consistent tangent matrices for substepping schemes a very simple and general expression of the consistent tangent matrix for substepping time integration schemes is presented if needed the derivatives required for the computation of the consistent tangent moduli can be obtained via numerical differentiation these two strategies substepping and numerical differentiation lead to quadratic convergence in complex nonlinear inelasticity problems

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

towards idempotent reduced density matrices via particle hole duality mcweeny s purification and beyond generalizations of mcweeny s purification formula are developed within the formalism of the particle hole duality from the theory of reduced density matrices each of the generalized purification formulas is expressed as a sum of the one particle reduced density matrix 1 rdm and a finite series in the product of the one particle and the one hole rdms a product which vanishes in the limit that the 1 rdm is idempotent two categories of purification formulas are explored i formulas which treat the occupied and the virtual occupation numbers equivalently and ii formulas which treat these occupation numbers differently the latter category includes and extends the purification formulas derived in the context of the 1 2 contracted schrodinger equation d a mazziotti j chem phys 115 8305 2001 while the mcweeny purification minimizes the absolute error in the occupation numbers quadratically the generalized purification formulas exhibit faster than quadratic convergence of the 1 rdm towards idempotency application of these purification formulas in existing algorithms for linear scaling will be explored and discussed including illustrative calculations on sodium wires of length 10 20 30 and 40 atoms

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

solution procedures for j3 plasticity and viscoplasticity abstract a solution strategy for plasticity and viscoplasticity models with isotropic yield surfaces depending upon all the principal invariants of the stress tensor is presented basically it requires the inversion of a fourth order positive definite tensor g both for the solution of the constitutive problem and for the evaluation of the consistent tangent operator it is proved that the assumption of isotropic elastic behaviour and the isotropy of the yield criterion entail an explicit representation formula for g 1 as linear combination of dyadic and square tensor products further an analogous representation formula for the consistent tangent operator is provided by exploiting basic composition rules between dyadic and square tensor products along with rivlin s identities for tensor polynomials all tensor operations required to compute the coefficients of the adopted representation formula for g 1 are carried out in intrinsic form it is thus shown that the relevant computational burden essentially amounts to solving a linear system of order three the performances of the proposed approach are illustrated by means of some numerical examples referred to the argyris failure criterion

on non corotational rates of oldroyd s type and relevant issues in rate constitutive formulations the lower and upper oldroyd rates are two wellknown objective noncorotational rates a remarkable property of these rates is that they establish direct relationships between finite strain measures

a novel approach to the solution of the tensor equation ax xa h a systematic approach to the solution of the tensor equation ax xa h where a is symmetric is presented it is based upon the reformulation of the original equation in the form ax h where a a 1 1 a is the fourth order tensor obtained from the square tensor product of the second order tensors a and 1 it is shown that the solution x which is known to be an isotropic function of a and h can be effectively obtained either by providing explicit formulas for a 1 or by reconverting to the format ax h the well known representation formulas for tensor valued isotropic functions the final form of the solution can thus be established a priori by suitably choosing a set of independent generators for a 1 the coefficients of the expansion of a 1 with respect to the assigned generators are then obtained by means of basic composition rules for square tensor products in this way it is possible to provide new expressions of the solution as well as to derive the existing ones in a simpler way both three dimensional and two dimensional cases are addressed in detail

two point constitutive equations and integration algorithms for isotropic hardening rate independent elastoplastic materials in large deformation this paper presents alternative forms of hyperelastic plastic constitutive equations and their integration algorithms for isotropic hardening materials at large strain which are established in two point tensor field namely between the first piola kirchhoff stress tensor and deformation gradient the eigenvalue problems for symmetric and non symmetric tensors are applied to kinematics of multiplicative plasticity which imply the transformation relationships of eigenvectors in current intermediate and initial configurations based on the principle of plastic maximum dissipation the two point hyperelastic stress strain relationships and the evolution equations are achieved in which it is considered that the plastic spin vanishes for isotropic plasticity on the computational side the exponential algorithm is used to integrate the plastic evolution equation the return mapping procedure in principal axes with respect to logarithmic elastic strain possesses the same structure as infinitesimal deformation theory then the theory of derivatives of non symmetric tensor functions is applied to derive the two point closed form consistent tangent modulus which is useful for newton s iterative solution of boundary value problem finally the numerical simulation illustrates the application of the proposed formulations

variationally consistent modeling of finite strain plasticity theory with non linear kinematic hardening abstract variational constitutive updates provide a physically and mathematically sound framework for the numerical implementation of material models in contrast to conventional schemes such as the return mapping algorithm they are directly and naturally based on the underlying variational principle hence the resulting numerical scheme inherits all properties of that principle in the present paper focus is on a certain class of those variational methods which relies on energy minimization consequently the algorithmic formulation is governed by energy minimization as well accordingly standard optimization algorithms can be applied to solve the numerical problem a further advantage compared to conventional approaches is the existence of a natural distance semi metric induced by the minimization principle such a distance is the foundation for error estimation and as a result for adaptive finite elements methods though variational constitutive updates are relatively well developed for so called standard dissipative solids i e solids characterized by the normality rule the more general case i e generalized standard materials is far from being understood more precisely int j sol struct 2009 46 1676 1684 represents the first step towards this goal in the present paper a variational constitutive update suitable for a class of nonlinear kinematic hardening models at finite strains is presented two different prototypes of armstrong frederick type are re formulated into the aforementioned variationally consistent framework numerical tests demonstrate the consistency of the resulting implementation

on the curvature of piecewise flat spaces we consider analogs of the lipschitz killing curvatures of smooth riemannian manifolds for piecewise flat spaces in the special case of scalar curvature the definition is due to t regge considerations in this spirit date back to j steiner we show that if a piecewise flat space approximates a smooth space in a suitable sense then the corresponding curvatures are close in the sense of measures

a return mapping algorithm for plastic damage models 3 d and plane stress formulation three dimensional and plane stress formulations of the return mapping algorithm for a class of plastic damage models are derived using the spectral decomposition form of the stress an efficient plane stress computation scheme based on the spectral return mapping algorithm is developed the consistent algorithmic tangent stiffness for the present algorithm is formulated the validation and performance of the present return mapping algorithm is demonstrated by numerical examples copyright 2001 john wiley sons ltd

yield criteria for quasibrittle and frictional materials a generalization to surfaces with corners abstract convexity of a yield function or phase transformation function and its relations to convexity of the corresponding yield surface or phase transformation surface is essential to the invention definition and comparison with experiments of new yield or phase transformation criteria this issue was previously addressed only under the hypothesis of smoothness of the surface but yield surfaces with corners for instance the hill tresca or coulomb mohr yield criteria are known to be of fundamental importance in plasticity theory the generalization of a proposition relating convexity of the function and the corresponding surface to nonsmooth yield and phase transformation surfaces is provided in this paper together with the necessary to the proof extension of a theorem on nonsmooth elastic potential functions while the former of these generalizations is crucial for yield and phase transformation functions the latter may find applications for potential energy functions describing phase transforming materials or materials with discontinuous locking in tension or contact of a body with a discrete elastic frictional support

level set approach to mean curvature flow in arbitrary codimension we develop a level set theory for the mean curvature evolution of surfaces with arbitrary co dimension thus generalizing the previous work 8 15 on hypersurfaces the main idea is to surround the evolving surface of co dimension k in r by a family of hypersurfaces the level sets of a function evolving with normal velocity equal to the sum of the d k smallest principal curvatures the existence and the uniqueness of a weak level set solution is easily established using mainly the results of 8 and the theory of viscosity solutions for second order nonlinear parabolic equations the level set solutions coincide with the classical solutions whenever the latter exist the proof of this connection uses a careful analysis of the squared distance from the surfaces it is also shown that varifold solutions constructed by brakke 7 are included in the level set solutions the idea of surrounding the evolving surface by a family of hypersurfaces with a certain property is related to the barriers of de giorgi an introduction to the theory of barriers and his connection to the level set solutions is also provided

ordinary and strong ellipticity in the equilibrium theory of incompressible hyperelastic solids in this paper explicit necessary and sufficient conditions are established for the ordinary and strong ellipticity of the three dimensional field equations in the nonlinear equilibrium theory of incompressible homogeneous and isotropic hyperelastic solids the resulting system of inequalities involves the local principal stretches directly and in addition restricts the first and second partial derivatives of the strain energy density with respect to the deformation invariants or the principal stretches the conditions of ordinary and strong ellipticity are found to coalesce for materials that obey the baker ericksen inequalities and possess a positive shear modulus at infinitesimal deformations various implications of these ellipticity conditions for special classes of materials and deformations are explored

ellipticity and deformations with discontinuous gradients in finite elastostatics loss of ellipticity of the equilibrium equations of finite elastostatics is closely related to the possible emergence of elastostatic shocks i e deformations with discontinuous gradients in certain situations where constitutive response functions are essentially one dimentional such as anti plane shear or bar theories strong ellipticity is closely related to convexity of the elastic potential and invertibility of certain constitutive response functions the present work addresses the analogous issues within the context of three dimensional elastostatics of compressible but not necessarily isotropic hyperelastic materials a certain direction dependent resolution of the deformation gradient is introduced and its existence and uniqueness for a given direction are established the elastic potential is expressed as a function of kinematic variables arising from this resolution strong ellipticity is shown to be equivalent to the positive definiteness of the hessian matrix of this function thus sufficing for its strict convexity the underlying variables are interpretable physically as simple shears and extensions their work conjugates define a traction response mapping it is shown that discontinuous deformation gradients are sustainable if and only if this mapping fails to be invertible this result is explicit in the sense that it characterizes the set of all possible piecewise homogeneous deformations given the elastic potential function

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

universal anisotropic yield criterion based on superquadric functional representation part 1 algorithmic issues and accuracy analysis abstract a robust and efficient stress update algorithm for the anisotropic yield criterion represented in the form of superquadric function introduced by barlat et al is presented it relies on a discrete variational formulation of the lagrangian functional which results from the principle of maximum plastic dissipation numerical solution of the discretized equations of evolution is based on the operator split methodology and the newton raphson method a line search algorithm is implemented to overcome numerical instabilities and to expand the convergence region of the basic newton raphson solution procedure the consistent tangent modulus is expressed in a closed form as a result of the exact linearization of the discrete kuhn tucker condition numerical testing of the integration algorithm based on iso error maps is provided for several variants of the yield function

brownian motion in cones we study the asymptotic behavior of brownian motion and its conditioned process in cones using an infinite series representation of its transition density a concise probabilistic interpretation of this series in terms of the skew product decomposition of brownian motion is derived and used to show properties of the transition density

witt spaces a geometric cycle theory for ko homology at odd primes introduction this paper studies a class of stratified piecewiselinear pseudomanifolds which we call witt spaces characterized by natural local intersection homology conditions 11 we compute the cobordism groups by introducing an invariant taking values in the witt group of symmetric bilinear forms over the rationals w q these pseudomanifolds solve a problem posed by d sullivan 25 to construct a class of p l cycles with signature which represent the connected version of ko homology at odd primes ko 0d z 1 2 the result was one of the first applications of the intersection homology theory of goresky and macpherson 11 specifically the rational intersection homology groups of witt spaces satisfy a poincare duality theorem to each witt space x we associate a p l invariant w x with values in w q this invariant generalizes the signature of manifolds and satisfies cobordism invariance additivity and a product formula adapting classical surgery spherical modification to this setting we prove that w x determines the cobordism class of x and obtain an explicit description of the witt cobordism groups the only nontrivial groups occur in dimensions 4k and for k 0 they are w q sullivan 25 27 has shown that a class of p l pseudomanifolds equipped with such an invariant possesses canonical orientations in ko 0 z 1 2 the orientations induce a natural transformation it of homology theories from witt space bordism to ko 0 z 1 2 the structure of w q is known 14 and we conclude that it is an equivalence at odd primes in this paper we study the cobordism theory of a class of stratified p l pseudomanifolds by means of the recent intersection homology theory of goresky and macpherson 11 goresky and macpherson were interested in finding a class of spaces with cobordism invariant signature for the purpose of extending the hirzebruch l class to the setting of manifolds with

derivation of the fourth order tangent operator based on a generalized eigenvalue problem continuous and algorithmic forms of the fourth order tangent operator corresponding to isotropic multiplicative elasto plasticity are derived by generalizing an approach originally developed for finite elasticity the lagrangian description of large strain elasto plasticity leads to a generalized eigenvalue problem which facilitates certain tensor representations with respect to a reciprocal set of left and right eigenvectors the tangent operators take an extremely simple form due to the resolution in the basis spanned by the right eigenvectors remarkably these new developments reveal that the algorithmic version of the tangent operator preserves the structure of the continuous counterpart

consistent derivation of the constitutive algorithm for plane stress isotropic plasticity part ii computational issues abstract the implementation of the projected algorithm and of the consistent tangent tensor for general isotropic three invariant elastoplastic models under plane stress conditions discussed in part i of this paper valoroso n rosati l 2008 consistent derivation of the constitutive algorithm for plane stress isotropic plasticity part i theoretical formulation international journal of solids and structures doi 10 1016 j ijsolstr 2008 08 012 is addressed the connections between the general three dimensional case and the plane stress problem are analyzed in detail and an algorithmic treatment taking full advantage of the isotropic properties of the model is presented in particular intrinsic matrix free expressions are provided for all steps of the stress computation scheme that allow one to carry out the numerical implementation in a way that is completely independent from the matrix representations the numerical performances of the present solution scheme are evaluated through representative numerical examples

a unified exact analysis for the poynting effects of cylindrical tubes made of hill s class of hookean compressible elastic materials at finite strain abstract a direct natural extension of hooke s law to finite strain was achieved by r hill in 1978 employing the notion of work conjugate measures of stress and strain with seth hill doyle ericksen class of finite strain measures this extension actually defines a broad class of compressible hyperelastic materials at finite strain each of which retains the simple linear structure of hooke s law as stress strain relationship several known simple elasticity models at finite strain are included as its particular examples with a novel idea of utilizing a suitable parametric variable here we present a unified study of the free end torsion problem poynting effects of thin walled cylindrical tubes made of the foregoing hill s class of hookean type hyperelastic materials we show that it is possible to derive a unified exact solution to the nonlinear coupling equations relating the torque the shear stress and the controlling deformation quantities including in particular the axial length change discussions and comparisons concerning various hookean type elasticity models are made based on the exact solution obtained

fast spectral projection algorithms for density matrix computations we present a fast algorithm for the construction of a spectral projector this algorithm allows us to compute the density matrix as used in e g the kohn sham iteration and so obtain the electron density we compute the spectral projector by constructing the matrix sign function through a simple polynomial recursion we present several matrix representations for fast computation within this recursion using bases with controlled space spatial frequency localization in particular we consider wavelet and local cosine bases since spectral projectors appear in many contexts we expect many additional applications of our approach

an automatic load stepping algorithm with error control summary this paper presents an algorithm for controlling the error in non linear finite element analysis which is caused by the use of finite load steps in contrast to most recent schemes the proposed technique is non iterative and treats the governing load deflection relations as a system of ordinary differential equations this permits the governing equations to be integrated adaptively where the step size is controlled by monitoring the local truncation error the latter is measured by computing the difference between two estimates of the displacement increments for each load step with the initial estimate being found from the first order euler scheme and the improved estimate being found from the second order modified euler scheme if the local truncation error exceeds a specified tolerance then the load step is abandoned and the integration is repeated with a smaller load step whose size is found by local extrapolation local extrapolation is also used to predict the size of the next load step following a successful update in order to control not only the local load path error but also the global load path error the proposed scheme incorporates a correction for the unbalanced forces overall the cost of the automatic error control is modest since it requires only one additional equation solution for each successful load step because the solution scheme is non iterative and founded on successful techniques for integrating systems of ordinary differential equations it is particularly robust to illustrate the ability of the scheme to constrain the load path error to lie near a desired tolerance detailed results are presented for a variety of elastoplastic boundary value problems

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 stabilized mixed finite element method for finite elasticity formulation for linear displacement and pressure interpolation abstract a stabilized mixed finite element method for finite elasticity is presented the method circumvents the fulfillment of the ladyzenskaya babuska brezzi condition by adding mesh dependent terms which are functions of the residuals of the euler lagrange equations to the usual galerkin method the weak form and the linearized weak form are presented in terms of the reference and current configuration numerical experiments using a tetrahedral element with linear shape functions for the displacements and for the pressure show that the method successfully yields a stabilized element

anisotropic elastic plastic analysis of shells at large strains a comparison of multiplicative and additive approaches to enhanced finite element design and constitutive modelling the article presents new aspects of large strain anisotropic elastoplastic analyses of shells on the side of computational shell analysis we focus on recently developed brick type mixed finite shell elements based on trilinear displacement interpolations equipped with enhanced strain modes and shell typical assumed strain modifications here we compare two classes of this shell element design based on a multiplicative and an additive definition of an enhanced strain measure respectively furthermore for both types of continuum based shell elements we outline unified interfaces to strain driven constitutive stress update algorithms of anisotropic finite plasticity on the side of computational plasticity we investigate two classes of constitutive models suitable for the description of anisotropic elastoplastic response at finite strains the first framework uses a multiplicative definition of an elastic strain measure based on a plastic map the second an additively defined elastic strain measure based on a plastic metric both constitutive frameworks use hencky type logarithmic strain measures and are specified to a model problem of orthotropic elastic plastic response of a standard material the algorithmic treatment of the two constitutive models is based on an incremental variational formulation that defines the stresses and consistent tangent moduli in terms of a function evaluation we compare the performances of the two finite element formulations and the two constitutive models by means of numerical simulations of sheet drawing processes for the range of metal plasticity at moderate strains it is shown that results obtained with the different approaches are close to each other while the additive approaches provide simpler and more efficient settings copyright 2004 john wiley sons ltd

on the formulation of closest point projection algorithms in elastoplasticity part ii globally convergent schemes this paper presents the formulation of numerical algorithms for the solution of the closest point projection equations that appear in typical implementations of return mapping algorithms in elastoplasticity the main motivation behind this work is to avoid the poor global convergence properties of a straight application of a newton scheme in the solution of these equations the so called newton cppm the mathematical structure behind the closest point projection equations identified in part i of this work delineates clearly different strategies for the successful solution of these equations in particular primal and dual closest point projection algorithms are proposed in non augmented and augmented lagrangian versions for the imposition of the consistency condition the primal algorithms involve a direct solution of the original closest point projection equations whereas the dual schemes involve a two level structure by which the original system of equations is staggered with the imposition of the consistency condition driving alone the iterative process newton schemes in combination with appropriate line search strategies are considered resulting in the desired asymptotically quadratic local rate of convergence and the sought global convergence character of the iterative schemes these properties together with the computational performance of the different schemes are evaluated through representative numerical examples involving different models of finite strain plasticity in particular the avoidance of the large regions of no convergence in the trial state observed in the standard newton cppm is clearly illustrated

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

a simple constitutive relationship for isotropic solids with stress state type dependent properties abstract the general form of the relationships between two symmetric coaxial tensors of second rank in an isotropic medium is considered the condition under which the simple tensor linear form of these relationships which includes the lode s angle can be used is determined the range of validity of the proposed relationships is studied by means of drucker s stability postulate and the existence and uniqueness conditions of the generalised solution of the problems the applications that are built on the proposed form of the constitutive relationships that cover creep plastic and behaviour are given briefly

a sparse approximate inverse preconditioner for the conjugate gradient method a method for computing a sparse incomplete factorization of the inverse of a symmetric positive definite matrix a is developed and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient calculations it is proved that in exact arithmetic the preconditioner is well defined if a is an h matrix the results of numerical experiments are presented

calculus on surfaces with general closest point functions the closest point method for solving partial differential equations pdes posed on surfaces was recently introduced by ruuth and merriman j comput phys 227 2008 pp 1943 1961 and successfully applied to a variety of surface pdes in this paper we study the theoretical foundations of this method the main idea is that surface differentials of a surface function can be replaced with cartesian differentials of its closest point extension i e its composition with a closest point function we introduce a general class of these closest point functions a subset of differentiable retractions show that these are exactly the functions necessary to satisfy the above idea and give a geometric characterization of this class finally we construct some closest point functions and demonstrate their effectiveness numerically on surface pdes

spectral geometry of singular riemannian spaces on considere la trace du noyau de la chaleur et l application de la methode de l equation de la chaleur au theoreme d indice pour la caracteristique d euler et des complexes signatures

a return map algorithm for general isotropic elasto visco plastic materials in principal space we describe a methodology for solving the constitutive problem and evaluating the consistent tangent operator for isotropic elasto visco plastic models whose yield function incorporates the third stress invariant the developments presented are based upon original results proved in the paper concerning the derivatives of eigenvalues and eigenprojectors of symmetric second order tensors with respect to the tensor itself and upon an original algebra of fourth order tensors obtained as second derivatives of isotropic scalar functions of a symmetric tensor argument the analysis initially referred to the small strain case is then extended to a formulation for the large deformation regime for both cases we provide a derivation of the consistent tangent tensor which shows the analogy between the two formulations and the close relationship with the tangent tensors of the lagrangian description of large strain elastoplasticity copyright 2004 john wiley sons ltd

groupoids and an index theorem for conical pseudo manifolds we define an analytical index map and a topological index map for conical pseudomanifolds these constructions generalize the analogous constructions used by atiyah and singer in the proof of their topological index theorem for a smooth compact manifold m a main ingredient is a non commutative algebra that plays in our setting the role of c 0 t m we prove a thom isomorphism between non commutative algebras which gives a new example of wrong way functoriality in k theory we then give a new proof of the atiyah singer index theorem using deformation groupoids and show how it generalizes to conical pseudomanifolds we thus prove a topological index theorem for conical pseudomanifolds

numerical methods for electronic structure calculations of materials the goal of this article is to give an overview of numerical problems encountered when determining the electronic structure of materials and the rich variety of techniques used to solve these problems the paper is intended for a diverse scientific computing audience for this reason we assume the reader does not have an extensive background in the related physics our overview focuses on the nature of the numerical problems to be solved their origin and the methods used to solve the resulting linear algebra or nonlinear optimization problems it is common knowledge that the behavior of matter at the nanoscale is in principle entirely determined by the schrodinger equation in practice this equation in its original form is not tractable successful but approximate versions of this equation which allow one to study nontrivial systems took about five or six decades to develop in particular the last two decades saw a flurry of activity in developing effective software one of the main practical variants of the schrodinger equation is based on what is referred to as density functional theory dft the combination of dft with pseudopotentials allows one to obtain in an efficient way the ground state configuration for many materials this article will emphasize pseudopotential density functional theory but other techniques will be discussed as well

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

controlling errors in recursive fermi dirac operator expansions with applications in electronic structure theory recursive fermi dirac operator expansion is an efficient way to compute one electron density matrices in electronic structure theory the convergence is rapid and depends only weakly on the conditioning of the problem and for many systems the computational cost increases only linearly with system size in this article errors introduced when evaluating the recursive expansion are analyzed and schemes to control the forward error are proposed the error has previously been analyzed for explicit schemes working at zero electronic temperature j chem phys 128 2008 074106 here implicit schemes phys rev b 68 2003 233104 working at zero or finite temperature are treated the proposed schemes for error control are demonstrated by tight binding as well as density functional theory electronic structure calculations on several test systems condition numbers for the problem of computing the density matrix are derived giving quantitative insight into under what circumstances a temperature dependent formulation results in better conditioning it is shown that for the considered recursive expansions the number of matrix matrix multiplications needed to compute the density matrix increases only with the squared logarithm of the condition number of the problem

a family of metric strains and conjugate stresses prolonging usual material laws from small to large transformations abstract a new family of simple generalized strains and conjugate stresses based on the material metric right cauchy green tensor is proposed it includes an interesting quasilinear pair it is a close approximation of the seth hill family with the advantage of being easier to calculate it extends the realm of application of the classical theories of linear elasticity and perfect plasticity from small to large transformations for isotropic and anisotropic materials without any modification

hill s class of compressible elastic materials and finite bending problems exact solutions in unified form abstract hill 1978 proposed a natural extension of hooke s law to finite deformations with all seth hill finite strains hill s natural extension presents a broad class of compressible hyperelastic materials over the whole deformation range we show that a number of known hookean type finite hyperelasticity models are included as particular cases in hill s class and that bell s and ericksen s constraints may be derived as natural consequences from hill s class subjected to internal constraints also we present a unified study of finite bending problems for elastic hill materials to date exact results are available for certain particular classes of compressible elastic materials which do not cover hill s class here with a novel idea of circumventing the strong nonlinearity we show that it is possible to derive exact solutions in unified form for the whole class of elastic hill materials reduced results are also given for cases subjected to internal constraints

heat kernel bounds for second order elliptic operators on riemannian manifolds 1 introduction we investigate the relationship between ultracontractive bounds on heat kernels weighted sobolev inequalities and logarithmic sobolev inequalities in a more general context than previously we find conditions which imply these bounds for a wide class of second order elliptic operators on manifolds we apply our result to laplacebeltrami operators on manifolds with cusps and to operators on a manifold whose coefficients become degenerate or infinite on the boundary of the manifold in an earlier paper with b simon 11 we introduced the notion of intrinsic ultracontractivity for schrodinger operators on rn and for the dirichlet laplacian on certain regions q in rn kusuoka and stroock 13 independently discovered the same phenomena for a somewhat different class of operators using a probabilistic intuition at the end of their paper they remarked that their ideas could be extended to manifolds with

stabilized and block approximate inverse preconditioners for problems in solid and structural mechanics the solution of linear systems arising in the finite element analysis of shells and solids by the preconditioned conjugate gradient method is considered stabilized and block versions of the ainv factorized approximate inverse preconditioner are presented and tested on a variety of difficult problems comparisons with other preconditioning methods are also included

variational h adaption in finite deformation elasticity and plasticity we ropose a variational h adaption strategy in which the evolution of the mesh is driven directly by the governing minimum principle this minimum principle is the principle of minimum potential energy in the case of elastostatics and a minimum principle for the incremental static problem of elasto viscoplasticity in particular the mesh is refined locally when the resulting energy or incremental pseudo energy released exceeds a certain threshold value in order to avoid global recomputes we estimate the local energy released by mesh refinement by means of a lower bound obtained by relaxing a local patch of elements this bound can be computed locally which reduces the complexity of the refinement algorithm to o n we also demonstrate how variational h refinement can be combined with variational r refinement to obtain a variational hr refinement algorithm because of the strict variational nature of the h refinement algorithm the resulting meshes are anisotropic and outperform other refinement strategies based on aspect ratio or other purely geometrical measures of mesh quality the versatility and rate of convergence of the resulting approach are illustrated by means of selected numerical examples copyright 2007 john wiley sons ltd

diffusion generated motion of curves on surfaces we present a new method for computing the curvature driven motion of a curve constrained to move on a given surface it is based on the diffusion generated motion algorithm and retains both the novel simplicity of that method as well as the natural extension to curves with junctions to general geometric motion laws and to higher dimensions the result is an extremely simple algorithm for curvature dependent motion on surfaces wherein the only evolution operation is linear diffusion in three dimensional euclidean space

linearization and return mapping algorithms for elastoplasticity models the return mapping algorithm is one of the most efficient procedures to solve elasto plastic problems however a criticism that may be lodged against this method is the difficulty of the practical computation of the consistent tangent matrix when the return is non radial much research has been done to handle this matrix in this paper a unified approach is presented in such a way that a simple closed form expression gives the consistent tangent matrix for the classical constitutive relations von mises tresca mohr coulomb drucker prager the basic ideas are in the properties of eikonal equations appearing in several fields as image treatment short time computation in elastic waves and others the same kinds of ideas can be extended to non classical models copyright 2003 john wiley sons ltd

the implicit closest point method for the numerical solution of partial differential equations on surfaces many applications in the natural and applied sciences require the solutions of partial differential equations pdes on surfaces or more general manifolds the closest point method is a simple and accurate embedding method for numerically approximating pdes on rather general smooth surfaces however the original formulation is designed to use explicit time stepping this may lead to a strict time step restriction for some important pdes such as those involving the laplace beltrami operator or higher order derivative operators to achieve improved stability and efficiency we introduce a new implicit closest point method for surface pdes the method allows for large stable time steps while retaining the principal benefits of the original method in particular it maintains the order of accuracy of the discretization of the underlying embedding pde it works on sharply defined bands without degrading the accuracy of the method and it applies to general smooth surfaces it also is very simple and may be applied to a rather general class of surface pdes convergence studies for the in surface heat equation and a fourth order biharmonic problem are given to illustrate the accuracy of the method we demonstrate the flexibility and generality of the method by treating flows involving diffusion reaction diffusion and fourth order spatial derivatives on a variety of interesting surfaces including surfaces of mixed codimension

on the formulation of closest point projection algorithms in elastoplasticity part i the variational structure we present in this paper the characterization of the variational structure behind the discrete equations defining the closest point projection approximation in elastoplasticity rate independent and viscoplastic formulations are considered in the infinitesimal and the finite deformation range the later in the context of isotropic finite strain multiplicative plasticity primal variational principles in terms of the stresses and stress like hardening variables are presented first followed by the formulation of dual principles incorporating explicitly the plastic multiplier augmented lagrangian extensions are also presented allowing a complete regularization of the problem in the constrained rate independent limit the variational structure identified in this paper leads to the proper framework for the development of new improved numerical algorithms for the integration of the local constitutive equations of plasticity as it is undertaken in part ii of this work

the choice of objective rates in finite elastoplasticity general results on the uniqueness of the logarithmic rate a eulerian rate formulation of finite elastoplasticity is a composite one composed of a rate equation for elastic behaviour and a flow rule for plastic behaviour as well as an evolution equation for hardening behaviour in which objective eulerian tensor rates are used among a large variety of objective rates actually infinitely many how to choose suitable ones has been one of the crucial points in finite elastoplasticity it is realized that the foregoing composite formulation of elastoplasticity should fulfil certain consistency criteria in order to avoid inconsistencies or contradictions these criteria narrow the choice of objective rates these authors bruhns and co workers and xiao and co workers have recently introduced the self consistency criterion in a composite formulation of elastoplasticity the rate equation intended for characterization of elastic behaviour should be exactly integrable to deliver an elastic relation it has been demonstrated in the work of the aforementioned authors that if a composite formulation of elastoplasticity with objective rates is required to fulfil the just stated self consistency criterion as it should be then the newly discovered logarithmic rate is the only possible choice among all objective corotational rates including the zaremba jaumann rate and the green naghdi rate etc in the afore mentioned result non corotational rates including oldroyd rates cotter rivlin rate and truesdell rate etc are not taken into consideration in general it is the main goal of this paper to further establish the uniqueness of the logarithmic rate among all corotational and non corotational objective rates essential to the attainment of this goal is the use of the yielding stationarity criterion the vanishing of the stress rate implies that the yield function is stationary it is shown that the just stated criterion is necessary for a composite eulerian rate formulation of finite elastoplasticity to be consistent and means that the stress rate must be a corotational rate the main goal of this article is thus attained by combining the just stated result and the established result stated before

galerkin based mechanical integrators for finite elastodynamics formulated in principal stretches pitfalls and remedies in the present paper we deal with integrators relying on finite elements in time for general hyperelastic models which guarantee the conservation of the momentum maps as well as of the total energy within the calculation accuracy in the isotropic case eigenvalue based constitutive laws are on the one hand very significant to model the behaviour of various materials on the other hand it will be shown that the efficient algorithmic treatment of principal stretches based on a perturbation approach requires especially within the context of conserving schemes advanced techniques to circumvent numerical problems accordingly we propose an adequate solution strategy to avoid potential pitfalls which are related to numerical artefacts of the applied non standard quadrature rule finally the excellent numerical and mechanical performance of the resulting galerkin based time stepping schemes will be demonstrated by means of representative numerical examples

finite element implementation of non linear elastoplastic constitutive laws using local and global explicit algorithms with automatic error control implicit stress integration algorithms have been demonstrated to provide a robust formulation for finite element analyses in computational mechanics but are difficult and impractical to apply to increasingly complex non linear constitutive laws this paper discusses the performance of fully explicit local and global algorithms with automatic error control used to integrate general non linear constitutive laws into a non linear finite element computer code the local explicit stress integration procedure falls under the category of return mapping algorithm with standard operator split and does not require the determination of initial yield or the use of any form of stress adjustment to prevent drift from the yield surface the global equations are solved using an explicit load stepping with automatic error control algorithm in which the convergence criterion is used to compute automatically the coarse load increment size the proposed numerical procedure is illustrated here through the implementation of a set of elastoplastic constitutive relations including isotropic and kinematic hardening as well as small strain hysteretic non linearity a series of numerical simulations confirm the robustness accuracy and efficiency of the algorithms at the local and global level published in 2001 by john wiley sons ltd

strichartz estimates and wave equation in a conic singular space consider the metric cone x c y 0 infty r times y with metric g dr 2 r 2h where the cross section y is a compact n 1 dimensional riemannian manifold y h let delta g be the positive friedrichs extension laplacian on x and let delta h be the positive laplacian on y and consider the operator mathcal l v delta g v 0 r 2 where v 0 in mathcal c infty y such that delta h v 0 n 2 2 4 is a strictly positive operator on l 2 y in this paper we prove global in time strichartz estimates without loss regularity for the wave equation associated with the operator mathcal l v it verifies a conjecture in wang remark 2 4 in ann inst fourier 56 1903 1945 2006 for wave equation the range of the admissible pair is sharp and the range is influenced by the smallest eigenvalue of delta h v 0 n 2 2 4 to prove the result we show a sobolev inequality and a boundedness of a generalized riesz transform in this setting in addition as an application we study the well posed theory and scattering theory for energy critical wave equation with small data on this setting of dimension n ge 3

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

on copositive matrices and strong ellipticity for isotropic elastic materials on etablit les conditions necessaires et suffisantes pour une forte ellipticite des equations d un materiau elastique non lineaire isotrope compressible a l equilibre on utilise un theoreme de representation de matrices copositives du a cottle habetler et lemke 1970

a mixed tetrahedral element with nodal rotations for large displacement analysis of inelastic structures summary a novel mixed four node tetrahedral finite element equipped with nodal rotational degrees of freedom is presented its formulation is based on a hu washizu type functional suitable to the treatment of material nonlinearities rotation and skew symmetric stress fields are assumed as independent variables the latter entering the functional to impose rotational compatibility and suppress spurious modes exploiting the choice of equal interpolation for strain and symmetric stress fields a robust element state determination procedure requiring no element level iteration is proposed the mixed element stability is assessed by means of an original and effective numerical test the extension of the present formulation to geometric nonlinear problems is achieved through a polar decomposition based corotational framework after validation in both material and geometric nonlinear context the element performances are investigated in demanding simulations involving complex shape memory alloy structures supported by the comparison with available linear and quadratic tetrahedrons and hexahedrons the numerical results prove accuracy robustness and effectiveness of the proposed formulation copyright 2016 john wiley sons ltd

interior eigenvalues from density matrix expansions in quantum mechanical molecular dynamics an accelerated polynomial expansion scheme to construct the density matrix in quantum mechanical molecular dynamics simulations is proposed the scheme is based on recursive density matrix expansions e g a m n niklasson phys rev b 66 2002 155115 which are accelerated by a scale and fold technique e h rubensson j chem theory comput 7 2011 pp 1233 1236 the acceleration scheme requires interior eigenvalue estimates which may be expensive and cumbersome to come by here we show how such eigenvalue estimates can be extracted from the recursive expansion by a simple and robust procedure at a negligible computational cost our method is illustrated with density functional tight binding born oppenheimer molecular dynamics simulations where the computational effort is dominated by the density matrix construction in our analysis we identify two different phases of the recursive polynomial expansion the conditioning and purification phases and we show that the acceleration repres

on the numerical integration of three invariant elastoplastic constitutive models abstract we investigate the performance of a numerical algorithm for the integration of isotropically hardening three invariant elastoplastic constitutive models with convex yield surfaces the algorithm is based on a spectral representation of stresses and strains for infinitesimal and finite deformation plasticity and a return mapping in principal stress directions smooth three invariant representations of the mohr coulomb model such as the lade duncan and matsuoka nakai models are implemented within the framework of the proposed algorithm among the specific features incorporated into the formulation are the hardening softening responses and the tapering of the yield surfaces toward the hydrostatic axis with increasing confining pressure isoerror maps are generated to study the local accuracy of the numerical integration algorithm finally a boundary value problem involving loading of a strip foundation on a soil is analyzed with and without finite deformation effects to investigate the performance of the integration algorithm in a full scale non linear finite element simulation

constitutive inequalities for an isotropic elastic strain energy function based on hencky s logarithmic strain tensor hencky s strain energy function for finite isotropic elasticity is obtained by the replacement of the infinitesimal strain measure occurring in the classical strain energy function of infinitesimal

rank one convexity implies polyconvexity for isotropic objective and isochoric elastic energies in the two dimensional case we show that in the two dimensional case every objective isotropic and isochoric energy function which is rank one convex on gl 2 is already polyconvex on gl 2 thus we negatively answer morrey s conjecture in the subclass of isochoric nonlinear energies since polyconvexity implies quasiconvexity our methods are based on different representation formulae for objective and isotropic functions in general as well as for isochoric functions in particular we also state criteria for these convexity conditions in terms of the deviatoric part of the logarithmic strain tensor

analysis of three dimensional crack initiation and propagation using the extended finite element method an erratum has been published for this article in international journal for numerical methods in engineering 2005 63 8 1228 we present a new formulation and a numerical procedure for the quasi static analysis of three dimensional crack propagation in brittle and quasi brittle solids the extended finite element method xfem is combined with linear tetrahedral elements a viscosity regularized continuum damage constitutive model is used and coupled with the xfem formulation resulting in a regularized crack band version of xfem the evolving discontinuity surface is discretized through a c0 surface formed by the union of the triangles and quadrilaterals that separate each cracked element in two the element s properties allow a closed form integration and a particularly efficient implementation allowing large scale 3d problems to be studied several examples of crack propagation are shown illustrating the good results that can be achieved copyright 2005 john wiley sons ltd

general solution procedures in elasto viscoplasticity constitutive relations and numerical integration algorithms for elasto viscoplastic problems are investigated a fully implicit integration scheme is adopted and the relevant expression of the consistent tangent operator for yield criteria and flow functions of arbitrary type is derived by suitably generalizing the approach exploited for rate independent plasticity this is achieved by replacing the consistency condition of plasticity with a relation between the viscoplastic consistency parameter and the flow function of the constitutive model in use the methodology adopted simplifies alternative procedures for the evaluation of consistent tangent operators which necessitate the inversion of a viscoplastic compliance operator the general expression of the consistent tangent operator is then specialized to the von mises yield criterion endowed with commonly adopted viscoplastic constitutive models numerical examples are finally presented

zeta determinant for laplace operators on riemann caps the goal of this paper is to compute the zeta function determinant for the massive laplacian on riemann caps or spherical suspensions these manifolds are defined as compact and boundaryless d dimensional manifolds deformed by a singular riemannian structure the deformed spheres considered previously in the literature belong to this class after presenting the geometry and discussing the spectrum of the laplacian we illustrate a method to compute its zeta regularized determinant the special case of the deformed sphere is recovered as a limit of our general formulas

general invariant representations of the constitutive equations for isotropic nonlinearly elastic materials abstract this paper develops general invariant representations of the constitutive equations for isotropic nonlinearly elastic materials different sets of mutually orthogonal unit tensor bases are constructed from the strain argument tensor by using the representation theorem and corresponding irreducible invariants are defined their relations and geometrical interpretations are established in three dimensional principal space it is shown that the constitutive law linking the stress and strain tensors is revealed to be a simple relationship between two vectors in the principal space relative to two different sets of the basis tensors the constitutive equations are transformed according to the transformation rule of vectors when a potential function is assumed to exist the vector associated with the stress tensor is expressed in terms of its gradient with respect to the vector associated with the strain tensor the hill s stability condition is shown to be that the scalar product of the increment of those two vectors must be positive when potential function exists it becomes to be that the 3 3 constitutive matrix derived from its second order derivative with respect to the vector associated with the strain must be positive definite by decomposing the second order symmetric tensor space into the direct sum of a coaxial tensor subspace and another one orthogonal to it the closed form representations for the fourth order tangent operator and its inversion are derived in an extremely simple way

discontinuous modelling of shear bands using adaptive meshfree methods a simple methodology to model shear bands as strong displacement discontinuities in an adaptive meshfree method is presented the shear band is represented by a displacement jump at discrete particle positions the displacement jump in normal direction is suppressed with penalty method loss of material stability is used as transition criterion from continuum to discontinuum the method is two and three dimensional examples of complicated shear banding including transition from brittle to ductile failure are studied and compared to experimental data and other examples from the literature

an implicit integration algorithm for the finite element implementation of a nonlinear anisotropic material model including hysteretic nonlinearity abstract fully implicit integration schemes have been demonstrated to be very robust and efficient for nonlinear elastoplastic and elastic viscoplastic models and enjoy widespread use in finite element formulations the paper introduces a new form of fully implicit local and global algorithms for the integration of nonlinear elastoplastic constitutive laws including anisotropic plasticity and hysteretic small strain elastic nonlinearity the local stress integration algorithm is based on a single step backward differentiation method with iterative solution for the predictor as well as the corrector steps the global system of implicit nonlinear equations is solved with a quasi newton technique using a numerical tangent computed every load step by finite difference and optimized with iterative updating using the broyden fletcher goldfarb shano bfgs procedure the proposed numerical procedure is illustrated here through the implementation of a set of nonlinear constitutive equations describing the response of lightly overconsolidated cohesive materials numerical simulations of single element tests as well as a boundary value problem confirm the robustness accuracy and efficiency of the proposed algorithm at the local and global level

an embedding technique for the solution of reaction diffusion equations on algebraic surfaces with isolated singularities abstract in this paper we construct a parametrization free embedding technique for numerically evolving reaction diffusion pdes defined on algebraic curves that possess an isolated singularity in our approach we first desingularize the curve by appealing to techniques from algebraic geometry we create a family of smooth curves in higher dimensional space that correspond to the original curve by projection following this we pose the analogous reaction diffusion pde on each member of this family and show that the solutions their projection onto the original domain approximate the solution of the original problem finally we compute these approximants numerically by applying the closest point method which is an embedding technique for solving pdes on smooth surfaces of arbitrary dimension or codimension and is thus suitable for our situation in addition we discuss the potential to generalize the techniques presented for higher dimensional surfaces with multiple singularities

two scale shear band evolution by local partition of unity we introduce a methodology to model shear band evolution in the quasi static regime using the extended finite element method we enrich the finite element polynomial displacement field with a fine scale function which models the high displacement gradient in the shear band for this purpose we use a local partition of unity and a parameterized displacement enrichment based on closed form solutions for one dimensional shear bands a stabilized consistent penalty method is used to circumvent locking in the regularized elasto viscoplastic plane strain regime and to guarantee element stability the loss of stability of the boundary value problem is used as an indicator of shear band initiation point and direction shear band development examples are shown illustrating the capabilities of the method to track shear band evolution and strains as high as 1000 copyright 2005 john wiley sons ltd

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

anisotropic additive plasticity in the logarithmic strain space modular kinematic formulation and implementation based on incremental minimization principles for standard materials the paper presents a modular formulation and computational implementation of a class of anisotropic plasticity models at finite strains based on incremental minimization principles the modular kinematic setting consists of a constitutive model in the logarithmic strain space that is framed by a purely geometric pre and postprocessing on the theoretical side the point of departure is an a priori six dimensional approach to finite plasticity based on the notion of a plastic metric in a first step a geometric preprocessor defines a total and a plastic logarithmic strain measure obtained from the current and the plastic metrics respectively in a second step these strains enter in an additive format a constitutive model of anisotropic plasticity that may have a structure identical to the geometrically linear theory the model defines the stresses and consistent tangents work conjugate to the logarithmic strain measure in a third step these objects of the logarithmic space are then mapped back to nominal lagrangian or eulerian objects by a geometric postprocessor this geometric three step approach defines a broad class of anisotropic models of finite plasticity directly related to counterparts of the geometrically linear theory it is specified to a model problem of anisotropic metal plasticity on the computational side we develop an incremental variational formulation of the above outlined constitutive structure where a quasi hyperelastic stress potential is obtained from a local constitutive minimization problem with respect to the internal variables it is shown that this minimization problem is exclusively restricted to the logarithmic strain space in a structure identical to the small strain theory the minimization problem determines the internal state of the material for finite increments of time we develop a discrete formulation in terms of just one scalar parameter for the amount of incremental flow the existence of the incremental stress potential provides a natural basis for the definition of the geometric postprocessor based on function evaluations furthermore the global initial boundary value problem of the elastic plastic solid appears in the incremental setting as an energy minimization problem numerical examples show that the results obtained are surprisingly close to those obtained by a reference framework of multiplicative plasticity