo code construction nevertheless the nature of the relatively simple ad hoc turbo decoding algorithm has remained something of a mystery we present a geometric interpretation of the turbo decoding algorithm the geometric perspective clearly indicates the relationship between turbo decoding and maximum likelihood decoding analysis of the geometry leads to new results concerning existence of fixed points conditions for uniqueness conditions for stability and proximity to maximum likelihood decoding

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

a t 1 theorem for singular radon transforms we prove an analogue for singular radon transforms to the t 1 theorem of david and journe

metrics and smoothing of translation invariant radon transforms along curves abstract in this paper new l p l q estimates are proved for translation invariant radon transforms along curves for and p q for a fixed and if p is sufficiently close to 2 the best possible q is obtained up to e the method is related to that of greenblatt ph d thesis princeton university 1998

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

finite deformation post buckling analysis involving inelasticity and contact constraints this paper is concerned with the numerical solution of large deflection structural problems involving finite strains subject to contact constraints and unilateral boundary conditions and exhibiting inelastic constitutive response first a three dimensional finite strain beam model is summarized and its numerical implementation in the two dimensional case is discussed next a penalty formulation for the solution of contact problems is presented and the correct expression for consistent tangent matrix is developed finally basic strategies for tracing limit points are reviewed and a modification of the arc length method is proposed the good performance of the procedures discussed is illustrated by means of numerical examples

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

sobolev estimates for fractional and singular radon transforms abstract we prove sobolev inequalities for singular and fractional radon transforms which are defined as in a paper of phong and stein under certain hypothesis on the corresponding lagrangian n c which does not necessarily have to be a canonical graph in the proof we use oscillatory integrals the cotlar stein almost orthogonality theorem a sort of littlewood paley decomposition for a certain operator some basic facts about fourier integral operators and pseudodifferential operators the main ideas come from papers by phong and stein acta math 157 1986 99 157 and sogge and stein j analyse math 54 1990 165 188

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

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

boundedness of singular radon transforms on l p spaces under a finite type condition in this paper a new method is presented for proving boundedness of singular radon transforms on l p for 1 p two closely related results generalizing the corresponding theorem of christ nagel stein and wainger are proven 1 introduction in this paper a new method is presented for proving boundedness of singular radon transforms on l p for 1 p two closely related results generalizing the corresponding theorem of christ nagel stein and wainger in 3 are proved singular radon transforms are a type of singular integral operator a prototype for which is the hilbert transform along curves let 1 1 r n be a curve with 0 0 and let f be a schwarz function on r n 1

large elasto plastic finite element analysis of solids and shells with the enhanced assumed strain concept abstract a finite element simulation of arbitrarily large elasto plastic deformations of three dimensional and shell structures is described two numerical aspects originally developed by j c simo have been combined i e the multiplicative large strain plasticity and the enhanced assumed strain finite element concept the constitutive model is worked out in its algorithmic version applying projection methods and consistent linearization the enhanced strain field is added to the conventional hexahedral displacement elements avoiding volumetric locking in the plastic range in addition to solid structures the three dimensional material model without any modifications is also applied to thin walled shell structures here an extended shell formulation a so called seven parameter model is used in which the thickness strain is augmented by a linear term the applicability of the entire formulation is demonstrated by several numerical examples

singular and maximal radon transforms analysis and geometry part 2 geometric theory 8 curvature introduction 8 1 three notions of curvature 8 2 theorems 8 3 examples 9 curvature some details 9 1 the exponential representation 9 2 diffeomorphism invariance 9 3 curvature condition cy 9 4 two lemmas 9 5 double fibration formulation 10 equivalence of curvature conditions 10 1 invariant submanifolds and deficient lie algebras 10 2 vanishing jacobians 10 3 construction of invariant submanifolds

an integration scheme for prandtl reuss elastoplastic constitutive equations we investigate the generalized midpoint rule for the time integration of elastoplastic constitutive equations for pressure independent yield criteria the incremental equations are divided into one scalar hydrostatic pressure dilation rate equation and a stress deviator strain rate deviator tensorial equation this formulation is applied to two classical problems bulging of a tube under internal pressure and tension test on a notched specimen

efficient thermo mechanical model for solidification processes a new computationally efficient algorithm has been implemented to solve for thermal stresses strains and displacements in realistic solidification processes which involve highly nonlinear constitutive relations a general form of the transient heat equation including latent heat from phase transformations such as solidification and other temperature dependent properties is solved numerically for the temperature field history the resulting thermal stresses are solved by integrating the highly nonlinear thermo elastic viscoplastic constitutive equations using a two level method first an estimate of the stress and inelastic strain is obtained at each local integration point by implicit integration followed by a bounded newton raphson nr iteration of the constitutive law then the global finite element equations describing the boundary value problem are solved using full nr iteration the procedure has been implemented into the commercial package abaqus abaqus standard users manuals v6 4 abaqus inc 2004 using a user defined subroutine umat to integrate the constitutive equations at the local level two special treatments for treating the liquid mushy zone with a fixed grid approach are presented and compared the model is validated both with a semi analytical solution from weiner and boley j mech phys solids 1963 11 145 154 as well as with an in house finite element code con2d metal mater trans b 2004 35b 6 1151 1172 continuous casting consortium website http ccc me uiuc edu 30 october 2005 ph d thesis university of illinois 1993 proceedings of the 76th steelmaking conference iss vol 76 1993 specialized in thermo mechanical modelling of continuous casting both finite element codes are then applied to simulate temperature and stress development of a slice through the solidifying steel shell in a continuous casting mold under realistic operating conditions including a stress state of generalized plane strain and with actual temperature dependent properties other local integration methods as well as the explicit initial strain method used in con2d for solving this problem are also briefly reviewed and compared copyright 2006 john wiley sons ltd

hilbert integrals singular integrals and radon transforms i on introduit deux nouvelles classes d operateurs on etudie leur relation et on montre comment on peut les appliquer a l etude des problemes aux valeurs limites

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

design sensitivity analysis for parameters affecting geometry elastic viscoplastic material constant and boundary condition by consistent tangent operator based boundary element method abstract this paper presents a design sensitivity analysis method by the consistent tangent operator concept based boundary element implicit algorithm the design variables for sensitivity analysis include geometry parameters elastic viscoplastic material parameters and boundary condition parameters based on small strain theory perzyna s elastic viscoplastic material constitutive relation with a mixed hardening model and two flow functions is considered in the sensitivity analysis the related elastic viscoplastic radial return algorithm and the formula of elastic viscoplastic consistent tangent operator are derived and discussed based on the direct differentiation approach the incremental boundary integral equations and related algorithms for both geometric and elastic viscoplastic sensitivity analysis are developed a 2d boundary element program for geometry sensitivity elastic viscoplastic material constant sensitivity and boundary condition sensitivity has been developed comparison and discussion with the results of this paper analytical solution and finite element code ansys for four plane strain numerical examples are presented finally

uniqueness loss of ellipticity and localization for the time discretized rate dependent boundary value problem with softening the discretization in time of the initial boundary value problem for rate dependent elastic viscoplastic solid materials in presence of softening is investigated in this paper the emphasis is put on uniqueness loss of ellipticity and localization it is found that the time discretized problem resembles the incremental problem for rate independent materials and softening may lead to ill posedness loss of ellipticity if the time step is greater than a critical value it is well established that the implication of loss of ellipticity for the numerical simulations after spatial discretization is the pathological mesh dependency of the computed results we furnish a method to compute the critical time step and demonstrate its use for a simple example problem copyright 2010 john wiley sons ltd

classes of singular integrals along curves and surfaces this paper is concerned with singular convolution operators in rd d 2 with convolution kernels supported on radial surfaces yd r ly l we show that if r s log s then lp boundedness holds if and only if p 2 this statement can be reduced to a similar statement about the multiplier m r 71 lrl i 7 in r2 we also construct smooth r for which the corresponding operators are bounded for po p 2 but unbounded for p po for given po e 1 2 finally we discuss some examples of singular integrals along convex curves in the plane with odd extensions

numerical aspects in the finite element simulation of the portevin le chatelier effect abstract serrated yielding and propagation of localized bands of plastic strain rate are the apparent phenomena of the portevin le chatelier plc effect the finite element modeling of this effect is investigated using a model proposed by zhang et al 74 describing dynamic strain aging and material parameters for a nickel based superalloy at 500 c this work presents 1 an efficient implicit integration scheme of the constitutive equations in the presence of instabilities 2 a numerical tool to determine the type of plastic strain rate localization bands based on results of simulations and 3 a mesh and time discretization sensitivity analysis of the model regarding the characteristics of plc bands this analysis is carried out in 2d and 3d for axisymmetric smooth and notched specimens

coupled plastic damaged model abstract a constitutive model that couples plasticity and damage is presented the model is thermodynamically consistent and comes from a generalization of classical plasticity theory and isotropic damage theory of kachanov coupling between plasticity and damage is achieved through a simultaneous solution of the plastic and the damage problem after a description of the model a numerical algorithm for the integration of the resulting constitutive equations is presented it is an euler backward type of algorithm that is particularly suitable to solve plain stress non linear problems with a 2d finite element program the consistent stiffness matrix is also derived the paper is completed with some application examples that show that the model presented accurately reproduces the behaviour of elastic plastic damaged materials

elastoplastic materials with martensitic phase transition and twinning at finite strains numerical solution with the finite element method abstract a new quasistatic problem formulation and finite element fe algorithm for martensitic phase transition pt and twinning in elastoplastic materials at large strains based on a recently proposed thermomechanical approach 1 2 are presented the instantaneous occurrence of pt in some region based on thermodynamics without introduction of volume fraction and prescribing the kinetic equations for it is considered stress history dependence during the transformation process is a characteristic feature of the pt criterion the deformation model is based on the multiplicative decomposition of the total deformation gradient into elastic transformation and plastic parts and the generalization of prandtl reuss equations to the case of large strains and pt the case of small elastic but large plastic and transformation strains is assumed for numerical simulation of pt the inverse problem is considered i e the position and size of the pt region nucleus are prescribed in advance and then the condition for pt is defined from the pt criterion such an approach includes a finite element solution of the elastoplastic problem with the prescribed transformation deformation gradient and the changing elastoplastic properties in the transforming region during pt the usage of the current configuration and the true cauchy stresses along with assumptions of small elastic strains and zero modified plastic spin allows us to use with small modifications the radial return algorithm and the consistent elastoplastic moduli for the case of small strains some modifications of the iterative algorithm related to the numerical integration of constitutive equations along with the radial return algorithm are suggested in order to improve the accuracy of solutions for large increments of external load such modifications can be used for any elastoplastic problem without phase transition as well the model problems of nucleation at shear band intersection and appearance of a single martensitic plate and a single twin are solved and analyzed

radon transforms and finite type conditions the purpose of this paper is to study averaging operators of radon transform type we shall formulate suitable finite type conditions and prove lp sobolev and lplq estimates the results will be essentially sharp for operators associated with families of curves in the plane let xc and t be smooth manifolds dimx3 nl dim2 nr and let m be a submanifold in xc x t with conormal bundle n m we denote by t the codimension of m we shall always assume that the projections lry m x and 7rt m 42 are surjective with rank dirx nl rank dr9 nr this in particular implies that n m c t x o x t o where 0 refers to the zero sections in t x and t 2 respectively this is the usual assumption for the canonical relation associated with lagrangian distributions arising as kernels of fourier integral operators the assumptions on dirx d7rt imply that for fixed x e x y e 2 the sets amx y e t x y e mi m x ye2x x y em i

nonlinear thin shell analysis using a curved triangular element abstract this paper describes a simple but robust curved triangular thin shell element the element has twelve degrees of freedom namely the displacement components in the corner nodes and the rotations about the element sides the element is based upon the well known facet element with constant membrane strains and constant stress couples and is augmented to take into account the influence of the changes of curvature on the membrane deformations due to the quadratic character of this influence curved geometries can be modelled in order to permit arbitrarily large rotational increments reference vectors are attached to each element side these reference vectors are updated by means of orthogonal transformations the latter are determined uniquely by the subsequent orientations of the associated element sides the changes of curvature are evaluated using these reference vectors and a corotated reference configuration to describe time independent elastoplasticity a layered shell model is applied while besseling s fraction model is adopted for each layer a number of numerical examples illustrate the performance of the element

fully implicit formulation of elastoplastic homogenization problem for two scale analysis abstract in this study using a virtual work equation a micro macro kinematic relation and a linearized constitutive relation a boundary value problem is fully implicitly formulated to determine perturbed displacement increment fields in elastoplastic unit cells for two scale analysis it is shown that this implicit homogenization problem can be iteratively solved with quadratic convergences by successively updating strain increment fields in unit cells and that the boundary value problem formulated provides a computational algorithm which is versatile for initial setting of strain increment fields the computational algorithm developed is then examined by performing a two scale analysis of a holed plate with an elastoplastic micro structure subjected to tensile loading this demonstrates that the convergence in iteratively solving the implicit homogenization problem strongly depends on the initial setting of strain increment fields in unit cells

iterative decoding of binary block and convolutional codes iterative decoding of two dimensional systematic convolutional codes has been termed turbo de coding using log likelihood algebra we show that any decoder can be used which accepts soft inputs including a priori values and delivers soft outputs that can be split into three terms the soft channel and a priori inputs and the extrinsic value the extrinsic value is used as an a priori value for the next iteration decoding algorithms in the log likelihood domain are given not only for convolutional codes but also for any linear binary systematic block code the iteration is controlled by a stop criterion derived from cross entropy which results in a minimal number of iterations optimal and suboptimal decoders with reduced complexity are presented simulation results show that very simple component codes are sufficient block codes are appropriate for high rates and convolutional codes for lower rates less than 2 3 any combination of block and convolutional component codes is possible several interleaving techniques are described at a bit error rate ber of 10 sup 4 the performance is slightly above or around the bounds given by the cutoff rate for reasonably simple block convolutional component codes interleaver sizes less than 1000 and for three to six iterations

design sensitivity analysis of elastoplastic structures an iterative and incremental algorithm is presented for the design sensitivity analysis dsa of elastoplastic structures geometrical non linearity is included in the formulation and the structure may be subjected to a cyclic loading the key concept is discussed using an elastoplastic truss it is shown that the design sensitivity coefficients dscs are path dependent and discontinuous at the time at which yielding takes place in a member yield time in the proposed algorithm the yield time is considered to be a function of the design variables in this way the discontinuity in the dscs at the material transition points can be overcome in a simple and routine way incremental response analysis and dsa are carried out simultaneously using the newton raphson type iterative procedure since the proposed algorithm is completely consistent with the analysis procedure it can be implemented into an existing code for structural analysis application to distributed parameter structures with kinematic and or isotropic hardening is discussed using the von mises yield condition and the elastic predictor radial return method dsa is carried out for a ten bar truss with a piecewise linear constitutive relation it is shown that the dscs found using the proposed method agree quite well with those calculated by the central difference method finally an alternate method without any iteration for dsa is proposed and the results from the two methods are compared

singular integrals associated to hypersurfaces l2 theory abstract we consider singular integrals associated to a classical calderon zygmund kernel k and a hypersurface given by the graph of t where is an arbitrary c 1 function and is a smooth convex function of finite type we give a characterization of those calderon zygmund kernels k and convex functions so that the associated singular integral operator is bounded on l 2 for all c 1 functions

an inverse micro mechanical analysis toward the stochastic homogenization of nonlinear random composites abstract an inverse mean field homogenization mfh process is developed to improve the computational efficiency of non linear stochastic multiscale analyzes by relying on a micro mechanics model first full field simulations of composite stochastic volume element sve realizations are performed to characterize the homogenized stochastic behavior the uncertainties observed in the non linear homogenized response which result from the uncertainties of their micro structures are then translated to an incremental secant mfh formulation by defining the mfh input parameters as random effective properties these effective input parameters which correspond to the micro structure geometrical information and to the material phases model parameters are identified by conducting an inverse analysis from the full field homogenized responses compared to the direct finite element analyzes on sves the resulting stochastic mfh process reduces not only the computational cost but also the order of uncertain parameters in the composite micro structures leading to a stochastic mean field reduced order model mf rom a data driven stochastic model is then built in order to generate the random effective properties under the form of a random field used as entry for the stochastic mf rom embedded in a stochastic finite element method sfem the two cases of elastic unidirectional ud fibers embedded in an elasto plastic matrix and of elastic ud fibers embedded in a damage enhanced elasto plastic matrix are successively considered in order to illustrate the capabilities of the method the stochastic response of a ply is studied under transverse loading condition

a generalized approach to formulate the consistent tangent stiffness in plasticity with application to the gld porous material model abstract it has been shown that the use of the consistent tangent moduli is crucial for preserving the quadratic convergence rate of the global newton iterations in the solution of the incremental problem in this paper we present a general method to formulate the consistent tangent stiffness for plasticity the robustness and efficiency of the proposed approach are examined by applying it to the isotropic material with j2 flow plasticity and comparing the performance and the analysis results with the original implementation in the commercial finite element program abaqus the proposed approach is then applied to an anisotropic porous plasticity model the gologanu leblond devaux model performance comparison between the consistent tangent stiffness and the conventional continuum tangent stiffness demonstrates significant improvement in convergence characteristics of the overall newton iterations caused by using the consistent tangent matrix

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 representation and implicit integration of general isotropic elastoplasticity based on a set of mutually orthogonal unit basis tensors summary a simple and compact representation framework and the corresponding efficient numerical integration algorithm are developed for constitutive equations of isotropic elastoplasticity central to this work is the utilization of a set of mutually orthogonal unit tensor bases and the corresponding invariants the set of bases can be regarded equivalently as a local cylindrical coordinate system in the three dimensional coaxial tensor subspace namely the principal space the base tensors are given in the global coordinate system similar to the principal space approach the proposed method reduces the problem dimension from six to three in contrast to the conventional approach the transformation procedure between the principal space and the general space is avoided and explicit computation of the principal axes is bypassed with the proposed technique the matrices which need to be inverted during iteration take a simple form for the great majority of constitutive equations in use the tangent operator consistent with the proposed algorithm can be decomposed into the direct sum of two linear maps over the coaxial tensor subspace and the subspace orthogonal to it consequently its closed form is derived in an extremely simple manner finally numerical examples demonstrate the high quality performances of the proposed scheme copyright 2014 john wiley sons ltd

finite deformation formulation for embedded frictional crack with the extended finite element method we reformulate an extended finite element fe framework for embedded frictional cracks in elastoplastic solids to accommodate finite deformation including finite stretching and rotation for the fe representation we consider a galerkin approximation in which both the trial and weighting functions adapt to the current contact configuration contact and frictional constraints employ two kuhn tucker conditions a contact separation constraint nesting over a stick slip constraint for the case when the crack faces are in frictional sliding mode we integrate finite deformation bulk plasticity into the formulation using the multiplicative decomposition technique of nonlinear continuum mechanics we then present plane strain simulations demonstrating various aspects of the extended fe solutions the mechanisms considered include combined opening and frictional sliding in initially straight curved and s shaped cracks with and without bulk plasticity to gain further insight into the extended fe solutions we perform mesh convergence studies focusing on both the global and the local responses of structures with cracks including the distribution of the normal component of traction on the crack faces copyright 2009 john wiley sons ltd

material growth in thermoelastic continua theory algorithmics and simulation a theoretical formulation of stress induced volumetric material growth in thermoelastic continua is developed material growth is regulated by a three surface activation criterion and corresponding flow rules a simple model is proposed based on this formulation and its algorithmic implementation including a method for solving the underlying differential algebraic equations for growth is examined in the context of an implicit finite element method selected numerical simulations are presented that showcase the predictive capacity of the model for both soft and hard biomaterials

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

a family of integration algorithms for constitutive equations in finite deformation elasto viscoplasticity a two parameter family of incrementally objective integration schemes is proposed for the analysis of a broad range of unified rate dependent viscoplastic constitutive models in large deformation problems a similar scheme can be applied to rate independent solids as well these algorithms are a generalization of the mid point integration rule full linearization of the principle of virtual work is performed in an updated lagrangian framework together with a calculation of the consistent linearized moduli some details of the finite element implementation are given for plane strain and axisymmetric problems the method is compared with other objective integration schemes and is tested with several examples where large strains and rotations occur

numerical simulation of ductile fracture with the rousselier constitutive law this contribution aims at developing robust and reliable tools dedicated to predictive numerical simulation of ductile fracture description of damage mechanisms relies here on the rousselier constitutive law to achieve robustness and objectivity several points need then to be addressed reduction of the set of internal variables so as to recast the model into the framework of generalised standard materials proper expression of the normal plastic flow rule at the vertex of the yield surface finite strain formulation based on a multiplicative split of the deformation gradient fully implicit integration of the constitutive equations leading to a single scalar equation that admits a unique root use of mixed finite elements to avoid volumetric locking strain gradient based nonlocal model to control strain localisation and remedy spurious mesh dependency the capabilities of the resulting numerical formulation are demonstrated through simulating the cup cone fracture of a notched tensile specimen

internal symmetry groups for the drucker prager material model of plasticity and numerical integrating methods abstract internal symmetries for the drucker prager material model and numerical methods based on them are investigated here we first convert the non linear constitutive equations to a lie type system x a x t x where a sl 5 2 r is a lie algebra of the special orthochronous pseudo linear group sl 5 2 r the underlying space of drucker prager model in the plastic phase is a pseudo sphere in the pseudo riemann manifold which is locally a pseudo euclidean space e 7 5 2 and whose metric tensor is indefinite having signature 5 2 and also depends on the temporal component then we split the drucker prager yield condition into two sub yield conditions which together with two integrating factors idea led us to derive two lie type systems in the product space m 5 1 m 1 1 the lie algebra is the direct sum so 5 1 so 1 1 and the symmetry group is thus soo 5 1 soo 1 1 these results are essential from computational aspect based on these symmetry groups exponential mappings are developed which update stress points exactly on the yield surface at every time increment without any iteration as an example the results calculated by using the two different group preserving schemes are compared to that calculated by the runge kutta scheme together with the newton raphson iterative solution of a non linear algebraic equation which enforcing the consistency condition

a component based hybrid reduced basis finite element method for solid mechanics with local nonlinearities abstract the scrbe static condensation reduced basis element method is a component to system model order reduction approach for efficient many query and real time treatment of linear partial differential equations characterized by many spatially distributed constitutive geometry and topology parameters in this paper we incorporate the scrbe approach into a framework for analysis of problems in solid mechanics which are largely linear with the exception of local nonlinearities in particular we exploit a linear nonlinear domain decomposition to develop a hybrid formulation we consider a scrbe approximation over the assumed predominant part of the domain associated to a linear elasticity model we revert to a full finite element fe approximation over the part of the domain associated to the locally nonlinear model we adapt the scrbe port training procedures to anticipate the behavior of the field over the linear nonlinear interface and hence ensure an accurate solution over the entire domain we choose a globally conforming approximation which exploits the intrinsic port structure of the scrbe method and yields a decoupled non invasive formulation of the respective linear and nonlinear blocks of the residual vector and newton jacobian matrix we present numerical results for several local nonlinearities elastic contact with and without friction plastic contact which demonstrate substantial savings relative to standard fe approximation over the entire domain in particular in the regime in which the linear part of the domain represents the majority of the fe degrees of freedom

harmonic analysis on nilpotent groups and singular integrals i oscillatory integrals abstract this paper is devoted to the study of the operator given by where k is a standard calderon zygmund kernel and p is a real polynomial on r n r n we show t is bounded on lp to itself when 1

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

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

existence and uniqueness of the solution for turbo decoding of parallel concatenated single parity check codes we consider turbo decoding of parallel concatenated single parity check spc k 1 k codes with row column interleaving the existence and uniqueness of the asymptotic probability density evaluated with the turbo algorithm is proved for every length k and every signal to noise ratio snr