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

optimal codes for minimax criterion on error detection nonlinear quadratic codes that are optimal for the minimax error detection are presented characteristic functions for these codes are asymptotically bent for a given block size n and the number of codewords mod c mod these codes minimize max q e e not 0 where q e is the conditional error masking probability given the error pattern e the codewords are blocks of n symbols from gf q encoding and decoding procedures for the codes are described

finite deformation plasticity based on the additive split of the rate of deformation and hyperelasticity abstract finite deformation plasticity formulation based on additive split of rate of deformation and hyperelasticity is presented this approach is valid for finite elastic and plastic strains while rendering the choice and numerical integration of objective stress rates superfluous as the results are automatically objective for small elastic strains our method reduces to the classical hypoelastic corotational formulation provided that the dienes objective stress rate is employed while in the absence of inelastic deformation it coincides with the hyper elastic formulation the validity of the model has been examined on four test problems and the numerical results were found to be in good agreement with either the exact solution or experimental data

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

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

lacunary statistical summability abstract the sequence x is said to be s convergent to l if for each 0 lim r 1 h r the number of k i r x k l 0 where k r is an increasing sequnece of integers such that k 0 0 h r k r k r 1 as r and i r k r 1 k r in this paper we define the s analog of the cauchy criterion for convergence and show that tt is equivalent to s convergence also s convergence is compared to other summability methods and it is shown that the s method can not be included by any matrix method in addition a tauberian theorem for s convergence is given

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

on the implementation of inelastic constitutive equations with special reference to large deformation problems abstract methods for finite element analysis of inelastic problems are reviewed problems with currently popular methods based on rate principles of virtual work are pointed out a formulation is presented based on the exact incremental virtual work equation the procedure for integration of the constitutive rate equations to obtain incremental constitutive equations is based on the assumption of a constant strain rate or straight strain path during the increment full newton raphson iteration is used to solve the resulting set of nonlinear equations the treatment of the constitutive equations in this newton raphson scheme leads to a linearized form which is substantially different from the classical rate equations the procedure is implemented in a finite element program and its effectiveness is shown in a number of examples

maximal families of bent sequences in a recent paper olsen scholtz and welch osw describe the use of bent functions to construct families of sequences with asymptotically optimal correlation properties we show that the sequences produced by the osw construction possess the claimed correlation properties if and only if the underlying bent functions are pairwise orthogonal consequently the cardinality of a family of osw sequences of length 2 n 1 cannot exceed 2 n 2 we also describe methods of selecting a maximal set of orthogonal bent functions

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

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

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

design of universal test sequences for vlsi a test sequence is called s t universal if it exercises every function depending on t or fewer inputs on a very large scale integration vlsi chip with s inputs randomized and deterministic procedures are deseribed for the design of s t universal sequences and for the signature analysis of the test outputs

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

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

a formulation of the mitc4 shell element for finite strain elasto plastic analysis abstract a finite strain elasto plastic formulation is developed for the mitc4 shell element the developed formulation is based on lee s multiplicative decomposition of the deformation gradient and on the hyperelastic expression of von mises flow rule expressed in terms of hencky s strain tensor the formulation incorporates thickness stretching degrees of freedom that are condensed at the element level by imposing the classical in layer plane stress condition a symmetric and consistent tangent stiffness matrix is also developed

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

strong and a statistical comparisons for sequences abstract let t and a be two nonnegative regular summability matrices and w t p l and ca b denote the spaces of all bounded strongly t summable sequences with index p 0 and bounded summability domain of a respectively in this paper we show among other things that n is a multiplier from w t p l into ca b if and only if any subset k of positive integers that has t density zero implies that k has a density zero these results are used to characterize the a statistical comparisons for both bounded as well as arbitrary sequences using the concept of a statistical tauberian rate we also show that n is not a multiplier from w t p l into ca b that leads to a steinhaus type result

two dimensional elastoplasticity approximation by mixed finite elements two dimensional elastoplastic problems are used to assess the performance of a family of mixed finite elements in the non linear regime in particular four node bilinear quadrilateral elements that exhibit high accuracy in coarse meshes are used to simulate plane stress plane strain axisymmetric and shear deformable plate bending problems the excellent performance of these elements is demonstrated with a number of discriminating examples selected from the literature in addition agreement is observed in the limit load predicted by the axisymmetric solid and plate bending elements

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

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

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

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

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

bent function sequences in this paper we construct a new family of nonlinear binary signal sets which achieve welch s lower bound on simultaneous cross correlation and autocorrelation magnitudes given a parameter n with n 0 pmod 4 the period of the sequences is 2 n 1 the number of sequences in the set is 2 n 2 and the cross auto correlation function has three values with magnitudes leq 2 n 2 1 the equivalent linear span of the codes is bound above by sum i 1 n 4 left stackrel n i right these new signal sets have the same size and correlation properties as the small set of kasami codes but they have important advantages for use in spread spectrum multiple access communications systems first the sequences are balances which represents only a slight advantage second the sequence generators are easy to randomly initialize into any assigned code and hence can be rapidly hopped from sequence to sequence for code division multiple access operation most importantly the codes are nonlinear in that the order of the linear difference equation satisfied by the sequence can be orders of magnitude larger than the number of memory elements in the generator that produced it this high equivalent linear span assures that the code sequence cannot be readily analyzed by a sophisticated enemy and then used to neutralize the advantages of the spread spectrum processing

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

new class of nonlinear systematic error detecting codes a code c detects error e with probability 1 q e ifq e is a fraction of codewords y such that y y e spl isin c we present a class of optimal nonlinear q ary systematic n q sup k codes robust codes minimizing over all n q sup k codes the maximum of q e for nonzero e we also show that any linear n q sup k code v with n spl les 2k can be modified into a nonlinear n q sup k code c sub v with simple encoding and decoding procedures such that the set e e q e 1 of undetected errors for c sub v is a k r dimensional subspace of v e q sup k r instead of q sup k for v for the remaining q sup n q sup k r nonzero errors q e spl les q sup r for q spl ges 3 and q e spl les 2 sup r 1 for q 2

a general framework for the numerical solution of problems in finite elasto plasticity this article discusses a general framework for the analysis of initial boundary value problems of rate independent finite elasto plasticity based on the theory of green and naghdi a constitutive model is developed within the context of the above theory employing generalized measures of lagrangian strain and work conjugate measures of stress computational implications of the proposed formulation are discussed in conjunction with an implicit time integrator for the differential algebraic equations of plastic flow representative numerical simulations demonstrate the applicability and predictive capacity of the model in the presence of large plastic deformations

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

tauberian theorems via statistical convergence the concept of statistical convergence which is related to the usual concept of convergence in probability provides a regular summability method for abstract metric spaces by using probabilistic tools we provide some tauberian theorems which have best possible order tauberian conditions furthermore these methods can be used to unify and improve the classical pointwise tauberian theorems of summability theory for the random walk type methods as proved by bingham and hausdorff methods as proved by lorentz

statistical and computational performance of a class of generalized wiener filters corresp a class of suboptimal wiener filters is considered and their computational and statistical performances and the trade off between the two are studied and compared with those for known classes of suboptimal wiener filters a general model of a suboptimal wiener filter over a group is defined which includes as special cases the known filters based on the discrete fourier transform dft in the case of a cyclic group and the walsh hadamard transform wht in the case of a dyadic group statistical and computational performances of various group filters are investigated the cyclic and the dyadic group filters are known to be computationally the best ones among all the group filters however they are not always the best ones statistically and other not necessarily abelian group filters are studied results are compared with those for the cyclic group filters dft and the general problem of selecting the best group filter is posed that problem is solved numerically for small size signals leq 64 for the first order markov process and random sine wave corrupted by white noise for the first order markov process with the covariance matrix b s l rho s l as rho increases the use of various non abelian groups results in improved statistical performance of the filter as compared to the dft similarly for the random sine wave with covariance matrix b s l cos lambda s l as lambda decreases non abelian groups result in a better statistical performance of the filter than the dft does however that is compensated for by the increased number of computations to perform the filtering

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

three dimensional adaptive meshing by subdivision and edge collapse in finite deformation dynamic plasticity problems with application to adiabatic shear banding this paper is concerned with the development of a general framework for adaptive mesh refinement and coarsening in three dimensional finite deformation dynamic plasticity problems mesh adaption is driven by a posteriori global error bounds derived on the basis of a variational formulation of the incremental problem the particular mesh refinement strategy adopted is based on rivara s longest edge propagation path lepp bisection algorithm our strategy for mesh coarsening or unrefinement is based on the elimination of elements by edge collapse the convergence characteristics of the method in the presence of strong elastic singularities are tested numerically an application to the three dimensional simulation of adiabatic shear bands in dynamically loaded tantalum is also presented which demonstrates the robustness and versatility of the method copyright c 2001 john wiley sons ltd

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

a characterization of banach spaces with separable duals via weak statistical convergence abstract let b be a banach space a b valued sequence xk is weakly statistically null provided lim n 1 n k n f x k e 0 for all e 0 and every continuous linear functional f on b a banach space is finite dimensional if and only if every weakly statistically null b valued sequence has a bounded subsequence if b is separable b is separable if and only if every bounded weakly statistically null b valued sequence contains a large weakly null sequence a characterization of spaces containing an isomorphic copy of l1 is given and it is also shown that l2 has a statistical m basis which is not a schauder basis

minimax robust discrete time matched filters the problem of designing finite length discrete time matched filters is considered for situations in which exact knowledge of the input signal and or noise characteristics is not available such situations arise in many applications due to channel distortion incoherencies nonlinear effects and other modeling uncertainties in such cases it is often of interest to design a minimax robust matched filter i e a nonadaptive filter with an optimum level of worst case performance for the expected uncertainty class this problem is investigated here for three types of uncertainty models for the input signal namely the mean absolute mean square and maximum absolute distortion classes and for a wide generality of norm deviation models for the noise covariance matrix some numerical examples illustrate the robustness properties of the proposed designs

a measure theoretical subsequence characterization of statistical convergence the concept of statistical convergence of a sequence was first introduced by h fast statistical convergence was generalized by r c buck and studied by other authors using a regular nonnegative summability matrix a in place of c1 the main result in this paper is a theorem that gives meaning to the statement s s converges to l statistically t if and only if most of the subsequences of s converge in the ordinary sense to l here t is a regular nonnegative and triangular matrix corresponding results for lacunary statistical convergence recently defined and studied by j a fridy and c orhan are also presented introduction the concept of the statistical convergence of a sequence of reals s sn was first introduced by h fast 9 the sequence s sn is said to converge statistically to l and we write lim s l stat if for every e n oo rim n k e1 0 where jai denotes the cardinality of the set a properties of statistically convergent sequences were studied in 5 6 12 and 16 in 13 fridy and miller gave a characterization of statistical convergence for bounded sequences using a family of matrix summability methods statistical convergence can be generalized by using a regular nonnegative summability matrix a in place of c this idea was first mentioned by r c buck 3 in 1953 and has been further studied by sember and freedman 10 and 11 and connor 5 and 7 regular nonnegative summability matrices turn out to be too general for our purposes here instead we use the concept of a mean a matrix t amn will be called a mean if amn 0 when n m e iamn 1 for all m and limm 0oam 0 for each n if t amn is a mean following buck a sequence s sn is said to be statistically t summable to l and we write sn l stat t if for every e 0 received by the editors august 18 1993 and in revised form february 14 1994 originally communicated to the proceedings of the ams by andrew bruckner 1991 mathematics subject classification primary 40d25 secondary 40g99 28a12 1995 american mathematical society 0002 9947 95 1 00 s 25 per page

robust generalized punctured cubic codes security oriented codes are used in cryptographic devices to maximize the probability of detecting fault injection attacks this paper introduces a new class of binary security oriented codes of rate 1 2 the codes are derived from the cubic code by applying a linear transformation on the codewords before puncturing the codes are systematic and robust in that any nonzero error can be detected with a probability 0 the error masking probability of the codes is upper bounded by 2 r 1 where r is the number of redundancy bits it is shown that in some cases by choosing the proper transformation and puncturing matrices it is possible to increase the minimum distance of the code or to reduce the maximal error masking probability to meet its lower bound

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

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

finite element analysis of internally balanced elastic materials abstract this paper provides a finite element treatment for a generalized hyperelastic theory in which the deformation gradient is subject to the multiplicative two factor decomposition that is commonly used in large strain plasticity the multiplicative decomposition in the present context is motivated by a theory of balanced internal variables one of which is the first factor in the decomposition previous studies have shown how the associated continuum mechanical formulation then leads not only to the stress equations of equilibrium but also to an additional tensor balance equation that serves to determine the individual factors in the decomposition such a theory has been shown to predict loading thresholds associated with the emergence of slip surfaces at grip locations in well posed boundary value problems however previous numerical treatments focused on shooting method procedures that failed to resolve loading plateaus and other key features associated with the emergence of such singular surfaces in the present work we describe a finite element treatment that resolves such previously obscure details additional finite element simulations illustrate new aspects of singular surface emergence in this type of theory including the emergence of singular surfaces in the interior of the computational domain

on statistical limit points and the consistency of statistical convergence abstract this article extends the concept of a statistical limit cluster point of a sequencex as introduced by fridy to at statistical limit cluster point wheretis a nonnegative regular matrix summability method these definitions are reformulated in the setting of n n it is shown that for a bounded sequencex the set oft statistical cluster points ofxforms a compact subset of r it is also shown that iftandrare two nonnegative regular summability matrices thent statistical convergence andr statistical convergence are consistent if and only if the support sets oftandrhave nonempty intersection

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

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

formulation and finite element implementation of a multiplicative model of coupled poro plasticity at finite strains under fully saturated conditions in this paper we present the formulation and numerical analysis of a finite deformation model of coupled poro plasticity fully saturated conditions are assumed the model is based on a multiplicative decomposition of the deformation gradient in elastic and plastic parts together with an additive elastoplastic decomposition of the fluid content the final relations describing the evolution of the different fields are then obtained in the thermodynamic framework furnished by the principle of maximum plastic dissipation the particular case of an associated drucker prager model in effective stresses is considered as a model example a complete characterization of the dissipative structure of the problem of evolution is described through the derivation of an a priori stability estimate we describe in detail the finite element implementation of the model in the context of staggered algorithms for the solution of the physically coupled problem finally we present representative numerical simulations to illustrate the features of the proposed models in particular the case of strain localization in globally undrained conditions is studied in the proposed framework