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

thermal capacity and boundary regularity where a and b are respectively vector and scalar valued baire functions defined in i2 x r x r here b is an open subset of r points of f are denoted by x t with x e ip and c e i the symbols v and div denote gradient and divergence taken with respect to the x variable the functions a and b are assumed to satisfy the following structural conditions a x t u w a iwl a u t lul az x t b x t u w b iw12 b x t w b x i iui b x t 2 v a t u c x t c t

an efficient optimal normal basis type ii multiplier this paper presents a new parallel multiplier for the galois field gf 2 sup m whose elements are represented using the optimal normal basis of type ii the proposed multiplier requires 1 5 m sup 2 m xor gates as compared to 2 m sup 2 m xor gates required by the massey omura multiplier the time complexities of the proposed and the massey omura multipliers are similar

efficient modeling of localized material failure by means of a variationally consistent embedded strong discontinuity approach this paper is concerned with a novel embedded strong discontinuity approach suitable for the analysis of material failure at finite strains focus is on localized plastic deformation particularly relevant for slip bands in contrast to already existing models the proposed implementation allows to consider several interacting discontinuities in each finite element based on a proper re formulation of the kinematics an efficient parameterization of the deformation gradient is derived it permits to compute the strains explicitly that improves the performance significantly however the most important novel contribution of the present paper is the advocated variational constitutive update within this framework every aspect is naturally driven by energy minimization i e all unknown variables are jointly computed by minimizing the stress power the proposed update relies strongly on an extended principle of maximum dissipation this framework provides enough flexibility for different failure types and for a broad class of non associative evolution equations by discretizing the aforementioned continuous variational principle an efficient numerical implementation is obtained it shows in addition to its physical and mathematical elegance several practical advantages for instance the physical minimization principle itself specifies automatically and naturally the set of active strong discontinuities copyright 2011 john wiley sons ltd

fast normal basis multiplication using general purpose processors for cryptographic applications normal bases have received considerable attention especially for hardware implementation we consider fast software algorithms for normal basis multiplication over the extended binary field gf 2 sup m we present a vector level algorithm which essentially eliminates the bit wise inner products needed in the conventional approach to the normal basis multiplication we then present another algorithm which significantly reduces the dynamic instruction counts both algorithms utilize the full width of the data path of the general purpose processor on which the software is to be executed we also consider composite fields and present an algorithm which can provide further speed ups and an added flexibility toward hardware software codesign of processors for very large finite fields

towards variational constitutive updates for non associative plasticity models at finite strain models based on a volumetric deviatoric split in this paper an enhanced variational constitutive update suitable for a class of non associative plasticity theories at finite strain is proposed in line with classical numerical formulations for plasticity models such as the by now established return mapping algorithm variational constitutive updates represent a numerical method for computing the unknown state variables however in contrast to conventional algorithms variational constitutive updates are fully variational i e all unknown variables follow jointly from minimizing a certain potential in addition to the physical and mathematical elegance of these variational schemes they show several practical advantages as well for instance numerically efficient and robust optimization schemes can be directly employed for solving the resulting minimization problem since mathematically plasticity is a non smooth problem and often it leads to highly singular systems of equations as known from single crystal plasticity a robust implementation is of utmost importance so far variational constitutive updates have been developed for different classes of standard dissipative solids i e solids characterized by associative evolution equations and flow rules in the present paper this framework is extended to a certain class of non associative plasticity models at finite strain all models falling into this class show a volumetric deviatoric split of the helmholtz energy and the yield function typical prototypes are drucker prager or mohr coulomb models playing an important role in soil mechanics the efficiency and robustness of the resulting algorithmic formulation is demonstrated by means of selected numerical examples

quasistatic crack growth in nonlinear elasticity in this paper we prove a new existence result for a variational model of crack growth in brittle materials proposed in 19 we consider the case of n dimensional nonlinear elasticity for an arbitrary n 1 with a quasiconvex bulk energy and with prescribed boundary deformations and applied loads both depending on time

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

on the implementation of rate independent standard dissipative solids at finite strain variational constitutive updates this paper is concerned with an efficient variationally consistent implementation for rate independent dissipative solids at finite strain more precisely focus is on finite strain plasticity theory based on a multiplicative decomposition of the deformation gradient adopting the formalism of standard dissipative solids which allows to describe constitutive models by means of only two potentials being the helmholtz energy and the yield function or equivalently a dissipation functional finite strain plasticity is recast into an equivalent minimization problem in contrast to previous models the presented framework covers isotropic and kinematic hardening as well as isotropic and anisotropic elasticity and yield functions based on this approach a novel numerical implementation representing the main contribution of the paper is given in sharp contrast to by now classical approaches such as the return mapping algorithm and analogously to the theoretical part the numerical formulation is variationally consistent i e all unknown variables follow naturally from minimizing the energy of the considered system consequently several different numerically efficient and robust optimization schemes can be directly employed for solving the resulting minimization problem extending previously published works on variational constitutive updates the advocated model does not rely on any material symmetry and therefore it can be applied to a broad range of different plasticity theories as two examples an anisotropic hill type and a barlat type model are implemented numerical examples demonstrate the applicability and the performance of the proposed implementation

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 hybrid variationally consistent homogenization approach based on ritz s method summary multiscale approaches based on homogenization theory provide a suitable framework to incorporate information associated with a small scale microscale problem into the considered large scale macroscopic problem in this connection the present paper proposes a novel computationally efficient hybrid homogenization method its backbone is a variationally consistent fe2 approach in which every aspect is governed by energy minimization in particular scale bridging is realized by the canonical principle of energy equivalence as a direct implementation of the aforementioned variationally consistent fe2 approach is numerically extensive an efficient approximation based on ritz s method is advocated by doing so the material parameters defining an effective macroscopic material model capturing the underlying microstructure can be efficiently computed furthermore the variational scale bridging principle provides some guidance to choose a suitable family of macroscopic material models comparisons between the results predicted by the novel hybrid homogenization method and full field finite element simulations show that the novel method is indeed very promising for multiscale analyses copyright 2013 john wiley sons ltd

parabolic equations with exponential nonlinearity and measure data abstract let be a bounded domain in r n and t 0 we study the problem p u t u g u in q t 0 t u 0 on 0 t u 0 in where and are bounded measures in q t and respectively and g u e a u q with a 0 and q 1 we provide a sufficient condition in terms of fractional maximal potentials of and for solving p moreover we prove uniqueness for p

an incremental minimization principle suitable for the analysis of low cycle fatigue in metals a coupled ductile brittle damage model abstract the present paper is concerned with a novel variational constitutive update suitable for the analysis of low cycle fatigue in metals the underlying constitutive model originally advocated in 1 accounts for plastic deformation as well as for damage accumulation the latter is captured by a combination of two constitutive models while the first of those is associated with ductile damage the second material law is related to a quasi brittle response the complex overall model falls into the range of so called generalized standard materials and thus it is thermodynamically consistent however since the evolution equations are non associative it does not show an obvious variational structure by enforcing the flow rule as well as the evolution equations through a suitable parameterization a minimization principle can be derived nevertheless discretized in time this principle is employed for developing an effective numerical implementation since the mechanical subproblems corresponding to ductile damage and that of quasi brittle damage are uncoupled an efficient staggered scheme can be elaborated within both steps newton s method is applied while the evolution of the quasi brittle damage requires only the computation of a one dimensional optimization problem the ductile damage model is defined by a numerically more expensive tensor valued variable for further increasing the numerical performance of the respective minimization principle a closed form solution for the inverse of the hessian matrix is derived by numerically analyzing the prediction of mesocrack initiation in low cycle fatigue simulations the performance of the resulting algorithm is demonstrated

low complexity word level sequential normal basis multipliers for efficient hardware implementation of finite field arithmetic units the use of a normal basis is advantageous in this paper two classes of architectures for multipliers over the finite field gf 2 sup m are proposed these multipliers are of sequential type i e after receiving the coordinates of the two input field elements they go through k 1 spl les k spl les m iterations i e clock cycles to finally yield all the coordinates of the product in parallel the value of k depends on the word size w spl lceil m k spl rceil for w 1 these multipliers are highly area efficient and require fewer number of logic gates even when compared with the most area efficient multipliers available in the open literature this makes the proposed multipliers suitable for applications where the value of m is large but space is of concern e g resource constrained cryptographic systems additionally if the field dimension m is composite i e m kn then the extension of one class of the architectures yields a highly efficient multiplier over composite fields

on the relation between the principle of maximum dissipation and inelastic evolution given by dissipation potentials we study the evolution of systems described by internal variables after the introduction of thermodynamic forces and fluxes both the dissipation and dissipation potential are defined then the principle of maximum dissipation pmd and a minimum principle for the dissipation potential are developed in a variational formulation both principles are related to each other several cases are shown where both principles lead to the same evolution equations for the internal variables however also counterexamples are reported where such an equivalence is not valid in this case an extended pmd can be formulated

divisible difference sets relative difference sets and sequences with ideal autocorrelation abstract in this correspondence we consider the equivalent condition that a sequence possesses ideal autocorrelation function as we know for a binary sequence the equivalent condition is that the characteristic class of this sequence consists of two cyclic difference sets this paper proves that for a p ary sequence with d form property the equivalent condition is that its characteristic class consists of one cyclic divisible difference sets and p 1 relative difference sets moreover a new way to construct cyclic divisible difference sets is presented

wg a family of stream ciphers with designed randomness properties in this paper we present a family of stream ciphers which generate a keystream with ideal two level autocorrelation the design also guarantees other randomness properties i e balance long period ideal tuple distribution and high and exact linear complexity we discuss how these properties are achieved by the proposed design and show how to select various parameters to obtain an efficient stream cipher for the desired security level we also show that the proposed generators are secure against time memory data tradeoff attacks algebraic attacks and correlation attacks finally we present wg 128 as a concrete example of a wg stream cipher with a key size of 128bits

vlsi architectures for computing multiplications and inverses in gf 2 m finite field arithmetic logic is central in the implementation of reed solomon coders and in some cryptographic algorithms there is a need for good multiplication and inversion algorithms that can be easily realized on vlsi chips massey and omura 1 recently developed a new multiplication algorithm for galois fields based on a normal basis representation in this paper a pipeline structure is developed to realize the massey omura multiplier in the finite field gf 2m with the simple squaring property of the normal basis representation used together with this multiplier a pipeline architecture is also developed for computing inverse elements in gf 2m the designs developed for the massey omura multiplier and the computation of inverse elements are regular simple expandable and therefore naturally suitable for vlsi implementation

wiener s test for super brownian motion and the brownian snake we prove a wiener type criterion for super brownian motion and the brownian snake if f is a borel subset of d and x d we provide a necessary and sufficientcondition for super brownian motion started at x to immediately hit the set f equivalently this condition is necessary and sufficient for the hitting time of f by thebrownian snake with initial point x to be 0 a key ingredient of the proof isan estimate showing that the hitting probability of f is comparable up to multiplicative constants to the relevant capacity of f this estimate which is of independent interest refines previous results due to perkins and dynkin an important role is played by additivefunctionals of the brownian snake which are investigated here via the potentialtheory of symmetric markov processes as a direct application of our probabilisticresults we obtain a necessary and sufficient condition for the existence in a domain d of a positivesolution of the equation u u 2 which explodes at a given point of d

non convex potentials and microstructures in finite strain plasticity a mathematical model for a finite strain elastoplastic evolution problem is proposed in which one time step of an implicit time discretization leads to generally non convex minimization problems the elimination of all internal variables enables a mathematical and numerical analysis of a reduced problem within the general framework of calculus of variations and nonlinear partial differential equations the results for a single slip system and von mises plasticity illustrate that finite strain elastoplasticity generates reduced problems with non quasiconvex energy densities and so allows for non attainment of energy minimizers and microstructures

binary pseudorandom sequences of period 2 sup n 1 with ideal autocorrelation in this correspondence we present five new classes of binary sequences of period 2 sup n 1 with ideal autocorrelation these sequences which correspond to new cyclic hadamard difference sets were found by extensive computer search conjectures on the general construction of these sequences are formulated

wiener s criterion for the heat equation this paper establishes a necessary and sufficient condition for a boundary point of an arbitrary bounded open subset of r 1 to be regular for the heat equation our criterion is in the sense described below the exact analogue of winner s test w for boundary regularity of harmonic functions a careful statement of our result requires that we first of all introduce a great deal of terminology let 2 q r 1 n 1 denote any bounded open subset and 8 2 its topological boundary we will often write a typical point z e r 1 as z x t xer te r if ue c2 q r we may define the heat operator

a mixed interface finite element for cohesive zone models abstract the phenomena of crack initiation propagation and ultimate fracture are studied here under the following assumptions i the crack law is modelled by means of a cohesive zone model and ii the crack paths are postulated a priori in this context a variational formulation is proposed which relies on an augmented lagrangian a mixed interface finite element is introduced to discretise the crack paths the degrees of freedom of which consist in the displacement on both crack lips and the density of cohesive forces this enables an exact treatment of multi valued cohesive laws e g initial adhesion contact conditions possible rigid unloading etc without penalty regularisation a special attention is paid to the convergence with mesh refinement i e the well posedness of the problem on the basis of theoretical results of contact mechanics and some complementary numerical investigations fulfilment of the lbb condition is the key factor to gain the desired properties moreover it is shown that the integration of the constitutive law admits a unique solution as soon as some condition on the augmented lagrangian is enforced finally a 3d simulation shows the applicability to practical engineer problems including in particular the robustness of the formulation and its compatibility with classical solution algorithms newton method line search path following techniques

a new construction of massey omura parallel multiplier over gf 2 sup m the massey omura multiplier of gf 2 sup m uses a normal basis and its bit parallel version is usually implemented using m identical combinational logic blocks whose inputs are cyclically shifted from one another in the past it was shown that for a class of finite fields defined by irreducible all one polynomials the parallel massey omura multiplier had redundancy and a modified architecture of lower circuit complexity was proposed in this article it is shown that not only does this type of multiplier contain redundancy in that special class of finite fields but it also has redundancy in fields gf 2 sup m defined by any irreducible polynomial by removing the redundancy we propose a new architecture for the normal basis parallel multiplier which is applicable to any arbitrary finite field and has significantly lower circuit complexity compared to the original massey omura normal basis parallel multiplier the proposed multiplier structure is also modular and hence suitable for vlsi realization when applied to fields defined by the irreducible all one polynomials the multiplier s circuit complexity matches the best result available in the open literature

a model for the quasi static growth of brittle fractures existence and approximation results we give a precise mathematical formulation of a variational model for the irreversible quasi static evolution of brittle fractures proposed by g a francfort and j j marigo and based on griffith s theory of crack growth in the two dimensional case we prove an existence result for the quasi static evolution and show that the total energy is an absolutely continuous function of time although we cannot exclude the possibility that the bulk energy and the surface energy may present some jump discontinuities this existence result is proved by a time discretization process where at each step a global energy minimization is performed with the constraint that the new crack contains all cracks formed at the previous time steps this procedure provides an effective way to approximate the continuous time evolution

gradient damage models toward full scale computations abstract the description of localisation and structural failure through local damage constitutive laws leads to ill posed problems to retrieve a well posed problem the material state is described through the gradients of damage in addition to the strain and the damage under some assumptions it is shown that these gradient laws can be cast into a variational formulation its numerical treatment is reduced to the design of a mixed finite element so that algorithms such as newton s method and path following techniques are still available possible convergence difficulties related to the reduction of the damage band width and the appearance of micro instabilities are removed thanks to the design of a new class of brittle laws finally numerical applications show the convergence with mesh refinement the compatibility with coarser approaches such as griffith s theory and cohesive crack models the robustness in case of unstable multi cracking the applicability to full scale 3d situations and the physical relevance compared to experimental data

studies on the distribution of the shortest linear recurring sequences the distribution of the shortest linear recurrence slr sequences in the z p field and over the z p e ring is studied it is found that the length of the shortest linear recurrent slrl is always equal to n 2 if n is even and n 2 1 if n is odd in the z p field respectively on the other hand over the z p e ring the number of sequences with length n can also be calculated the recurring distribution regulation of the shortest linear recurring sequences is also found to solve the problem of calculating the slrl a new simple representation of the berlekamp massey algorithm is developed as well

wiener criteria for existence of large solutions of nonlinear parabolic equations with absorption in a non cylindrical domain abstract we obtain a necessary condition and a sufficient condition both expressed in terms of wiener type tests involving the parabolic w q 2 1 capacity where q q q 1 and q 1 for the existence of large solutions to equation t u u u q 0 in a non cylindrical domain we provide also a sufficient condition for the existence of such solutions to equation t u u e u 1 0 besides we apply our results to equation t u u a u p b u q 0 for a b 0 1 p 2 and q 1

new hardware implementationsof wg bf 29 11 and wg bf 16 streamciphers using polynomial basis the wg stream ciphers are based on the wg welch gong transformation and possess proved randomness properties in this paper we propose nine new hardware designs for the two classes of wg 29 11 and wg 16 for each class we design and implement three versions of standard pipelined and serial for the first time we use the polynomial basis pb representation to design and implement the wg 29 11 and wg 16 we consider traditional pb multiplier for the wg 29 11 and the traditional and karatsuba multipliers for the wg 16 for efficient field operations we propose an irreducible trinomial for the wg 29 11 for the wg 16 a new formulation of its permutation which requires only 8 multipliers is introduced in these designs the multipliers in the transforms arefurther reduced by utilizing a novel computation for the trace of the multiplication of two field elements we have implemented theproposed designs in asic using cmos 65 nm technology the results show that the proposed standard wg 29 11 consumes less area and slightly enhances the normalized throughput compared to the existing counterparts for the wg 16 throughput of theproposed pipelined instance outperforms the previous designs moreover the speed of the proposed wg 16 designs meet the peak bit rates for the 4 g specifications

the variational formulation of viscoplastic constitutive updates we present a class of constitutive updates for general viscoplastic solids including such aspects of material behavior as finite elastic and plastic deformations non newtonian viscosity rate sensitivity and arbitrary flow and hardening rules the distinguishing characteristic of the proposed constitutive updates is that by construction the corresponding incremental stress strain relations derive from a pseudo elastic strain energy density this in turn confers the incremental boundary value problem a variational structure in particular the incremental deformation mapping follows from a minimum principle this minimum principle may conveniently be taken as a basis for error estimation and mesh adaption the accuracy and robustness of the variational constitutive updates is demonstrated with the aid of convergence tests involving the finitely deforming mises solid and ductile single crystals the ability of the updates to resolve the complex patterns of slip activity which arise in the latter application is particularly noteworthy

a general construction of binary interleaved sequences of period 4n with optimal autocorrelation abstract a general construction of binary interleaved sequences of period 4 n with low autocorrelation are considered in the paper firstly some correlation properties of two general classes of binary interleaved sequences are presented secondly based on these results autocorrelation functions of a general construction of binary interleaved sequences of period 4 n are given finally we show that from these results for general cases several known binary sequences of these types with optimal autocorrelation and some other new binary sequences with low autocorrelation can be constructed

wiener s criterion for parabolic equations with variable coefficients and its consequences dans un ensemble borne de r n 1 on etudie la regularite des points limites pour le probleme de dirichlet pour un operateur parabolique a coefficients lisses on donne une caracterisation geometrique de ces points limites qui sont reguliers

cryptographic properties of the welch gong transformation sequence generators welch gong wg transformation sequences are binary sequences of period 2 sup n 1 with two level autocorrelation these sequences were discovered by golomb gong and gaal 1998 and they verified the validity of their construction for 5 spl les n spl les 20 later no chung and yun 1998 found another way to construct the wg sequences and verified their result for 5 spl les n spl les 20 dillon 1998 first proved this result for odd n and finally dobbertin and dillon 1999 proved it for even n in this paper we investigate a two faced property of the wg transformation sequences for application in stream ciphers and pseudorandom number generators one is to present the randomness or unpredictability of the wg transformation sequences the other is to exhibit the security properties of the wg transformations regarded as boolean functions in particular we prove that the wg transformation sequences in addition to the known two level autocorrelation and three level cross correlation with m sequences have the ideal 2 tuple distribution and large linear span increasing exponentially with n moreover it can be implemented efficiently this is the first type of pseudorandom sequences with good correlation statistic properties large linear span and efficient implementation when wg transformations are regarded as boolean functions they have high nonlinearity we derive a criterion for the boolean representation of wg transformations to be r resilient and show that they are at least 1 resilient under some basis of the finite field gf 2 sup n an algorithm to find such bases is given the degree and linear span of wg transformations are presented as well

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