almost exponential decay of periodic viscous surface waves without surface tension we consider a viscous fluid of finite depth below the air occupying a three dimensional domain bounded below by a fixed solid boundary and above by a free moving boundary the fluid dynamics are governed by the gravity driven incompressible navier stokes equations and the effect of surface tension is neglected on the free surface the long time behavior of solutions near equilibrium has been an intriguing question since the work of beale commun pure appl math 34 3 359 392 1981 this paper is the third in a series of three guo in local well posedness of the viscous surface wave problem without surface tension anal pde 2012 to appear in decay of viscous surface waves without surface tension in horizontally infinite domains preprint 2011 that answers this question here we consider the case in which the free interface is horizontally periodic we prove that the problem is globally well posed and that solutions decay to equilibrium at an almost exponential rate in particular the free interface decays to a flat surface our framework contains several novel techniques which include 1 a priori estimates that utilize a geometric reformulation of the equations 2 a two tier energy method that couples the boundedness of high order energy to the decay of low order energy the latter of which is necessary to balance out the growth of the highest derivatives of the free interface 3 a localization procedure that is compatible with the energy method and allows for curved lower surface geometry our decay estimates lead to the construction of global in time solutions to the surface wave problem

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

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

variational and projection methods for the volume constraint in finite deformation elasto plasticity this paper focuses on the treatment of volume constraints which in the context of elasto plasticity typically arise as a result of assuming volume preserving plastic flow projection methods based on the modification of the discrete gradient operator b often proposed on an ad hoc basis are systematically obtained in the variational context furnished by a three field hu washizu principle the fully nonlinear formulation proposed here is based on a local multiplicative split of the deformation gradient into volume preserving and dilatational parts without relying on rate forms of the weak form of momentum balance this approach fits naturally in a formulation of plasticity based on the multiplicative decomposition of the deformation gradient and enables one to exactly enforce the condition of volume preserving plastic flow within the framework proposed in this paper rate forms and incrementally objective algorithms are entirely bypassed

zero surface tension limit of viscous surface waves we consider the free boundary problem for a layer of viscous incompressible fluid in a uniform gravitational field lying above a rigid bottom and below the atmosphere for the semi small initial data we prove the zero surface tension limit of the problem within a local time interval the unique local strong solution with surface tension is constructed as the limit of a sequence of approximate solutions to a special parabolic regularization for the small initial data we prove the global in time zero surface tension limit of the problem

effective properties of composite materials with periodic microstructure a computational approach abstract this study reviews several problems which are specific of composites with periodic microstructure composed of linear or nonlinear constituents the theoretical background of the method is recalled first two different families of numerical methods are considered to solve the problem the first is based on the finite element method the concept of macroscopic degrees of freedom is presented the implementation of periodicity conditions is discussed a general framework permitting either a strain or stress control is proposed the second numerical method is based on fast fourier transforms it considers first the problem of a homogeneous linear reference material undergoing a nonhomogeneous periodic eigenstrain the solution of this problem is based on the explicit form of the periodic green s function of the reference medium the relative merits of the two methods are compared and several examples are discussed both methods give very comparable results on test examples and their domains of applications appear to be complementary

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

techniques for stress and strain controlled homogenization of inelastic periodic composites abstract a framework is developed within the context of the displacement finite element method for applying periodic boundary conditions to uni period basic cells under the influence of applied macroscopically homogeneous stresses the resulting approach supplements the more common strain controlled method which is also presented and which relies on an additive decomposition of the displacement field into linear imposed and periodic unknown contributions as implemented here the stress controlled method employs a penalty formulation to insure that the displacement solution satisfies the linearperiodic decomposition the performance of both the stress and strain driven methods are demonstrated and assessed on a complete set of homogenization computations for an elasto plastic composite

strain driven homogenization of inelastic microstructures and composites based on an incremental variational formulation the paper investigates computational procedures for the treatment of a homogenized macro continuum with locally attached micro structures of inelastic constituents undergoing small strains the point of departure is a general internal variable formulation that determines the inelastic response of the constituents of a typical micro structure as a generalized standard medium in terms of an energy storage and a dissipation function consistent with this type of inelasticity we develop a new incremental variational formulation of the local constitutive response where a quasi hyperelastic micro stress potential is obtained from a local minimization problem with respect to the internal variables it is shown that this local minimization problem determines the internal state of the material for finite increments of time we specify the local variational formulation for a setting of smooth single surface inelasticity and discuss its numerical solution based on a time discretization of the internal variables the existence of the quasi hyperelastic stress potential allows the extension of homogenization approaches of elasticity to the incremental setting of inelasticity focusing on macro strain driven micro structures we develop a new incremental variational formulation of the global homogenization problem where a quasi hyperelastic macro stress potential is obtained from a global minimization problem with respect to the fine scale displacement fluctuation field it is shown that this global minimization problem determines the state of the micro structure for finite increments of time we consider three different settings of the global variational problem for prescribed linear displacements periodic fluctuations and constant stresses on the boundary of the micro structure and discuss their numerical solutions based on a spatial discretization of the fine scale displacement fluctuation field the performance of the proposed methods is demonstrated for the model problem of von mises type elasto visco plasticity of the constituents and applied to a comparative study of micro to macro transitions of inelastic composites copyright 2002 john wiley sons ltd

a primal formulation for imposing periodic boundary conditions on conforming and nonconforming meshes abstract a variational multiscale discontinuous galerkin vmdg method is developed for microscale modeling of domains containing conforming and non conforming meshes essentially the product of the applied volume average strain or macro strain and the domain diameter acts as an imposed displacement jump within the vmdg terms hence the method is suitable for modeling deformation of both block and truly self periodic representative volume elements rves the primal displacement field and macro strain are the only unknowns because the method eliminates the lagrange multiplier lm enforcement of the kinematic constraint rigorous derivation of the method provides a framework to accommodate either the macro stress or macro strain as the driver of the microscale boundary value problem the method is developed first for finite deformations and then specialized to small deformation kinematics algorithmic modifications to the method are also studied for their effects on tangent symmetry and convergence rate the results from numerical studies for isotropic and anisotropic materials show that the proposed method is robust accurate stable and variationally consistent for modeling complicated conforming and nonconforming rves

shakedown and steady state responses of elastic plastic solids in large displacements abstract elastic perfectly plastic solids or structures subjected to loads quasi statically varying within a specified domain are addressed in the framework of large displacements and the additive strain decomposition rule on the ground of drucker s principle of stability in the large an appropriate stability requisite called d stability is formulated as the positive definiteness property of a specific functional sum of the second variation of the helmholtz free energy with an additional term depending on higher order geometry change effects for a d stable structure for which the additive strain decomposition rule is applicable melan s and koiter s theorems of classical shake down theory are reconsidered and reformulated for large displacements the extended melan and koiter theorems so established save the essential features of the classical ones but exhibit a greater formal complexity with consequent difficulties for engineering applications for structures subjected to periodic loads it is shown that as long as the structure does not incur loss of d stability a long term steady state response or steady cycle occurs which exhibits the same periodicity characteristics as in case of small displacements that is the second piola kirchhoff stresses and the plastic green lagrange strain rates become periodic as the load a few illustrative numerical results are presented

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

ray patterns of matrices and nonsingularity a complex matrix a is ray nonsingular if det x 0 a f 0 for every matrix x with positive entries a sufficient condition for ray nonsingularity is that the origin is not in the relative interior of the convex hull of the signed transversal products of a the concept of an isolated set of transversals is defined and used to obtain a neces

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

two stress update algorithms for large strains accuracy analysis and numerical implementation two algorithms for the stress update i e time integration of the constitutive equation in large strain solid mechanics are compared from an analytical point of view the order of the truncation error associated to the numerical integration is deduced for each algorithm a priori using standard numerical analysis this accuracy analysis has been performed by means of a convected frame formalism which also allows a unied derivation of both algorithms in spite of their inherent dierences then the two algorithms are adapted from convected frames to a xed cartesian frame and implemented in a small strain nite element code the implementation is validated by means of a set of simple deformation paths simple shear extension extension and compression extension and rotation and two benchmark tests in non linear mechanics the necking of a circular bar and a shell under ring loads in these numerical tests the observed order of convergence is in very good agreement with the theoretical order of convergence thus corroborating the accuracy analysis 1997 john wiley sons ltd

on the numerical implementation of inelastic time dependent and time independent finite strain constitutive equations in structural mechanics abstract a number of complex issues are resolved in a way that allows the incorporation of finite strain inelastic material behavior into the piecewise numerical construction of solutions in solid mechanics without recourse to extensive continuum mechanics preliminaries an elementary time independent plasticity model an elementary time dependent creep model and a viscoelastic model are introduced as examples of constitutive equations which are routinely used in engineering calculations the constitutive equations are all suitable for problems involving large deformations and finite strains the plasticity and creep models are in rate form and use the symmetric part of the velocity gradient or the stretching to compute the co rotational time derivative of the cauchy stress the viscoelastic model computes the current value of the cauchy stress from a hereditary integral of a materially invariant form of the stretching history the current configuration is selected for evaluation of equilibrium as opposed to either the reference configuration or the last established equilibrium configuration the process of strain incrementation is examined in some depth the stretching evaluated at the mid interval and multiplied by the time step is identified as the appropriate finite strain increment to use with the selected forms of the constitutive equations discussed is the conversion of rotation rates based on the spin into incremental orthogonal rotations these rotations are used to update stresses and state variables due to rigid body rotation during the load increment comments and references to the literature are directed at numerical integration of the constitutive equations with an emphasis on doing this accurately if not exactly for any time step and stretching this material taken collectively provides an approach to numerical implementation which is marked by its simplicity

sign determinancy in lu factorization of p matrices abstract for an n by n p matrix a a ij having lu factorization a lu with u u ij we determine combinatorial circumstances for which u ij is unambiguously signed for a given pair i j or all such pairs and give corresponding results for l a qualitative p matrix is a sign nonsingular matrix with all diagonal entries positive for such a matrix a we give additional sufficient conditions for an entry u ij or the matrix u to be unambiguous if a is a qualitative p matrix with a 1 unambiguously signed we prove that the matrices l u l 1 and u 1 are all unambiguous

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

voigt reuss topology optimization for structures with nonlinear material behaviors this work is directed toward optimizing concept designs of structures featuring inelastic material behaviours by using topology optimization in the proposed framework alternative structural designs are described with the aid of spatial distributions of volume fraction design variables throughout a prescribed design domain since two or more materials are permitted to simultaneously occupy local regions of the design domain small strain integration algorithms for general two material mixtures of solids are developed for the voigt isostrain and reuss isostress assumptions and hybrid combinations thereof structural topology optimization problems involving non linear material behaviours are formulated and algorithms for incremental topology design sensitivity analysis dsa of energy type functionals are presented the consistency between the structural topology design formulation and the developed sensitivity analysis algorithms is established on three small structural topology problems separately involving linear elastic materials elastoplastic materials and viscoelastic materials the good performance of the proposed framework is demonstrated by solving two topology optimization problems to maximize the limit strength of elastoplastic structures it is demonstrated through the second example that structures optimized for maximal strength can be significantly different than those optimized for minimal elastic compliance 1997 john wiley sons ltd

nearly sign nonsingular matrices abstract a real matrix a is nearly sign nonsingular if every term in the expansion of det a but one has the same sign we show such matrices can be put into a normal form in which all diagonal entries are negative all other nonzero entries are positive and the directed graph of the matrix is intercyclic with the help of recent results of metzlar mccuaig and thomassen on intercyclic digraphs we are able to separate the nearly sign nonsingular matrices into five classes and to characterize each of these classes we also obtain two results showing where real matrices having intercyclic digraphs can or cannot be signed in such a way as to belong both to the class of sign nonsingular matrices and the class of nearly sign nonsingular matrices

when the sign pattern of a square matrix determines uniquely the sign pattern of its inverse abstract we give a precise characterization in terms of parity digraphs of those square matrices a such that for every matrix b with the same sign pattern as a b 1 exists and has the same sign pattern as a 1

on energy based coupled elastoplastic damage theories constitutive modeling and computational aspects abstract novel energy based coupled elastoplastic damage theories are presented in this paper the proposed formulation employs irreversible thermodynamics and internal state variable theory for ductile and brittle materials at variance with lemaitre s work on damage elastoplasticity the present formulation renders rational thermodynamic potential and damage energy release rate in contrast to previous work by simo and ju featuring an additive split of the stress tensor current formulation assumes an additive split of the strain tensor it is shown that the strain split damage elastoplasticity formulation leads to more robust tangent moduli than the stress split formulation the plastic flow rule and hardening law are characterized in terms of the effective quantities viz the effective stress space plasticity this mechanism is both physically well motivated and computationally efficient further a fourth order anisotropic damage mechanism is proposed for brittle materials rational mechanisms are also presented to account for the microcrack opening and closing operations as well as the strain rate dependency of microcrack growth efficient computational algorithms for proposed elasloplaslic damage models are subsequently explored by making use of the operator splitting methodology in particular new three step operator split algorithms are presented application is made to a class of inviseid and rate dependent cap damage models for concrete and mortar experimental validations are also given to illustrate the applicability of the proposed damage models

some computational aspects of large deformation rate dependent plasticity problems abstract the governing equations for a finite element formulation of boundary value problems for large deformation metal forming processes are derived using a principle of virtual work formulated in a lagrangian reference system the updated lagrangian method is used to simplify the equations the resulting nonlinear equilibrium equations are solved using newton s method a constitutive model for large deformation rate dependent plasticity is developed the model incorporates a one parameter implicit integration operator for stability and accuracy the stressrate strain rate relation is written in terms of the jaumann rate of stress numerous example problems are solved to demonstrate the effectiveness of the numerical algorithms

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

two scale kinematics and linearization for simultaneous two scale analysis of periodic heterogeneous solids at finite strain abstract we introduce the notion of two scale kinematics and the procedure of two scale linearization which are indispensable to the simultaneous two scale analysis method for the mechanical behavior of periodic heterogeneous solids at finite strain these are accomplished by formulating the two scale boundary value problem in both material and spatial descriptions with reference to the two scale modeling strategy developed in comput methods appl mech engrg 190 40 41 2001 5427 that utilized the convergence results of mathematical homogenization the formulation brings the intimate relationship between micro and macro scale kinematics in describing the micro macro coupling behavior inherent in heterogeneous media it is also shown that the two scale linearization necessitates the strict consistency with the micro scale equilibrated state and naturally invites the tangential homogenization process for both material and spatial descriptions several numerical examples of simultaneous two scale computations are presented to illustrate the two scale nature of the deformation of a heterogeneous solid at finite strain

isogeometric kirchhoff love shell formulation for elasto plasticity abstract an isogeometric thin shell formulation allowing for large strain plastic deformation is presented a stress based approach is adopted which means that the constitutive equations are evaluated at different integration points through the thickness allowing the use of general 3d material models the plane stress constraint is satisfied by iteratively updating the thickness stretch at the integration points the deformation of the shell structure is completely described by the deformation of its midsurface and furthermore the formulation is rotation free which means that the discrete shell model involves only three degrees of freedom several numerical benchmark examples with comparison to fully 3d solid simulations confirm the accuracy and efficiency of the proposed formulation

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

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

finite strain generalization of smallstrain constitutive relations for any finite strain tensor and additive volumetric deviatoric split abstract the paper deals with finite strain generalization of small strain constitutive equations for isotropic materials for which the strain is split into a volumetric part and a deviatoric part the latter characterizing the isochoric strain i e a strain at constant volume the volumetric deviatoric split has so far been handled by a multiplicative decomposition of the transformation tensor but the existing sophisticated complex constitutive models for small strains of cohesive pressure sensitive dilatant materials such as concrete and geomaterials involve an additive decomposition and would be difficult to convert a multiplicative decomposition it is shown that an additive decomposition of any finite strain tensor and of the green lagrange strain tensor in particular is possible provided that the higher order terms of the deviatoric strain tensor are allowed to depend on the volumetric strain this dependence is negligible for concrete and geomaterials because the volumetric strains are normally small whether or not the deviatoric strains are large furthermore the related question of the choice of the finite strain measure to be used for the finite strain generalization is analysed a transformation of the green lagrange finite strain tensor whose parameters approximately reflect the degrees of freedom equivalent to replacing the small strain tensor by any other possible finite strain measure is proposed finally a method by which the stress tensor that is workconjugate to any finite strain tensor can be converted to the green lagrange strain tensor is presented

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

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

computational micro to macro transitions for discretized micro structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy the paper investigates algorithms for the computation of homogenized stresses and overall tangent moduli of micro structures undergoing large strain deformations typically these micro structures define representative volumes of nonlinear heterogeneous materials such as inelastic composites polycrystalline aggregates or particle assemblies we consider a priori given discretized micro structures without focussing on details of specific discretization techniques for space and time the key contribution of the paper is the construction of a family of algorithms and matrix representations of overall properties of discretized micro structures which are motivated by a minimization of averaged incremental energy it is shown that the overall stresses and tangent moduli of a typical micro structure may exclusively be defined in terms of discrete forces and stiffness properties on the boundary we focus on deformation driven micro structures where the overall macroscopic deformation is controlled in this context three classical types of boundary conditions are investigated i linear deformation ii uniform tractions and iii periodic deformation and antiperiodic tractions incorporated by lagrangian multiplier methods these conditions generate three classes of constrained minimization problems with associated solution algorithms for the computation of equilibrium states and overall properties of micro structures the proposed algorithms and matrix representations of the overall properties are formally independent of the interior spatial structure and the local constitutive response of the micro structure and are therefore applicable to a broad class of model problems we demonstrate their performance for some representative model problems including finite elastic plastic deformations of composites texture developments in polycrystalline materials and equilibrium states of particle assemblies

a new solution procedure for application of energy conserving algorithms to general constitutive models in nonlinear elastodynamics abstract this paper develops a novel solution strategy for temporal discretization of initial value problems in nonlinear elastodynamics enabling exact energy and momentum conservation for a spatially discretized problem this new energy momentum algorithm fits into the general framework established by simo and tarnow z angew math phys 43 1992 757 however in contrast to the presentation given in that reference the current approach extends the critical stress update formula to encompass generic stored energy functions for the hyperelastic continuum in a manner which also allows for quadratically convergent newton raphson solution of the nonlinear algorithmic equations numerical examples using a neo hookean material model are given to illustrate the excellent performance of the proposed scheme not only is the new algorithm guaranteed to be second order accurate and unconditionally stable in the fully nonlinear regime as are other energy momentum strategies but also the approach advocated is demonstrated to be more robust and versatile than its predecessors

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

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

elastic plastic multiplicative decomposition with a stressed intermediate configuration abstract this paper presents an extension to the elastic plastic multiplicative decomposition to permit the origin in stress space to reside outside the closure of the elastic domain in this work the classical assumption of a stress free intermediate configuration is abandoned in favor of a new one where the intermediate configuration could be stressed this stress is identified as the maximal unloading point in stress space and denoted the plastic stress to motivate the discussion the infinitesimal plasticity model is considered first a remarkable result is obtained where for the case of linear elastic response the classical infinitesimal model is after some reinterpretation recovered the fully nonlinear model is developed and is shown to reduce to the classical one when the intermediate configuration is stress free the new framework is then applied to the case of j 2 plasticity where it is shown that when coupled with neo hookean elasticity as in the infinitesimal case after some reinterpretation the classical model is recovered i e the total stress is independent of the plastic stress numerical simulations are used to illustrate the importance of properly modeling the hardening behavior even during external loading in cases where load redistribution may take place

design sensitivity analysis in large deformation elasto plastic and elasto viscoplastic problems implicit time integration algorithm derived by simo for his large deformation elasto plastic constitutive model is generalized for the case of isotropy and associative flow rule towards viscoplastic material behaviour and consistently differentiated with respect to its input parameters combining it with the general formulation of design sensitivity analysis dsa for non linear finite element transient equilibrium problem we come at a numerically efficient closed form finite element formulation of dsa for large deformation elasto plastic and elasto viscoplastic problems with various types of design variables material constants shape parameters the paper handles several specific issues like the use of a non algorithmic coefficient matrix or sensitivity discontinuities at points of instantaneous structural stiffness change computational examples demonstrate abilities of the formulation and quality of results copyright 2005 john wiley sons ltd

some possible new directions for combinatorial matrix analysis using the facts that 1 much of the combinatorial matrix analysis to date has been concerned with properties of trees and 2 trees as digraphs have many important special properties we suggest several classes of matrices which can probably be successfully studied with the help of combinatorial methods these classes include the following a unipethic matrices a class derived by retaining the property that in the irreducible case the digraph defined in the usual way is strong and unipathic if it is a tree b bipartite matrices a class obtained by retaining the property that a tree is a bipartite digraph these matrices are closely related to 2 cyclic matrices but they are not the same class c matrices such that their digraph has at least one cycle of length p and no longer cycle these matrices are an obvious generalization of trees they are primarily of interest for small values of p relative to the size of the matrix d hessenberg matrices because their successive principal minors can be shown to always satisfy a difference equation and therefore a are one sort of generalization of the tridiagonal matrices outside of the class of trees e matrices which are such that the digraph is a k tree for k 1 in particular the 2 trees it is easy to show that k trees are a natural generalization of trees and they include the band matrices five diagonal matrices are for example 2 trees

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

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

on the localization properties of multiplicative hyperelasto plastic continua with strong discontinuities abstract the objective of this work is to examine the large strain localization properties of hyperelasto plastic materials which are based on the multiplicative decomposition of the deformation gradient thereby the case of strong discontinuities is investigated to this end first an explicit expression for the spatial tangent operator is given taking into account anisotropic as well as nonassociated material behaviour then the structure of a regularized discontinuous velocity gradient is elaborated and discussed in detail based on these two results the localization condition is derived with special emphasis on the loading conditions inside and outside an anticipated localization band thereby the intriguingly simple structure of the tangent operator which resembles the structure of the geometrically linear theory is extensively exploited this similarity carries over to the general representation for the critical hardening modulus which is exemplified for isotropic materials as a result analytical solutions are available under the assumption of small elastic strains which is justified for metals finally examples are given for the special case of the associated von mises flow rule to this end the critical localization direction and the critical hardening modulus are investigated with respect to the amount of finite elastic strain within different modes of homogeneous elasto plastic deformations

a cascade optimization methodology for automatic parameter identification and shape process optimization in metal forming simulation computer simulations of metal forming processes using the finite element method fem are today well established this form of simulation uses an increasing number of sophisticated geometrical and material models relying on a certain number of input data which are not always readily available the aim of inverse problems which will be considered here is to determine one or more of the input data relating to these forming process simulations thereby leading to a desired result in this paper we will focus on two categories of such inverse problems the first category consists of parameter identification inverse problems these involve evaluating the material parameters for material constitutive models that would lead to the most accurate results with respect to physical experiments i e minimizing the difference between experimental results and fem simulations the second category consists of shape process optimization inverse problems these involve determining the initial geometry of the specimen and or the shape of the forming tools as well as some parameters of the process itself in order to provide the desired final geometry after the forming process these two categories of inverse problems can be formulated as optimization problems in a similar way i e by using identical optimization algorithms in this paper we intend firstly to solve these two types of optimization problems by using different non linear gradient based optimization methods and secondly to compare their efficiency and robustness in a variety of numerical applications

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

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

model based control of dynamic frictional contact problems using the example of hot rolling abstract we consider hot forming processes in which a metal solid body is deformed by several rolls in order to obtain a desired final shape to minimize cutting scrap and to ensure that this shape satisfies the required tolerances as precisely as possible we formulate an optimal control problem where we use the trajectories of the rolls as control functions the deformation of the solid body is described through the basic equations of nonlinear continuum mechanics which are here coupled with an elasto viscoplastic material model based on a multiplicative split of the deformation gradient we assume that the deformations of the rolls can be neglected thus we add unilateral frictional contact boundary conditions resulting in an evolutionary quasi variational inclusion the associated control to observation map is non differentiable due to changes of state between elastic and plastic material behavior contact and separation and stick and slip motion yet we still want to apply gradient based methods to solve the optimal control problem and therefore have to make sure that derivatives of cost functional and constraints exist to resolve this issue we first regularize all non differentiabilities and subsequently apply the direct differentiation method to obtain sensitivity information finally we formulate a suitable algorithm and discuss numerical results for a real world example to illustrate its capability

quadrilateral elements for the solution of elasto plastic finite strain problems in this paper two plane strain quadrilateral elements with two and four variables are proposed these elements are applied to the analysis of finite strain elasto plastic problems the elements are based on the enhanced strain and b bar methodologies and possess a stabilizing term the pressure and dilatation fields are assumed to be constant in each element s domain and the deformation gradient is enriched with additional variables as in the enhanced strain methodology the formulation is deduced from a four field functional based on the imposition of two constraints annulment of the enhanced part of the deformation gradient and the relation between the assumed dilatation and the deformation gradient determinant the discretized form of equilibrium is presented and the analytical linearization is deduced to ensure the asymptotically quadratic rate of convergence in the newton raphson method the proposed formulation for the enhanced terms is carried out in the isoparametric domain and does not need the usually adopted procedure of evaluating the jacobian matrix in the centre of the element the elements are very effective for the particular class of problems analysed and do not present any locking or instability tendencies as illustrated by various representative examples copyright 2001 john wiley sons ltd

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

adaptive finite element methods in computational mechanics we present a general approach to adaptivity for finite element methods and give applications to linear elasticity non linear elasto plasticity and nonlinear conservation laws including numerical results

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

newton like methods with limited storage for the solution of elasto viscoplasticity problems quasi newton and secant newton methods have been successful in solving problems of elasto plasticity in this paper these methods are applied to elasto viscoplastic analyses in an algorithm coupling the global solution for displacement increments with local newton raphson stress iteration at each sampling point the familiar rank two dfp and bfgs methods are generalized to the broyden family of algorithms and this generalization is also used to produce a secant newton algorithm corresponding to hoshino s method consideration is given to the most effective strategy when only a limited number of quasi newton iterates may be stored overwriting re start or continuation in secant newton form results are presented for a tunnelling problem using both plane strain and axisymmetric formulations

numerical homogenization of periodic composite materials with non linear material components in this paper a numerically developed homogenized constitutive relation for the global behaviour of periodic composite materials with elasto plastic components is derived the algorithm presented is general and can be applied to any kind of non linear material behaviour respecting the complementarity rule the method different from those presented in the literature is currently restricted to small strains plane problems and monotonic proportional loading conditions copyright 1999 john wiley sons ltd

numerical integration of rate constitutive equations in finite deformation analysis abstract in analysis of finite deformation problems the use of constitutive equations in rate form is often required in a spatial setting these equations may express a relationship between some objective rate of spatial stress tensor and the rate of deformation constitutive equations of this type characterize a variety of material models including hyperelasticity hypoelasticity and elastoplasticity employing geometrical concepts a family of unconditionally stable and incrementally objective algorithms is proposed for the integration of such rate constitutive equations these algorithms which are appropriate for finite deformation analysis are applicable to any choice of stress rate and in most cases employ quantities that arise naturally in the context of finite element analysis examples illustrate the objectivity and accuracy of the algorithms

b and f projection methods for nearly incompressible linear and non linear elasticity and plasticity using higher order nurbs elements abstract this paper presents projection methods to treat the incompressibility constraint in small and large deformation elasticity and plasticity within the framework of isogeometric analysis after reviewing some fundamentals of isogeometric analysis we investigate the use of higher order non uniform rational b splines nurbs within the b projection method the higher continuity property of such functions is explored in nearly incompressible applications and shown to produce accurate and robust results a new non linear f projection method based on a modified minimum potential energy principle and inspired by the b method is proposed for the large deformation case it leads to a symmetric formulation for which the consistent linearized operator for fully non linear elasticity is derived and used in a newton raphson iterative procedure the performance of the methods is assessed on several numerical examples and results obtained are shown to compare favorably with other published techniques

the convected description in large deformation frictional contact problems abstract the converted description is introduced for finite deformation frictional contact problems such that both coulomb and more general friction criteria can be conveniently and reliably numerically implemented in lagrangian finite element calculations the discussion includes careful definition of the convected frame from the standpoint of differential geometry complete with physical interpretations of the frame and the associated slip and traction rate measures as demonstrated use of these measures enables prescription of frictional constitutive relationships with virtually no more complexity than is required by the kinematically linear theory while ensuring the required frame indifference of the description as a result the work provides a sound mathematical and continuum mechanical foundation for future implementations of general friction laws in large deformation solid mechanics computing architectures

decaying solution of the navier stokes flow of infinite volume without surface tension abstract in this short paper we report global existence and temporal decay properties for the solution of the navier stokes equations with free boundary describing the motion of infinite mass of viscous incompressible fluid without surface tension

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

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

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

three dimensional extension of non linear shell formulation based on the enhanced assumed strain concept conventional shell formulations such as 3 or 5 parameter theories or even 6 parameter theories including the thickness change as extra parameter require a condensation of the constitutive law in order to avoid a significant error due to the assumption of a linear displacement field across the thickness this means that the normal stress in thickness direction has to either vanish or be constant in general these extra constraints cannot be satisfied explicitly or they lead to elaborate strain expressions the main objective of the present study is to introduce directly a complete 3 d constitutive law without modification therefore a 7 parameter theory is utilized which includes a linear varying thickness stretch as extra variable allowing also large strain effects

anisotropic decay and global well posedness of viscous surface waves without surface tension abstract we consider a viscous incompressible fluid below the air and above a fixed bottom the fluid dynamics is governed by the gravity driven incompressible navier stokes equations and the effect of surface tension is neglected on the free surface the global well posedness and long time behavior of solutions near equilibrium have been intriguing questions since beale 1981 2 it was proved by guo and tice 2013 6 that with certain additional low horizontal frequency assumption of the initial data in 3d an integrable decay rate of the velocity is obtained so that the global unique solution can be constructed while the global well posedness in 2d was left open in this paper by exploiting the anisotropic decay rates of the velocity which are even not integrable we prove the global well posedness in both 2d and 3d without any low frequency assumption of the initial data one of key observations here is a cancellation in nonlinear estimates of the viscous stress tensor term in the bulk by using alinhac good unknowns when estimating the energy evolution of the highest order horizontal spatial derivatives of the solution