bounds on the rate of 2 d bit stuffing encoders a method for bounding the rate of bit stuffing encoders for 2 d constraints is presented instead of considering the original encoder we consider a related one which is quasi stationary we use the quasi stationary property in order to formulate linear requirements that must hold on the probabilities of the constrained arrays that are generated by the encoder these requirements are used as part of a linear program the minimum and maximum of the linear program bound the rate of the encoder from below and from above respectively a lower bound on the rate of an encoder is also a lower bound on the capacity of the corresponding constraint for some constraints our results lead to tighter lower bounds than what was previously known

stress computation and consistent tangent operator using non linear kinematic hardening models one possibility of formulating the tinite element method is founded on the principle of virtual displacement in which we want to include a rate independent elastoplastic constitutive model based on the assumption of a yield surface the constitutive equations result from the assumptions of small deformations hooke s law for the elastic domain the normality rule for the evolution of plastic strains the von mises yield condition and a special kind of kinematic hardening due to armstrong and frederick 1 in which linear kinematic hardening is generalized with a saturation term we show that it is not generally recommendable to propose large load steps to this end we investigate the influences of the non linear kinematic hardening model on the stress computation and the resulting consistent elastoplastic tangent operator the main topics of this paper are 1 development of a problem optimized backward euler method with regard to the kinematic hardening model 2 study of the influence of the saturation term on the numerical accuracy through isoerror maps and 3 computation of the consistent elastoplastic tangent operator

the positive capacity region of two dimensional run length constrained channels a binary sequence satisfies a one dimensional d k constraint if every run of zeros with possible exception of the first and the last runs has length at least d and at most k a binary two dimensional array satisfies a d k constraint if each row and each column satisfies the one dimensional d k constraint few models have been proposed in the literature to handle two dimensional data the diamond model the square model the hexagonal model and the triangular model the constraints in the different directions might be asymmetric and hence many kind of constraints are defined depending on the number of directions in the model for example a two dimensional array in the diamond model satisfies a d1 k1 d2 k 2 constraint if it satisfies the one dimensional d1 k1 constraint horizontally and the one dimensional d 2 k2 constraint vertically in this correspondence the region in which the capacity is zero or positive in the various models is examined asymmetric constraints in the diamond model and symmetric constraints in the other models are considered in particular an almost complete solution for asymmetric constraints in the diamond model is provided

geometrical numerical algorithms for a plasticity model with armstrong frederick kinematic hardening rule under strain and stress controls in this paper we approach the numerical integration problem of a plasticity model with the armstrong frederick kinematic hardening rule on back stress through a combination of the techniques of integral representation and geometrical integrator first the internal symmetry group of the constitutive model is investigated then we develop two geometrical integrators for strain control and stress control respectively these integrators are obtained by a discretization of the integral representation of the constitutive equations and an exponential approximation of the quasi linear differential equations system for the relative stress which guarantee to retain the consistency condition exactly without the need for any iterations some numerical examples are used to assess the performance of the new algorithms the measures in terms of stress relative errors and also isoerror maps confirm that our schemes are superior to the classical radial return methods

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

algorithmic issues for three invariant hyperplastic critical state models implicit stress integration and the consistent tangents are presented for critical state hyperplasticity models which include a dependence on the third invariant of stress an elliptical deviatoric yielding criterion 43 is incorporated within the family of geotechnical models first proposed by collins and hilder 8 an alternative expression for the yield function is proposed and the consequences of different forms of that function are revealed in terms of the stability and efficiency of the stress return algorithm errors associated with the integration scheme are presented it is shown how calibration of the two new material constants is achieved through examining one dimesional consolidation tests and undrained triaxial compression data material point simulations of drained triaxial compression tests are then compared with established experimental results strain probe analyses are used to demonstrate the concepts of energy dissipation and stored plastic work along with the robustness of the integration method over twenty finite element boundary value problems are then simulated these include single three dimensional element tests plane strain footing analyses and cavity expansion tests the rapid convergence of the global newton raphson procedure using the consistent tangent is demonstrated in small strain and finite deformation simulations

material instabilities in inelastic saturated porous media under dynamic loadings abstract instabilities in inelastic saturated porous media are investigated here for general three dimensional states under dynamic loadings using a perturbation approach under quasi static conditions unbounded growth of perturbations is related to the emergence of stationary discontinuities under drained or undrained conditions while under dynamic conditions unbounded growth is related either to the emergence of stationary discontinuities and these are set by drained conditions or to the appearance of the flutter phenomenon acceleration waves for associative behaviour unbounded growth always corresponds to localization under drained conditions and the onset of growth of perturbations occurs here only through divergence growth it is only for non associative flow that unbounded growth may correspond to undrained localization in quasi static conditions and to flutter under dynamic conditions

non smooth multisurface plasticity and viscoplasticity loading unloading conditions and numerical algorithms rate independent plasticity and viscoplasticity in which the boundary of the elastic domain is defined by an arbitrary number of yield surfaces intersecting in a non smooth fashion are considered in detail it is shown that the standard kuhn tucker optimality conditions lead to the only computationally useful characterization of plastic loading on the computational side an unconditionally convergent return mapping algorithm is developed which places no restrictions aside from convexity on the functional forms of the yield condition flow rule and hardening law the proposed general purpose procedure is amenable to exact linearization leading to a closed form expression of the so called consistent algorithmic tangent moduli for viscoplasticity a closed form algorithm is developed based on the rate independent solution the methodology is applied to structural elements in which the elastic domain possesses a non smooth boundary numerical simulations are presented that illustrate the excellent performance of the algorithm

optimal prefix codes with fewer distinct codeword lengths are faster to construct abstract a new method for constructing minimum redundancy binary prefix codes is described our method does not explicitly build a huffman tree instead it uses a property of optimal prefix codes to compute the codeword lengths corresponding to the input weights let n be the number of weights and k be the number of distinct codeword lengths as produced by the algorithm for the optimal code the running time of our algorithm is o k n following our previous work no algorithm can possibly construct optimal prefix codes in o k n time if the given weights are presorted our algorithm performs o 9 k log 2 k n comparisons

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

on the numerical resolution of the discontinuous material bifurcation problem the work focuses on the numerical resolution of the discontinuous material bifurcation problem as a relevant ingredient in computational material failure mechanics the problem consists of finding the conditions for the strain localization onset in terms of the so called bifurcation time localization directions and localization modes a numerical algorithm based on the iterative resolution of a coupled eigenvalue problem in terms of the localization tensor is proposed for such purpose the algorithm is shown to be always convergent to the exact solution for the symmetric case major and minor symmetries of the tangent constitutive operator in the unsymmetric case only minor symmetries the solution is no longer exact although it is shown that using the symmetric part of the localization tensor in the proposed algorithms provides enough accurate solutions for most of cases numerical examples illustrate the benefits of the proposed methodology in terms of accuracy and savings in the computational cost associated with the problem copyright 2010 john wiley sons ltd

implementation of cyclic plasticity models based on a general form of kinematic hardening this paper deals with implementation of cyclic plastic constitutive models in which a general form of strain hardening and dynamic recovery is employed to represent the multilinear as well as non linear evolution of back stress first in order to incorporate such a general form of kinematic hardening in finite element methods successive substitution and its convergence are discussed for implicitly integrating stress moreover a new expression of consistent tangent modulus is derived by introducing a set of fourth rank constitutive parameters into discretized kinematic hardening then the constitutive parameters introduced are specified in three cases of the general form of kinematic hardening the three cases have distinct capabilities of simulating ratcheting and cyclic stress relaxation numerical examples are given to verify the convergence in successive substitution and the new expression of consistent tangent stiffness error maps for implicitly integrating stress under non proportional as well as proportional loading are also given to show that the multilinear case of the general form provides high accuracy even if strain increment is very large copyright 2002 john wiley sons ltd

on the capacity of two dimensional run length constrained channels two dimensional binary patterns that satisfy one dimensional d k run length constraints both horizontally and vertically are considered for a given d and k the capacity c sub d k is defined as c sub d k lim sub m n spl rarr spl infin log sub 2 n sub m n sup d k mn where n sub m n sup d k denotes the number of m spl times n rectangular patterns that satisfy the two dimensional d k run length constraint bounds on c sub d k are given and it is proven for every d spl ges 1 and every k d that c sub d k 0 if and only if k d 1 encoding algorithms are also discussed

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

on the theoretical and numerical modelling of armstrong frederick kinematic hardening in the finite strain regime abstract on the theoretical level the present paper presents a detailed comparison of recent finite strain models for armstrong frederick kinematic hardening thereby two strategies are discussed 1 chaboche type concepts considering the back stress as internal variable 2 continuum mechanical extensions of the classical rheological model using only strain like internal variables it is shown in the paper that models of the second kind can be recast in the format of anisotropic inelasticity with structure tensors second the work focuses on the algorithmic treatment of the kinematic hardening concepts presented before this problem has been tackled up to now only in the context of linearized models in contrast to isotropic finite elastoplasticity the integration cannot be carried out with respect to principal axes therefore a new integration algorithm is developed which is suitable for the anisotropic case but still retains plastic incompressibility in the case of small elastic deformation the algorithm reduces to a system of only one non linear equation and twelve linear equations in general the computational effort of the new scheme does not exceed the one of the backward euler scheme which has the disadvantage that plastic incompressibility is not fulfilled automatically several numerical examples show that the representatives of both approaches 1 and 2 yield similar results if physically reasonable material parameters are chosen

two dimensional constrained coding based on tiling a new variable rate coding technique is presented for two dimensional 2 d constraints for certain constraints such as the 0 2 runlength limited rll and 3 rll constraints the technique is shown to improve on previously published lower bounds on the capacity of the constraint

operator split methods for the numerical solution of the elastoplastic dynamic problem the elastoplastic dynamic problem is first formulated in a form that facilitates the application of product formula techniques the additive decomposition of the dynamic equations into elastic and plastic parts is taken as a basis for the definition of product algorithms that exploit such decomposition in the context of a finite element discretization these product algorithms entail for every time step the solution of an elastic problem followed by the application of plastic algorithms that operate on the stresses and internal variables at the integration points and bring in the plastic constitutive relations suitable plastic algorithms are discussed for the cases of perfect and hardening plasticity and viscoplasticity the proposed formalism does not depend on any notion of smoothness of the yield surface and is applicable to arbitrary convex elastic regions with or without corners the stability properties of the product algorithm are identical to those of the elastic algorithm used whereas the computational expense is practically equal to that of an elastic problem

implicit integration of plasticity models for granular materials a stress integration algorithm for granular materials based on fully implicit integration with explicit updating is presented in the implicit method the solution makes use of the gradient to the potential surface at the final stress state which is unknown the final stress and hardening parameters are determined solving the non linear equations iteratively so that the stress increment fulfills the consistency condition the integration algorithm is applicable for models depending on all the three stress invariants and it is applied to a characteristic state model for granular material since tensile stresses are not supported the functions and their derivatives are not representative outside the compressive octant of the principal stress space the elastic predictor is therefore preconditioned in order to ensure that the first predictor is within the valid region capability and robustness of the integration algorithm are illustrated by simulating both drained and undrained triaxial tests on sand the algorithm is developed in a standard format which can be implemented in several general purpose finite element codes it has been implemented as an abaqus subroutine and a traditional geotechnical problem of a flexible strip footing resting on a surface of sand is investigated in order to demonstrate the global accuracy and stability of the numerical solution

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

on nonisothermal elastoplastic analysis of shell components employing realistic hardening responses abstract in the present paper efficient numerical algorithms for elastoplastic analysis of shell like structural components will be proposed employing nonisothermal realistic highly nonlinear hardening responses the closest point projection integration algorithm is presented using a reissner mindlin type kinematic shell model completely formulated in tensor notation further a consistent elastoplastic tangent modulus is derived which ensures high convergence rates in the global iteration approach the integration algorithm has been implemented into a layered assumed strain isoparametric finite element which also enables geometrical nonlinearities including finite rotations the nonisothermal elastoplastic response of a circular cylindrical shell and a box column under axial compression is analysed under the assumption of an adiabatic process the increase in temperature is computed during elastoplastic deformation robustness and numerical stability of the proposed algorithms are demonstrated

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

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

integration methods for complex plastic constitutive equations abstract this paper shows new results concerning the finite element computations with complex plastic and viscoplastic constitutive equations the integration procedure then needs special numerical treatments when a large number of internal variables are present or for stiff non linearities implicit and explicit integration methods are compared the general solution proposed can be applied either in plasticity or in viscoplasticity for isotropic or anisotropic materials several options are proposed in the numerical scheme and for the completion step for the semi implicit scheme numerical tests are performed in order to compare the relative performances of the various approaches

design and analysis of dynamic huffman codes a new one pass algorithm for constructing dynamic huffman codes is introduced and analyzed we also analyze the one pass algorithm due to faller gallager and knuth in each algorithm both the sender and the receiver maintain equivalent dynamically varying huffman trees and the coding is done in real time we show that the number of bits used by the new algorithm to encode a message containing t letters is t bits more than that used by the conventional two pass huffman scheme independent of the alphabet size this is best possible in the worst case for any one pass huffman method tight upper and lower bounds are derived empirical tests show that the encodings produced by the new algorithm are shorter than those of the other one pass algorithm and except for long messages are shorter than those of the two pass method the new algorithm is well suited for on line encoding decoding in data networks and for tile compression

localization analysis via a geometrical method a geometrical technique is proposed in order to solve explicitly the critical conditions at localization for a quite general constitutive behaviour with isotropic elastic properties these critical conditions are shown to be closely related to the spectral properties eigenvalues and eigenvectors of the sum and difference of two tensors describing the inelastic effects when these two tensors are coaxial it is shown that the normal to a potential localization plane always lies in one of their principal planes it is also demonstrated that depending on the constitutive behaviour and the loading conditions several expressions for the critical hardening modulus at localization are available and their respective domain of validity well defined the roles and interactions of both deviatoric and hydrostatic non associativities in the critical conditions of localization are emphasized

verification of minimum redundancy prefix codes we show that verifying a given prefix code for optimality requires spl omega nlogn time indicating that the verification problem is not asymptotically easier than the construction problem alternatively we give linear time verification algorithms for several special cases that are either typical in practice or theoretically interesting

symmetry preserving return mapping algorithms and incrementally extremal paths a unification of concepts in this work we seek to characterize the conditions under which an elastic plastic stress update algorithm preserves the symmetries inherent to the material response from a numerical standpoint the aim is to determine under what conditions a stress update algorithm produces symmetric consistent tangents when applied to materials obeying normality for the ideally plastic solid we show that only the fully implicit or closest point return mapping algorithm is symmetry preserving for hardening plasticity symmetry cannot be preserved in general unless suitable restrictions are imposed on the constitutive equations we show that these restrictions amount to the existence of a pseudo internal energy function acting as a joint potential for both the direction of plastic flow and the hardening moduli in view of the fact that holonomic methods based on incrementally extremal paths also result in update rules possessing a potential structure and hence in symmetric tangents we address the question of whether any connections exist between the two approaches we show that holonomic methods and the fully implicit algorithm may indeed be brought into correspondence

a generalized elastoplastic plate theory and its algorithmic implementation in continuum mechanics within specific classes of problems one or two dimensional theories are often simpler to apply than the more complete three dimensional one this is for example the case of thin bodies such as plates or shells which may be studied using appropriate two dimensionai theories within this approach the reduction of the dimension is traded for a loss of information relative to the motion in the transverse direction for example in the case of non linear material behaviour classical plasticity plate theories are usually not able to model the effects related to the spreading of plasticity through the cross section in the present paper we discuss a generalized plasticity plate model which can be used to reproduce some of the three dimensional effects in a two dimensional setting we present the continuous and the discrete time model including both isotropic and kinematic hardening mechanisms moreover the form of the tangent matrix consistent with the discrete model is addressed finally some examples cantilever beam clamped circular plate and clamped square plate under monotonic and cyclic loading are studied numerically using a three dimensional classical plasticity theory a classical plasticity plate theory and the proposed plate theory the generalized plasticity plate model matches the three dimensional response with greater accuracy than the classical plasticity plate model

generalized midpoint integration algorithms for j2 plasticity with linear hardening we consider four schemes based on generalized midpoint rule and return map algorithm for the integration of the classical j2 plasticity model with linear hardening the comparison aiming to establish which is the preferable scheme among the four considered is both theoretical and numerical on one side extending and completing the existing results in the literature we investigate the four schemes from the theoretical viewpoint addressing in particular the existence of solution long term behaviour accuracy and stability on the other hand we develop an extensive set of numerical tests based on pointwise stress strain loading histories iso error maps and initial boundary value problems copyright 2007 john wiley sons ltd

uniqueness and localization i associative and non associative elastoplasticity abstract localization of deformation into a planar band in the incremental response of elasto plastic material is studied in the case of small strains and rotations the critical hardening modulus for localization is given in an explicit form uncoupled from the band normal for an arbitrary rate independent non associative plasticity loss of uniqueness of the response is investigated in terms of positiveness of the second order work density criteria for loss of second order work positiveness and localization are compared for plane stress and plane strain in these cases for the associative flow rule the threshold for the second order work positiveness coincides with the threshold for shear band formation this coincidence may not however occur if localization into splitting mode is attained

constrained codes as networks of relations we address the well known problem of determining the capacity of constrained coding systems while the one dimensional case is well understood to the extent that there are techniques for rigorously deriving the exact capacity in contrast computing the exact capacity of a two dimensional constrained coding system is still an elusive research challenge the only known exception in the two dimensional case is an exact however not rigorous solution to the run length limited rll system on the hexagonal lattice furthermore only exponential time algorithms are known for the related problem of counting the exact number of constrained two dimensional information arrays we present the first known rigorous technique that yields an exact capacity of a two dimensional constrained coding system in addition we devise an efficient polynomial time algorithm for counting the exact number of constrained arrays of any given size our approach is a composition of a number of ideas and techniques describing the capacity problem as a solution to a counting problem in networks of relations graph theoretic tools originally developed in the field of statistical mechanics techniques for efficiently simulating quantum circuits as well as ideas from the theory related to the spectral distribution of toeplitz matrices using our technique we derive a closed form solution to the capacity related to the path cover constraint in a two dimensional triangular array the resulting calculated capacity is path cover is a generalization of the well known one dimensional rll constraint for which the capacity is known to be

comments on loss of strong ellipticity in elastoplasticity the loss of strong ellipticity is analyzed for a rate independent infinitesimal elastoplastic model this local stability condition corresponds to the loss of positive definiteness of the symmetric part of the acoustic tensor first in the case of multisurface plasticity some expressions for the plastic hardening moduli are obtained for various bifurcation criteria next explicit expressions for the critical plastic hardening modulus and the critical orientation are obtained in the case of single surface plasticity hill type comparison solid the analysis is based on a geometric method linear isotropic elasticity and a general nonassociative flow rule are assumed however the principal axes of the second order tensors of the plastic potential and yield surfaces gradients are coaxial it is shown that similar to the loss of ellipticity the direction of the critical orientation is identical to one of the principal directions except in the particular case where the gradient of the plastic potential and yield surfaces each have a double eigenvalue in particular explicit expression for the plastic hardening modulus using the same geometric method is also presented for the raniecki type comparison solid as an illustrative example the critical orientation for the loss of strong ellipticity and the classical shear band localization loss of ellipticity are compared for axially symmetric compression and tension

the ultimate planar convex hull algorithm we present a new planar convex hull algorithm with worst case time complexity o n log h where n is the size of the input set and h is the size of the output set i e the number of vertices found to be on the hull we also show that this algorithm is asymptotically worst case optimal on a rather realistic model of computation even if the complexity of the problem is measured in terms of input as well as output size the algorithm relies on a variation of the divide and conquer paradigm which we call the marriage before conquest principle and which appears to be interesting in its own right

on failure indicators in multidissipative materials abstract multi dissipative constitutive descriptions of irreversible material degradation result in tangent operators that are made up of multiple rank one updates of the elasticity tensors multisurface elastoplasticity plastic yielding combined with elastic degradation and multicrack models are representative examples the spectral properties of these tangent operators determine failure conditions at the material level in terms of loss of uniqueness and discontinuous bifurcation of the incremental response these failure properties are analysed herein by studying the eigensolution of the sum of n rank one m m matrices and the eigensolution of n rank one updates of the m m identity matrix whereby the tangent material tensors are written in matrix form analytical eigensolutions are presented and interpreted mechanically in terms of continuous and discontinuous failure indicators in the light of these spectral properties the failure indicators of single dissipative materials are revisited and explicit results are presented for double dissipative models in the form of plasticity combined with elastic damage in particular it is shown that the activation and interaction of two dissipation processes may destabilize the tangent operators beyond the state resulting from a single active mechanism

on the implicit integration of rate dependent inelastic constitutive models although there are many different algorithms for the integration of inelastic constitutive models the fully implicit backward euler method has become the most popular one in this study further investigations on the accuracy of the backward euler method have been carried out also the performance of the discontinuous galerkin family and some implicit runge kutta time integrators is evaluated by using a simple scalar model problem accuracy of some integrators is studied when a single finite time step is applied conclusions drawn from this scalar model problem has been verified to apply also to a full six dimensional strain space formulation by numerical means special emphasis is placed on rate dependent inelastic creep models copyright 2005 john wiley sons ltd

new bounds on the capacity of multidimensional run length constraints we examine the well known problem of determining the capacity of multidimensional run length limited constrained systems by recasting the problem which is essentially a combinatorial counting problem into a probabilistic setting we are able to derive new lower and upper bounds on the capacity of 0 k rll systems these bounds are better than all previously known analytical bounds for k 2 and are tight asymptotically thus we settle the open question what is the rate at which the capacity of 0 k rll systems converges to 1 as k we also provide the first nontrivial upper bound on the capacity of general d k rll systems

capacity bounds for the three dimensional 0 1 run length limited channel the capacity c sub 0 1 sup 8 of a three dimensional 0 1 run length constrained channel is shown to satisfy 0 522501741838 spl les c sub 0 1 sup 8 spl les 0 526880847825

three space economical algorithms for calculating minimum redundancy prefix codes the minimum redundancy prefix code problem is to determine for a given list w spl omega sub 1 spl omega sub n of n positive symbol weights a list l l sub 1 l sub n of n corresponding integer codeword lengths such that spl sigma sub i 1 sup n 2 sup li spl les 1 and spl sigma sub i 1 sup n spl omega sub i l sub i is minimized let us consider the case where w is already sorted in this case the output list l can be represented by a list m m sub 1 m sub h where m sub l for l 1 h denotes the multiplicity of the codeword length l in l and h is the length of the greatest codeword fortunately h is proved to be o min log 1 p sub 1 n where p sub 1 is the smallest symbol probability given by spl omega sub 1 spl sigma sub i 1 sup n spl omega sub i we present the fast lazyhuff f lazyhuff the economical lazyhuff e lazyhuff and the best lazyhuff b lazyhuff algorithms f lazyhuff runs in o n time but requires o min h sup 2 n additional space on the other hand e lazyhuff runs in o n nlog n h time requiring only o h additional space finally b lazyhuff asymptotically overcomes the previous algorithms requiring only o n time and o h additional space moreover our three algorithms have the advantage of not writing over the input buffer during code calculation a feature that is very useful in some applications

non linear b stability and symmetry preserving return mapping algorithms for plasticity and viscoplasticity a class of second order accurate return mapping algorithms is presented which lead to symmetric algorithmic tangent moduli and contain the classical backward euler return maps as a particular case more importantly it is shown that this class of return maps is contractive relative to the natural norm defined by the complementary helmholz free energy function b stability since the equations of classical plasticity and viscoplasticity are shown to be contractive relative to this natural norm the requirement of b stability furnishes the appropriate notion of unconditionally stable algorithms for plasticity and viscoplasticity the analysis that follows depends critically on the assumption of convexity in particular the models of plasticity and viscoplasticity considered obey the principle of maximum plastic dissipation the proposed algorithms obey the discrete counterpart of this classical principle

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

properties of discontinuous bifurcation solutions in elasto plasticity explicit expressions for the spectral properties of the bifurcation problem involving discontinuities for general elastic plastic materials are presented it then follows that the classical value of the critical hardening modulus derived by rice 1976 proc 14th iutam congr delft the netherlands pp 207 220 north holland amsterdam is in fact the only possible one furthermore from the spectral analysis it follows in a very straightforward fashion that bifurcation displaying elastic unloading on one side of the singular surface can never precede bifurcation with plastic loading on both sides of this surface explicit analytical results for the critical bifurcation directions and the corresponding hardening modulus are derived for non associated volumetric flow rules while the devialoric portion is associated the considered yield and potential functions may depend on all three stress invariants and may involve mixed isotropic and kinematic hardening the result obtained by rudnicki and rice 1975 j mech phys solids 23 371 394 for a drucker pruger material appear as a special case other criteria that are investigated arc those of coulomb and rankine less

improved lower bounds on capacities of symmetric 2d constraints using rayleigh quotients a method for computing lower bounds on capacities of two dimensional 2d constraints having a symmetric presentation in either the horizontal or the vertical direction is presented the method is a generalization of the method of calkin and wilf siam j discrete math 1998 previous best lower bounds on capacities of certain constraints are improved using the method it is also shown how this method as well as their method for computing upper bounds on the capacity can be applied to constraints which are not of finite type additionally capacities of two families of multidimensional constraints are given exactly

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

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 return mapping algorithm for cyclic viscoplastic constitutive models abstract this paper presents a return mapping algorithm for cyclic viscoplastic constitutive models that include material memory effects the constitutive model is based on multi component forms of kinematic and isotropic hardening variables in conjunction with von mises yield criterion armstrong frederick a f type rules are used to describe the nonlinear evolution of each of the multi component kinematic hardening variables a saturation type exponential rule is used to describe the nonlinear evolution of each of the isotropic hardening variables the concept of memory surface is used to describe the strain range dependent material memory effects that are induced by the prior strain histories in this paper the above class of cyclic viscoplastic constitutive models is formulated within a consistent thermodynamic framework that encompasses the standard generalized materials framework furthermore a complete algorithmic treatment of the above rate dependent constitutive model is also presented for any desired stress or strain constrained configuration subspace a generalized midpoint algorithm is used to integrate the rate constitutive equations the consistent tangent operator is obtained by linearizing the return mapping algorithm and is found to be unsymmetric due to the presence of nonlinear evolution rules for the kinematic hardening variables several numerical examples representing the cyclic hardening and softening behavior transient and stabilized hysteresis behavior and the non fading memory effects of the material are presented these examples demonstrate the accuracy and robustness of the present algorithmic framework for modeling the cyclic viscoplastic behavior of the material

numerical differentiation for local and global tangent operators in computational plasticity in this paper numerical differentiation is applied to integrate plastic constitutive laws and to compute the corresponding consistent tangent operators the derivatives of the constitutive equations are approximated by means of difference schemes these derivatives are needed to achieve quadratic convergence in the integration at gauss point level and in the solution of the boundary value problem numerical differentiation is shown to be a simple robust and competitive alternative to analytical derivatives quadratic convergence is maintained provided that adequate schemes and stepsizes are chosen this point is illustrated by means of some numerical examples