recovery procedures in error estimation and adaptivity part ii adaptivity in nonlinear problems of elasto plasticity behaviour the first part of this paper 1 discusses in some detail the use of recovery procedures for stress strain or gradients for efficient error estimator and the methods of arriving at adaptive h refinement in this paper we extend such procedure to deal with elasto plasticity and discuss in detail some special features of such computation

exact integration of constitutive equations in elasto plasticity a unified approach is presented for establishing exact integration of the constitutive equations in elastoplasticity assuming the total strain rate direction to be constant this unified approach includes all previous exact integration procedures as special cases and in addition some new closed form solutions are derived for combined kinematic and isotropic hardening special emphasis is laid on combined kinematic and isotropic hardening for von mises material and on isotropic hardening for mohr coulomb and tresca materials

implicit algorithm for finite deformation hypoelastic viscoplasticity in fcc metals an implicit objective stress update algorithm is proposed for a hypoelastic viscoplastic model a thermal dynamic yield function which is derived based on the thermal activation analysis and dislocation interaction mechanisms is used along with the consistency approach and the framework of additive viscoplasticity in deriving the proposed model for fcc metals the corotational formulation approach is utilized in developing the proposed model in the finite deformation field for the case of the newton raphson iteration method a new expression for the consistent algorithmic tangent stiffness matrix of rate dependent metals is derived by direct linearization of the stress update algorithm finite element simulations are performed by implementing the proposed viscoplasticity constitutive models in the commercial finite element program abaqus numerical implementation for a simple tensile problem is used for validating the material parameters of the ofhc copper under low and high strain rates and temperatures the numerical results of the adiabatic true stress true strain curves compare very well with the experimental data the effectiveness of the present approach is tested by studying strain localization in a simple plane strain problem results indicate excellent performance of the present framework in describing the strain localization problem and in obtaining mesh independent results copyright 2006 john wiley sons ltd

elastoplastic damage modelling including the gradient of damage formulation and computational aspects a framework for continuum elastoplastic damage modelling which employs irreversible thermodynamics and internal state variables is investigated the damage part of the modelling involves the gradient of damage quantity which together with the equations of motion are issued from a new formulation of the principle of virtual power recently proposed it is shown how the plastic part of the modelling takes its standard format next we consider in detail the variational formulation and subsequent numerical implementation of the elastoplastic damage models the development of an algorithm consistent with the present formulation is given where for the plastic part it leaves the standard return mapping algorithms unchanged application is made to different classical rate independent and rate dependent plastic models with the presence of a damage mechanism the numerical implementation in the context of the finite element method is discussed in detail and a set of representative applications and numerical examples is given

remarks on rate constitutive equations for finite deformation problems computational implications it is explicitly shown that if the spatial elasticity tensor of an elastic material is taken as isotropic for all possible configurations then its coefficients cannot be constants they must depend nontrivially on the jacobian determinant of the deformation gradient moreover the assumption typically made for computational purposes that its coefficients remain constant for all possible configurations is incompatible with elasticity it is further shown that an assumption widely used in the computational literature in the context of finite deformation plasticity namely relating an objective stress rate to the rate of deformation tensor through a fourth rank constant isotropic tensor is also incompatible with elasticity thus furnishing an example of an hypoelastic material which is not elastic

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

analysis of the anisotropic viscoplastic damage response of composite laminates continuum basis and computational algorithms the mathematical structure underlying the rate equations of a recently developed constitutive model for the coupled viscoplastic damage response of anisotropic composites is critically examined in this regard a number of tensor projection operators have been identified and their properties were exploited to enable the development of a general computational framework for their numerical implementation using the euler fully implicit integration method in particular this facilitated i the derivation of explicit expressions of the consistent material tangent stiffnesses that are valid for both three dimensional as well as subspace e g plane stress formulations ii the implications of the symmetry or unsymmetry properties of these tangent operators from a thermodynamic standpoint and iii the development of an effective time step control strategy to ensure accuracy and convergence of the solution in addition the special limiting case of inviscid elastoplasticity is treated the results of several numerical simulations are given to demonstrate the effectiveness of the schemes developed

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

qualitative properties of systems of two complex homogeneous ode s a connection to polygonal billiards a correspondence between the orbits of a system of two complex homogeneous polynomial ordinary differential equations with real coefficients and those of a polygonal billiard is displayed this correspondence is general in the sense that it applies to an open set of systems of ordinary differential equations of the specified kind this allows us to transfer results well known from the theory of polygonal billiards such as ergodicity the existence of periodic orbits the absence of exponential divergence the existence of additional conservation laws and the presence of discontinuities in the dynamics to the corresponding systems of ordinary differential equations it also shows that the considerable intricacy known to exist for polygonal billiards also attends these apparently simpler systems of ordinary differential equations

the boundary of an affine invariant submanifold we study the boundary of an affine invariant submanifold of a stratum of translation surfaces in a partial compactification consisting of all finite area abelian differentials over nodal riemann surfaces modulo zero area components the main result is a formula for the tangent space to the boundary we also prove finiteness results concerning cylinders a partial converse to the cylinder deformation theorem and a result generalizing part of the veech dichotomy

a return mapping algorithm for a class of cyclic plasticity models a return mapping algorithm for a class of cyclic plasticity models is presented the constitutive model includes a quadratic yield criterion and multi component formulations of non linear isotropic and kinematic hardening thus both initially isotropic and anisotropic materials can be described and a proper description of the hysteresis loops and the cyclic hardening response of materials under cyclic loading is obtained the return mapping algorithm employs the closest point projection scheme in combination with a decomposition method to obtain an efficient and robust integration of the constitutive model the consistent tangent operator is derived in closed form and is found to be unsymmetric due to the non linear evolution of the kinematic hardening terms the accuracy and robustness of the algorithm are assessed through numerical examples

an implicit integration algorithm with a projection method for viscoplastic constitutive equations robinson s viscoplastic model a representative of the so called overstress models is integrated by use of the generalized midpoint rule the solution of the non linear system of algebraic equations arising from time discretization of the constitutive equations is determined using a projection method in combination with newton s method consistent tangent moduli are calculated and the quadratic convergence of the global newton equilibrium iteration is shown the time increment size is controlled by the convergence behaviour of the equilibrium iteration and the accuracy of the numerical integration various numerical examples are considered to demonstrate the efficiency of the methods

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

efficient and modular algorithms in modeling finite inelastic deformations objective integration parameter identification and sub stepping techniques this paper presents a general algorithmic formulation for constitutive equations describing inelastic material deformation the algorithmic representation focuses on the generality and modularity which is a key aspect within the development phase of constitutive equations it is shown explicitly how to solve the incremental constitutive equations by use of objective algorithms and an implicit integration scheme applying numerical as well as analytical derivatives although it is shown that using numerical gradients is significantly slower their application is easier especially in the development phase it is also demonstrated that having the constitutive equations modeled in the general context introduced the issue of parameter identification can be tackled by the same implementation using a driver algorithm besides parameter identification the general structure is also applied to two different fe simulations first the objectivity of different integration methods will be presented considering a simple shear loading superposed by a rigid rotation using a strain rate independent material model as example in the second example it is shown for a strain rate dependent material model how the simulation of the wire drawing process can be accelerated crucially by using sub stepping techniques

on the numerical treatment of finite deformations in elastoviscoplasticity abstract this paper deals with the generalization of a geometric linear viscoplastic model to finite strains and its numerical application we owe the original formulation of the applied model to perzyna and chaboche it includes nonlinear isotropic and kinematic hardening as well as a nonlinear rate dependence the constitutive equations are integrated numerically in the context of a finite element formulation from theoretical considerations it is known that in the case of vanishing viscosity or slow processes rate independent plasticity arises as an asymptotic limit accordingly the numerical formulation includes this property in fact the stress algorithm corresponding to viscoplasticity is reduced to the asymptotic limit in a most simple way namely by setting the viscosity parameter equal to zero furthermore it is shown that the numerical integration of the constitutive model involves the solution of only one nonlinear equation for one scalar unknown this even applies to a sum of armstrong frederick terms the algorithm incorporates the inelastic incompressibility on the level of the gau points numerical computations of examples taken from metal forming technology show the physical significance of the model and the reliability of the numerical algorithm these calculations have been carried out by means of the finite element program psu

geometrically non linear and elastoplastic three dimensional shear flexible beam element of von mises type hardening material a three dimensional elastoplastic beam element being capable of incorporating large displacement and large rotation is developed and examined elastoplastic constitutive equations are applied to the beam element based upon the assumption of small deformational strain leading to a material formulation which is completely objective for the application of stress update procedures the continuum type equations of plastic model of j2 mixed hardening are transformed into the beam equations by satisfying beam hypotheses an effective stress update algorithm is proposed to integrate elastoplastic rate equations by means of the so called multistep method which is a method of successive control of residuals on yield surfaces it avoids severe divergence when the displacement increments become large which is usual for the continuation methods material tangent stiffness matrix is derived by using consistent elastoplastic modulus resulting from the integration algorithm and is combined with geometric tangent stiffness matrix different from other elements the present element is shear flexible and can satisfy the plasticity condition in a pointwise fashion a great number of numerical examples are analysed and compared with the literature the proposed beam element is verified to be not only quite accurate but also very effective for the analyses of pre buckling and large deflection collapse of spatial framed structures

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

using partial probability weighted moments to fit the extreme value distributions to censored samples the estimation of floods of large return periods from lower bound censored samples may often be advantageous because interpolation and extrapolation are made by exploring the trend of larger floods in each of the records the method of partial probability weighted moments partial pwms is an useful technique for fitting distributions to censored samples in this paper partial pwms are redefined along with a brief discussion on the definition of ordinary pwms the expression for partial pwms is derived for the extreme value type i or gumbel distribution combined with those for the extreme value type ii and iii distributions an unified expression for partial pwms is presented for the generalized extreme value gev distribution the equations for solving the distribution parameters are provided monte carlo simulation shows that lower bound censoring at a moderate level does not unduly reduce the efficiency of high quantile estimation even if the samples have come from a true gev distribution

billiards in polygons survey of recent results in the ten or so years since the publication of ref 19 polygonal billiards have remained an active subject of research in the mathematics and physics literature as a result our understanding of the subject although still far from being complete is much better than it was ten years ago this survey attempts to give a broad overview of the dynamics of billiards in polygons with an emphasis on the material that was not in the literature in 1985 this is not a survey of the publications on polygonal billiards and we apologize to authors whose work has not been included the selection of topics has been strongly influenced by the personal taste of the author and by space limitations thus we do not discuss quantum polygonal billiards in particular quantum chaos see e g refs 41 44 and 45 we hope that somebody will write a survey on this important subject in the near future a fascinating aspect of the subject is the interplay between the geometric shape of the billiard table i e a planar curve and the qualitative features of the billiard dynamics hence it is instructive to compare polygonal billiard tables with other classes of billiard tables in particular the smooth strictly convex tables and the dispersing or sinai tables produce strikingly different types of billiard dynamics we recommend refs 46 and 15 for a general overview of the subject and a comparative study of billiard dynamics for various types of billiard tables

completely periodic directions and orbit closures of many pseudo anosov teichmueller discs in q 1 1 1 1 in this paper we investigate the closure of a large class of teichmuller discs in the stratum mathcal q 1 1 1 1 or equivalently in a rm gl 2 mathbb r invariant locus mathcal l of translation surfaces of genus three we describe a systematic way to prove that the rm gl 2 mathbb r orbit closure of a translation surface in mathcal l is the whole locus mathcal l the strategy of the proof is an analysis of completely periodic directions on such a surface and an iterated application of ratner s theorem to unipotent subgroups acting on an adequate splitting this analysis applies for example to all teichmuller discs obtained by the thurston veech s construction with a trace field of degree three which are moreover obviously not veech we produce an infinite series of such examples and show moreover that the favourable splitting situation does not arise everywhere on mathcal l contrary to the situation in genus two we also study completely periodic directions on translation surfaces in mathcal l for instance we prove that completely periodic directions are dense on surfaces obtained by the thurston veech s construction

a displacement like finite element model for j2 elastoplasticity variational formulation and finite step solution abstract the displacement like finite element formulation for finite step j2 elastoplasticity is revisited in this paper the classical computational strategy according to which plastic loading is tested at the gauss points of each element and an independent return mapping algorithm is performed for given incremental displacements is consistently derived from a suitably discretized version of a min max variational principle the sequence of solution phases to be performed within each load step adopting a full newton s method is illustrated in detail and the importance of a correct update of the plastic strains is emphasized it is further shown that in order to increase the rate of convergence and the stability properties of the newton s method the consistent elastoplastic tangent operator must be exploited even at the first iteration of each load step subsequent to the first yielding of the structural model this is in contrast with the traditional implementation according to which the elastic operator is used at the first iteration of each load step the effectiveness of the present approach is shown by a set of numerical examples referred to plane strain problems

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

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

a return mapping algorithm for elastoplastic and ductile damage constitutive equations using the subloading surface method summary in this paper is presented a return mapping algorithm for an elastoplastic damage model that couples the constitutive equations of an unconventional plasticity model with the phenomenological description of ductile damage in the continuum damage mechanics framework this approach combines the advantages of describing the mechanical property degradation by using the lemaitre model with the realistic accumulation of plastic deformation in cyclic mobility problems from the subloading surface model most of the damage models for ductile failure focus on monotonic loading conditions whereas the present model aims to extend the investigation to cyclic loading and low cycles fatigue problems a cutting plane algorithm is adopted to describe the material behavior that consider both isotropic and kinematic hardening laws two simple numerical studies show that the elastoplastic and damage model is implemented correctly displaying a quadratic rate of convergence for local equilibria and precise solutions even for large prescribed strain increments

an evaluation of substepping and implicit stress point algorithms abstract elasto plastic finite element analyses of geotechnical boundary value problems involve the use of a non linear solution strategy a popular and efficient strategy is the modified newton raphson approach of which a key element is the integration of the constitutive laws over a finite strain step two algorithms for performing such an integration are the substepping and return methods in this paper the basic assumptions behind these methods are described and the associated errors compared this comparative study is undertaken both at a fundamental level and when applied to a typical boundary value problem the errors associated with both methods are increment size dependent it is shown in the problems considered that for a particular increment size the substepping method is the more accurate

periodic billiard orbits are dense in rational polygons we show that periodic orbits are dense in the phase space for billiards in polygons for which the angle between each pair of sides is a rational multiple of 7r

elasto plastic finite element method based on incremental deformation theory and continuum based shell elements for planar anisotropic sheet materials abstract an implicit approach for the incremental analysis of planar anisotropic sheet forming processes is developed based on the incremental deformation theory the incremental deformation theory based on the minimum plastic work path enables convenient decoupling of deformation and rotation by the polar decomposition the mathematical description of a constitutive law for the incremental deformation theory is obtained from the flow theory along the minimum plastic work path the resulting constitutive law is then incorporated in an elasto plastic finite element analysis code in the elasto plastic formulation continuum based resultant cbr shell element is employed the cbr shell allows large rotation and large membrane bending strain the laminar coordinate system is taken to coincide with planar anisotropic material axes then planar anisotropic axes during deformation are updated using a newly developed algorithm based on the polar decomposition an iterative solving method based on the incremental deformation theory is also developed for an accurate and stable stress integration the planar anisotropy is incorporated into the formulation for sheet forming by introducing non quadratic barlat s yield function for verification purposes two examples have been simulated and compared with experimental results the good verification results show that the present elasto plastic formulation for planar anisotropic sheet materials can provide a good theoretical basis for more extended analyses of sheet forming processes

lh moments for statistical analysis of extreme events statistical analysis of extremes is often conducted for predicting large return period events in this paper lh moments a generalization of l moments that are based on linear combinations of higher order statistics are introduced for characterizing the upper part of distributions and larger events in data using lh moments reduces undesirable influences that small sample events may have on the estimation of large return period events the method of lh moments is formulated for the generalized extreme value gev distribution along with two detailed examples monte carlo simulations are conducted to illustrate the performance of using the method of lh moments to fit the gev distribution to both gev and non gev samples lh moment diagrams are constructed using annual maximum flow data for 107 streams worldwide to examine the ability of the gev distribution to model those series

existence of closed geodesics through a regular point on translation surfaces we show that on any translation surface if a regular point is contained in some simple closed geodesic then it is contained in infinitely many simple closed geodesics whose directions are dense in mathbb rp 1 moreover the set of points that are not contained in any simple closed geodesic is finite we also construct explicit examples showing that such points exist on some translation surfaces for a surface in any hyperelliptic component we show that this finite exceptional set is actually empty the proofs of our results use apisa s classifications of periodic points and of text gl 2 mathbb r orbit closures in hyperelliptic components as well as a recent result of eskin filip wright

coupled plastic damaged model abstract a constitutive model that couples plasticity and damage is presented the model is thermodynamically consistent and comes from a generalization of classical plasticity theory and isotropic damage theory of kachanov coupling between plasticity and damage is achieved through a simultaneous solution of the plastic and the damage problem after a description of the model a numerical algorithm for the integration of the resulting constitutive equations is presented it is an euler backward type of algorithm that is particularly suitable to solve plain stress non linear problems with a 2d finite element program the consistent stiffness matrix is also derived the paper is completed with some application examples that show that the model presented accurately reproduces the behaviour of elastic plastic damaged materials

on periodic billiard trajectories in obtuse triangles in 1775 j f de tuschis a fagnano observed that in every acute triangle the orthoptic triangle represents a periodic billiard trajectory but to the present day it is not known whether or not in every obtuse triangle a periodic billiard trajectory exists the limiting case of right triangles was settled in 1993 by f holt who proved that all right triangles possess periodic trajectories the same result had appeared independently in the russian literature in 1991 namely in the work of g a gal perin a m stepin and y b vorobets the latter authors discovered in 1992 a class of obtuse triangles which contain particular periodic billiard paths in this article we review the above mentioned results and some of the techniques used in the proofs and at the same time show for an extended class of obtuse triangles that they contain periodic billiard trajectories

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

l moment diagrams should replace product moment diagrams it is well known that product moment ratio estimators of the coefficient of variation c skewness and kurtosis exhibit substantial bias and variance for the small n 100 samples normally encountered in hydrologic applications consequently l moment ratio estimators termed l coefficient of variation 2 l skewness 3 and l kurtosis 4 are now advocated because they are nearly unbiased for all underlying distributions the advantages of l moment ratio estimators over product moment ratio estimators are not limited to small samples monte carlo experiments reveal that product moment estimators of c and are also remarkably biased for extremely large samples n 1000 from highly skewed distributions a case study using large samples n 5000 of average daily streamflow in massachusetts reveals that conventional moment diagrams based on estimates of product moments c and reveal almost no information about the distributional properties of daily streamflow whereas l moment diagrams based on estimators of 2 3 and 4 enabled us to discriminate among alternate distributional hypotheses

approximate goodness of fit tests of fitted generalized extreme value distributions using lh moments approximate goodness of fit tests of fitted generalized extreme value gev distributions using lh moments are formulated on the basis of comparison of sample lh kurtosis estimates and theoretical lh kurtosis values of the fitted distributions these tests are different from those that have been derived for testing the gev distributions of which parameter values are known a priori the tests are intended to answer the following questions does a fitted gev distribution describe adequately a given data series if not can the gev distribution function describe adequately the larger events in that data series for use for high quantile estimation if so what degree of emphasis on the larger events is needed in order that the gev distribution becomes acceptable the use of the gev distribution in conjunction with the lh moment estimation method and the formulated tests should alleviate the need for finding the correct distribution the tests are evaluated by monte carlo simulations using generated samples of both gev and wakeby distributions applications of the tests to observed annual maximum streamflow data are presented

the b bar method and the limitation principles abstract the generalized elastic material provides a reference model to cast in a unitary framework many structural models which are based on nonlinear monotone multivalued relations such as viscoelasticity plasticity and unilateral models the modified forms of the hu washizu and hellinger reissner principles and the displacement based variational formulation are recovered for the generalized elastic material starting from a functional in the complete set of state variables the related limitation principles are derived and their specialization to elasticity and elastoplasticity with mixed hardening are provided it is shown that the interpolating fields for the pressure and the volumetric strain usually adopted in the b bar method lead to a limitation principle accordingly the same elastic and elastoplastic solutions can be obtained by means of an approximate mixed displacement pressure variational principle a second application is concerned with the conditions ensuring the coincidence of the solutions between an approximate two field mixed formulation and the displacement based method numerical examples are provided to show the coincidence of the solutions obtained from different mixed finite element formulations in elasticity or elastoplasticity under the validity of the limitation principles

convergence of newton type methods in incremental return mapping analysis of elasto plastic problems abstract the incremental finite element algorithm with return mapping stress computation is considered for the solution of problems of elasto plasticity this algorithm performed in load steps leads to the necessity of solving large scale nonlinear systems the properties of these systems are investigated in the presented paper together with two iterative techniques for their solution the main results of the paper are rigorous proofs of the convergence of the inexact initial stiffness method and the local quadratic convergence of the inexact newton method with the consistent tangent operator

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

multi time step explicit implicit method for non linear structural dynamics we present a method with domain decomposition to solve time dependent non linear problems this method enables arbitrary numeric schemes of the newmark family to be coupled with different time steps in each subdomain this coupling is achieved by prescribing continuity of velocities at the interface we are more specifically interested in the coupling of implicit explicit numeric schemes taking into account material and geometric non linearities the interfaces are modelled using a dual schur formulation where the lagrange multipliers represent the interfacial forces unlike the continuous formulation the discretized formulation of the dynamic problem is unable to verify simultaneously the continuity of displacements velocities and accelerations at the interfaces we show that within the framework of the newmark family of numeric schemes continuity of velocities at the interfaces enables the definition of an algorithm which is stable for all cases envisaged to prove this stability we use an energy method i e a global method over the whole time interval in order to verify the algorithms properties then we propose to extend this to non linear situations in the following cases implicit linear explicit non linear explicit non linear explicit non linear and implicit non linear explicit non linear finally we present some examples showing the feasibility of the method copyright 2001 john wiley sons ltd

ergodicity of billiard flows and quadratic differentials on considere un systeme billard de 2 objets de masses m 1 et m 2 on montre que pour un ensemble dense de paires m 1 m 2 ce systeme est ergodique

generalized extreme value distribution fitted by lh moments for low flow frequency analysis 1 this study introduces a method based on lh moments to use the generalized extreme value gev distribution for low flow frequency analysis and investigates the capability of the gev distribution fitted by lh moments to effectively model the lower tail of the low flow frequency curve without explicitly censoring the data sample the performance of the gev l moment the gev distribution fitted by l moments and gev lh moment the gev distribution fitted by lh moments methods are assessed by evaluating the bias mean square error and relative accuracy of quantile estimates through monte carlo simulations it is shown that when both frequent low flows and extreme low flows can be adequately described by an assumed parent distribution both gev l2 moment and gev l moment methods make equally accurate quantile estimates however when frequent low flows and extreme low flows do not follow a single trend the bias of the gev l2 moment estimator is negligible while the bias of the gev l moment estimator is significant at large annual recurrence intervals on average the gev l2 moment quantile estimator displays less bias than the gev l moment quantile estimator furthermore as the annual recurrence interval increases the relative accuracy of the gev l2 moment method consistently improves over the gev l moment method the gev lh moment method is thus considered to be the more suitable method to model low flows

fully implicit integration and consistent tangent modulus in elasto plasticity this paper deals with the numerical integration of a class of rate independent elasto plastic models the backward euler scheme is used to integrate the rate constitutive relations the non linear equations obtained are solved by the newton method the consistent tangent modulus is obtained by exact linearization of the algorithm in the case of j 2 elastoplasticity with non linear isotropic hardening and non linear kinematic hardening chaboche marquis model explicit formulas are derived without any approximations

closed trajectories for quadratic differentials with an application to billiards on considere les orbites periodiques pour le systeme dynamique d une table polygonale avec des angles multiples rationnels de le billard rationnel

adaptive return mapping algorithms for j2 elasto viscoplastic flow in this paper a new class of integration algorithms for elasto viscoplastic constitutive equations is proposed it is based on the generalized trapezoidal rule which is a weighted combination of the start and end of the increment but instead of taking constant weights the weights are a function of the plastic multiplier in this way the magnitude of the plastic strain increment determines the way the integration is performed the stress update and consistent tangent are derived for the case of j2 flow several candidates within the class of adaptive return mapping algorithms are investigated it is shown numerically that some of the proposed algorithms are more accurate than commonly used algorithms such as mean normal and radial return

arbitrary lagrangian eulerian finite element analysis of large deformation in contacting bodies the primary aim of this research is to implement the arbitrary lagrangian eulerian finite element description to model large deformation of interacting bodies a pure lagrangian description is often incapable of representing their contact with sufficient precision in this work the arbitrary lagrangian eulerian ale description has been extended to the surface nodes of interacting bodies to overcome these limitations a penalty formulation has been implemented to account for the impenetrability constraint the materials have been characterized as elastic viscoplastic implicit integration schemes have been used at the global and constitutive levels for improved stability

variational principles for a class of finite step elastoplastic problems with non linear mixed hardening a class of elastoplastic relations with non linear mixed hardening is addressed in the framework of an internal variable theory the relevant finite step structural problem resulting from the time integration of the constitutive laws according to a backward difference scheme is then formulated in a geometrically linear range convex analysis and potential theory for monotone multi valued operators are shown to provide the rationale for the development of a consistent variational theory as a special result a convex minimum principle in the final values of displacements plastic strains and plastic parameters is formulated and a critical comparison with an analogous result proposed in the literature is presented

estimation of moments and quantiles using censored data censored data sets are often encountered in water quality investigations and streamflow analyses a monte carlo analysis examined the performance of three techniques for estimating the moments and quantiles of a distribution using censored data sets these techniques include a lognormal maximum likelihood estimator mle a log probability plot regression estimator and a new log partial probability weighted moment estimator data sets were generated from a number of distributions commonly used to describe water quality and water quantity variables a robust fill in method which circumvents transformation bias in the real space moments was implemented with all three estimation techniques to obtain a complete sample for computation of the sample mean and standard deviation regardless of the underlying distribution the mle generally performed as well as or better than the other estimators though the moment and quantile estimators using all three techniques had comparable log space root mean square errors rmse for censoring at or below the 20th percentile for samples sizes of n 10 the 40th percentile for n 25 and the 60th percentile for n 50 comparison of the log space rmse and real space rmse indicated that a log space rmse was a better overall metric of estimator precision

length spectra and degeneration of flat metrics in this paper we consider flat metrics semi translation structures on surfaces of finite type there are two main results the first is a complete description of when a set of simple closed curves is spectrally rigid that is when the length vector determines a metric among the class of flat metrics secondly we give an embedding into the space of geodesic currents and use this to obtain a compactification for the space of flat metrics the geometric interpretation is that flat metrics degenerate to mixed structures on the surface part flat metric and part measured foliation

line search methods in general return mapping algorithms with application to porous plasticity the present paper focuses on the application of line search methods in general return mapping algorithms two inexact line search methods and an exact line search method are investigated regarding their convergence properties within an automatic time incrementation in finite element calculations as an example for the assessment of the algorithms an elastic plastic and an elastic viscoplastic version of gurson s porous plasticity model are used in simulations of the necking of a tensile bar it is shown that larger time increments are possible and therefore a smaller number of increments are required when using line search methods the exact line search method shows the best performance concerning the required number of increments but takes more cpu time to complete the simulation the application of the inexact line search methods in general lowers the number of increments along with a reduction in the cpu time as compared with the case when no line search is used copyright 2007 john wiley sons ltd

holonomy limits of complex projective structures abstract we study the limits of holonomy representations of complex projective structures on a compact riemann surface in the morgan shalen compactification of the character variety we show that the dual r trees of the quadratic differentials associated to a divergent sequence of projective structures determine the morgan shalen limit points up to a natural folding operation for quadratic differentials with simple zeros no folding is possible and the limit of holonomy representations is isometric to the dual tree we also derive an estimate for the growth rate of the holonomy map in terms of a norm on the space of quadratic differentials

cam clay plasticity part iii extension of the infinitesimal model to include finite strains the infinitesimal version of the modified cam clay model of critical state soil mechanics is reformulated to include finite deformation effects central to the formulation are the choice of a hardening law that is appropriate for cases involving large plastic volumetric strains and the use of a class of two invariant stored energy functions appropriate for cam clay type models that includes as special cases the constant elastic shear modulus approximation as well as the pressure dependent shear modulus elastic model the analytical model is cast within the framework of finite deformation theory based on a multiplicative decomposition of the deformation gradient for the fully elasto plastic case return mapping is done implicitly in the space defined by the invariants of the elastic logarithmic principal stretches which requires the solution at each stress point of no more than three simultaneous non linear equations a finite element analysis of a strip footing problem is presented to illustrate a prototype example where finite deformation effects significantly impact the predicted response

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

second order accurate integration algorithms for von mises plasticity with a nonlinear kinematic hardening mechanism abstract two second order numerical schemes for von mises plasticity with a combination of linear isotropic and nonlinear kinematic hardening are presented the first scheme is the generalized midpoint integration procedure originally introduced by ortiz and popov in 1985 detailed and applied here to the case of armstrong frederick nonlinear kinematic hardening the second algorithm is based on the constitutive model exponential based reformulation and on the integration procedure previously introduced by the authors in the context of linearly hardening materials there are two main targets to the work firstly we wish to extensively test the generalized midpoint procedure since in the scientific literature no thorough numerical testing campaign has been carried out on this second order algorithm secondly we wish to extend the exponential based integration technique also to nonlinear hardening materials a wide numerical investigation is carried out in order to compare the performance of the two methods