strain and stress based continuum damage models ii computational aspects abstract in part i of this work we developed continuum isotropic and anisotropic elastoplastic damage models formulated either in strain space on the basis of the effective stress concept or in stress space and employing the dual notion of effective strain in part ii we consider in detail the variational formulation and subsequent numerical implementation of these models the former relies crucially on the notions of maximum plastic and maximum damage dissipation the latter makes systematic use of the operator splitting methodology to derive unconditionally stable algorithms for the numerical integration of the elastoplastic damage equations of evolution appropriate extensions to treat the proposed rate dependent viscous damage are also presented for stress based damage models our numerical treatment relies on a new three step operator split the algorithms developed lead to simple and efficient stress update procedures suitable for large scale finite element calculations application is made to a class of inviscid and rate dependent cap models with an isotropic strain based damage mechanism remarkably good agreement with existing experimental data that includes complicated stress paths is obtained numerical examples are also presented that demonstrate the good performance of the proposed algorithms

border collision period doubling scenario using a one dimensional dynamical system representing a poincare return map for dynamical systems ofthe lorenz type we investigate the border collision period doubling bifurcation scenario in contrast to theclassical period doubling scenario this scenario is formed by a sequence of pairs of bifurcations whereby eachpair consists of a border collision bifurcation and a pitchfork bifurcation the characteristic properties of thisscenario like symmetry breaking and symmetry recovering as well as emergence of coexisting attractors andnoninvariant attractive sets are investigated doi 10 1103 physreve 70 026222 pacs number s 05 45 ac 82 40 bj 95 10 fhi introduction

topological gauge theories and group cohomology we show that three dimensional chern simons gauge theories with a compact gauge groupg not necessarily connected or simply connected can be classified by the integer cohomology grouph4 bg z in a similar way possible wess zumino interactions of such a groupg are classified byh3 g z the relation between three dimensional chern simons gauge theory and two dimensional sigma models involves a certain natural map fromh4 bg z toh3 g z we generalize this correspondence to topological spin theories which are defined on three manifolds with spin structure and are related to what might be calledz2 graded chiral algebras or chiral superalgebras in two dimensions finally we discuss in some detail the formulation of these topological gauge theories for the special case of a finite group establishing links with two dimensional holomorphic orbifold models

a constitutive framework of plastically deformed damaged continuum and a formulation using theendochronic concept abstract the concepts of continuum damage mechanics cdm are discussed and aconstitutive framework of cdm is proposed for infinitesimal deformation based on the internalvariables approach the framework involves transforming the actual damaged continuum into anequivalent fictitious undamaged continuum a distinction is made between the state of damageand the damage measure the development makes use of the concept of damage force thenegative of the damage force is related to the energy required to restore the fictitious undamagedcontinuum to its undamaged state after each step of deformation and damage a set of equationand constraint governs the deformation of the fictitious continuum while another set of equationand constraint governs the damage behavior the coupling between the deformation and damageprocesses is provided for by the damage restoring force concept within the proposedconstitutive framework the endochronic concept has been used to derive explicit constitutiveequations the proposed model has been shown to describe the three dimensional state ofdeformation of a cylindrical concrete specimen subjected to uniaxial compression

a model for simulating the deterioration of structural scale material responses of microheterogeneous solids abstract in this paper we develop a model to characterize the deterioration of mechanical responses of microheterogeneous solids due to progressive microstructural failure with increased loading in the approach the effects of microscopic failure so called relaxation are described by a variational boundary value problem with constraints on the microfields the extent of the relaxation which is induced by reducing the eigenvalues of the elasticity tensor at a point in the heterogeneous body is dictated by the condition that the solution must satisfy the equations of equilibrium and simultaneously the constraints at that point theoretical properties of the model are determined and a computational algorithm is developed to simulate the deterioration of the material microstructure numerical simulations involving the finite element method are given to illustrate various aspects of the model

an augmented multicrack elastoplastic damage model for tensile cracking abstract in this paper we present the general formulation and numerical aspects of an augmented multicrack elastoplastic damage model aiming to reflect the crack induced anisotropy in concrete like quasi brittle materials consistent evolution laws for the involved internal variables are derived based on the augmented lagrangian method the time discrete formulation and the corresponding variational structure are investigated with the euler lagrangian equations defining the closest point projection approximation of the proposed model the numerical aspects such as the stress updating algorithm and the algorithmic consistent tangent moduli are also discussed in details it is found that in the developed numerical algorithm the active loading surfaces are determined in such a posterior manner that potential numerical problems due to the iteratively updating procedure in classical algorithms can be avoided the proposed model is applied to the modeling of tensile cracking in concrete the behavior of a single crack is characterized by an elliptical cracking surface and a hyperbolic softening function with the orientations of potential cracks determined by mohr s postulate the model is verified by calculating the single point stress vs strain relations of concrete under several typical proportional and non proportional loading cases finally two benchmark tests of concrete structures i e four point bending beam under cyclic loading hordijk 1992 and double edge notched specimens under mixed tension shear forces nooru mohamed 1992 are numerically simulated both predicted load vs displacement curves and crack patterns agree well with the experimental data

damage integration in the strain space the focus is on isotropic elastodamaging softening materials where the damage parameter is expressed as a function of the total strain by integrating the mechanical work in the strain space along a stepwise holonomic loading history an incremental strain energy is obtained a coaxiality condition for the incremental strain energy to be potential is identified and its implications on the associativity of the damage evolution are discussed under some hypotheses the increment of the mechanical work is shown to be minimum along strain radial paths these results are used to construct a multifield variational framework supporting finite element nonlocal formulations

localisation in a cosserat continuum under static and dynamic loading conditions abstract localisation studies have been carried out for an unconstrained elasto plastic strain softening cosserat continuum because of the presence of an internal length scale in this continuum model a perfect convergence is found upon mesh refinement a finite constant width of the localisation zone and a finite energy dissipation are computed under static as well as under transient loading conditions because of the existence of rotational degrees of freedom in a cosserat continuum additional wave types arise and wave propagation becomes dispersive this has been investigated analytically and numerically for an elastic cosserat continuum and an excellent agreement has been found between both solutions

fracture mechanics analysis using the wavelet galerkin method and extended finite element method summary this paper presents fracture mechanics analysis using the wavelet galerkin method and extended finite element method the wavelet galerkin method is a new methodology to solve partial differential equations where scaling wavelet functions are used as basis functions in solid structural analyses the analysis domain is divided into equally spaced structured cells and scaling functions are periodically placed throughout the domain to improve accuracy wavelet functions are superposed on the scaling functions within a region having a high stress concentration such as near a hole or notch thus the method can be considered a refinement technique in fixed grid approaches however because the basis functions are assumed to be continuous in applications of the wavelet galerkin method there are difficulties in treating displacement discontinuities across the crack surface in the present research we introduce enrichment functions in the wavelet galerkin formulation to take into account the discontinuous displacements and high stress concentration around the crack tip by applying the concept of the extended finite element method this paper presents the mathematical formulation and numerical implementation of the proposed technique as numerical examples stress intensity factor evaluations and crack propagation analyses for two dimensional cracks are presented copyright 2012 john wiley sons ltd

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

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

damage tensors and the crack density distribution abstract the paper presents an algorithm for the derivation of damage tensors emphasizing its relationship with the actual and approximate crack density distributions the proposed model is illustrated using scalar second and fourth order continuous tensor approximations of some typical two and three dimensional crack distributions it is also shown that the occurrence of regions with negative crack density anticrack regions is in many cases a common and as yet unexplored feature of the approximate solutions

high performance parallel simulation of structure degradation using non local damage models simulating damage and failure of metallic or composite structures often fails when using standard finite element discretizations and a newton raphson solving procedure the difficulties arise from an uncontrolled mesh dependency caused by damage localization to structural instabilities and to an increase of computational costs the first problem can be overcome by using non local damage constitutive equations together with a specific finite element model the second problem can then be solved with an arc length method which manages instabilities and snap backs they are caused by the loss of strength carrying capacity of the damaged material finally the whole computational scheme is parallelized the main contribution of this paper consists in bringing together the three numerical techniques non local material model piloting and parallel computations the resulting numerical scheme allows to go beyond the overly simplistic cases often encountered in the literature it allows robust industrial simulations with a high number of degrees of freedom both in two and three dimensions and deepened studies involving a large number of simulations

stochastic dynamics of invasion and fixation we study evolutionary game dynamics in finite populations we analyze an evolutionary process which we call pairwise comparison for which we adopt the ubiquitous fermi distribution function from statistical mechanics the inverse temperature in this process controls the intensity of selection leading to a unified framework for evolutionary dynamics at all intensities of selection from random drift to imitation dynamics we derive a simple closed formula that determines the feasibility of cooperation in finite populations whenever cooperation is modeled in terms of any symmetric two person game in contrast with previous results the present formula is valid at all intensities of selection and for any initial condition we investigate the evolutionary dynamics of cooperators in finite populations and study the interplay between intensity of selection and the remnants of interior fixed points in infinite populations as a function of a given initial number of cooperators showing how this interplay strongly affects the approach to fixation of a given trait in finite populations leading to counterintuitive results at different intensities of selection

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

the variational multiscale method a paradigm for computational mechanics abstract we present a general treatment of the variational multiscale method in the context of an abstract dirichlet problem we show how the exact theory represents a paradigm for subgrid scale models and a posteriori error estimation we examine hierarchical p methods and bubbles in order to understand and ultimately approximate the fine scale green s function which appears in the theory we review relationships between residual free bubbles element green s functions and stabilized methods these suggest the applicability of the methodology to physically interesting problems in fluid mechanics acoustics and electromagnetics

on the determinant of elliptic differential and finite difference operators in vector bundles over s 1 for an elliptic differential operatora overs 1 a sum limits k 0 n a k x d k witha k x in end r and as a principal angle the regularized determinant det a is computed in terms of the monodromy mapp a associated toa and some invariant expressed in terms ofa n anda n 1 a similar formula holds for finite difference operators a number of applications and implications are given in particular we present a formula for the signature ofa whena is self adjoint and show that the determinant ofa is the limit of a sequence of computable expressions involving determinants of difference approximation ofa

biorthogonal bases of compactly supported wavelets orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide we show here that under fairly general conditions exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual riesz bases of compactly supported wavelets we give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions and we present a sufficient condition for the decay of their fourier transforms we study the regularity of these biorthogonal bases we provide several families of examples all symmetric corresponding to linear phase filters in particular we can construct symmetric biorthogonal wavelet bases with arbitrarily high preassigned regularity we also show how to construct symmetric biorthogonal wavelet bases close to a nonsymmetric orthonormal basis

transforms associated to square integrable group representations i general results let g be a locally compact group which need not be unimodular let x u x x g be an irreducible unitary representation of g in a hilbert space h u assume that u is square integrable i e that there exists in h u at least one nonzero vector g such that u x g g 2 dx we give here a reasonably self contained analysis of the correspondence associating to every vector f h u the function u x g f on g discussing its isometry characterization of the range inversion and simplest interpolation properties this correspondence underlies many properties of generalized coherent states

a unified theory of elastic degradation and damage based on a loading surface a number of new models with stiffness degradation have been proposd in recent literature in the small strain regime however most of these works represent specific formulations each using its own terminology notation and assumptions and relatively little effort has been spent so far towards achieving a common theoretical framework similar for instance to the theory of elastoplasticity moreover most of the existing damage models are presented with intensive recourse to abstract thermodynamics concepts and they combine stiffness degradation with plasticity which though being ultimately necessary to represent the actual material behavior makes it much more difficult to isolate analyse and understand the properties of the formulation for elastic stiffness degradation as a contribution in this field this paper presents a unifying theoretical framework to describe a class of models for elastic stiffness degradation based on the concept of loading surface the derivation includes two consecutive steps first the constitutive framework for elastic degrading models with evolution laws which are expressed directly in terms of the secant stiffness or compliance tensor and second the elastic damage models in which the scant stiffness or compliance is assumed to depend on a reduced set of damage variables with clearer physical meaning and simpler evolution laws whenever possible terminology is borrowed from the classical formulation of elastoplasticity and thermodynamic concepts are introduced only as needed both stress based and strain based developments are compared throughout the paper and the concept of associativity is reanalysed and generalized within the new unified framework of elastic degradation the most significant scalar damage models found in the literature are reinterpreted in the context of this unified theory finally a general expression is obtained for the tangential stiffness operator of associated scalar models stress and strain based of the 1 d type that includes all the models considered as particular cases more general damage formulations scalar non 1 d vectorial tensorial are reviewed and discussed systematically in a sequel paper

the use of displacement discontinuities in a rate dependent medium abstract this paper illustrates the use of displacement discontinuities in a rate dependent elastoplastic damage model rate dependency is considered in the framework of perzyna viscoplasticity displacement discontinuities are incorporated using the partition of unity property of finite element shape functions a combined continuous discontinuous approach is proposed in which a discontinuity is only inserted after a certain amount of damage various examples illustrate the applicability of the combined approach to granular and quasi brittle materials with and without fibre reinforcement

on energy based coupled elastoplastic damage theories constitutive modeling and computational aspects abstract novel energy based coupled elastoplastic damage theories are presented in this paper the proposed formulation employs irreversible thermodynamics and internal state variable theory for ductile and brittle materials at variance with lemaitre s work on damage elastoplasticity the present formulation renders rational thermodynamic potential and damage energy release rate in contrast to previous work by simo and ju featuring an additive split of the stress tensor current formulation assumes an additive split of the strain tensor it is shown that the strain split damage elastoplasticity formulation leads to more robust tangent moduli than the stress split formulation the plastic flow rule and hardening law are characterized in terms of the effective quantities viz the effective stress space plasticity this mechanism is both physically well motivated and computationally efficient further a fourth order anisotropic damage mechanism is proposed for brittle materials rational mechanisms are also presented to account for the microcrack opening and closing operations as well as the strain rate dependency of microcrack growth efficient computational algorithms for proposed elasloplaslic damage models are subsequently explored by making use of the operator splitting methodology in particular new three step operator split algorithms are presented application is made to a class of inviseid and rate dependent cap damage models for concrete and mortar experimental validations are also given to illustrate the applicability of the proposed damage models

scaling behavior in a proportional voting process we perform a statistical analysis on the proportional elections held in brazil in october 1998 we show that the distribution of votes among candidates for the whole country follows a power law n v ensuremath propto v ensuremath ensuremath alpha with ensuremath alpha 1 00 ifmmode pm else textpm fi 0 02 extending over two orders of magnitude the voting distributions for several states of the federation also display scale invariant behavior with ensuremath alpha ensuremath approx 1 we argue that this particular voting system can be modeled as a typical multiplicative process in which the choice of the candidate is governed by a product of probabilities

numerical shakedown analysis of damaged structures a numerical method is proposed to predict the failure of mechanical structures it is based on the generalization of the classical static shakedown theorem to damaged inelastic structures ductile plastic damage is taken into account by using the models of lemaitre and shichun hua the obtained results are compared in the special case of limit analysis to those obtained by incremental methods

border collision bifurcations an explanation for observed bifurcation phenomena recently physical and computer experiments involving systems describable by continuous maps that are nondifferentiable on some surface in phase space have revealed novel bifurcation phenomena these phenomena are part of a rich new class of bifurcations which we call border collision bifurcations a general criterion for the occurrence of border collision bifurcations is given illustrative numerical results including transitions to chaotic attractors are presented these border collision bifurcations are found in a variety of physical experiments

reconsideration on the elastic damage degradation theory for the modeling of microcrack closure reopening mcr effects abstract despite the substantial and noteworthy contributions the modeling of damage induced anisotropy remains an unsolved issue especially when the microcrack closure reopening mcr effects are accounted for theoretically speaking the most challenging problem might be the lack of energy conservation for all the existing models employing the spectral decomposition of the stress or strain tensor and the associated positive negative projection operators carol and willam 1996 in this paper this crucial problem is solved by introducing a new definition of thermodynamically consistent projection operators into the classical elastic damage degradation model the orthogonality between the rates of the new projection operators and the stress or strain automatically guarantees the fulfillment of energy conservation under any arbitrary proportional or non proportional load history moreover with this extra orthogonal property the thermodynamically consistent projection operators can be exclusively determined in a unique form the above advantages lend to their promising use in the modeling of damage induced anisotropy and mcr effects simultaneously with the aid of the thermodynamically consistent projection operators the existing elastic damage degradation models can be reformulated so that the energy conservation is restored only with minor modifications as a prototype example a stress based elastic damage degradation model with multiple loading surfaces is developed analogously to the classical multisurface plasticity model finally a simple closed loop load path accompanied with rotation of principal stress directions is constructed to verify its thermodynamically consistency

numerical analysis of anisotropic ductile continuum damage abstract the paper deals with the numerical analysis of large elastic plastic deformation behavior of anisotropically damaged ductile solids based on a generalized macroscopic theory within the framework of nonlinear continuum damage mechanics estimates of the stress and strain histories are obtained from a straightforward numerical integration algorithm based on operator split methodology which employs an inelastic damage plastic predictor followed by an elastic corrector step the finite element method is used to approximate the linearized variational problem furthermore identification of material parameters is discussed numerical simulation of the elastic plastic deformation behavior of damaged tension specimens demonstrate the efficiency of the formulation

application of the sinc method to a dynamic elasto plastic problem this paper presents the application of sinc bases to simulate numerically the dynamic behavior of a one dimensional elastoplastic problem the numerical methods that are traditionally employed to solve elastoplastic problems include finite difference finite element and spectral methods however more recently biorthogonal wavelet bases have been used to study the dynamic response of a uniaxial elasto plastic rod giovanni f naldi karsten urban paolo venini a wavelet galerkin method for elastoplasticity problems report 181 rwth aachen igpm and math modelling and scient computing vol 10 2000 in this paper the sinc galerkin method is used to solve the straight elasto plastic rod problem due to their exponential convergence rates and their need for a relatively fewer nodal points sinc based methods can significantly outperform traditional numerical methods j lund k l bowers sinc methods for quadrature and differential equations siam philadelphia 1992 however the potential of sinc based methods for solving elastoplasticity problems has not yet been explored the aim of this paper is to demonstrate the possible application of sinc methods through the numerical investigation of the unsteady one dimensional elastic plastic rod problem

on nonlocal damage models for interface problems abstract consistent with thermodynamic restrictions nonlocal formulations of damage models are investigated with regard to their analytical and numerical capabilities for predicting the evolution of microcracking to trace the post limit structural response with an efficient numerical algorithm an incremental iterative solution strategy is constructed through the use of an initial elasticity stiffness matrix and an evolving localization constraint the constraint is related to a suitable measure of microcracking at the most severely damaged element that changes with the evolution of a localization zone as a simple phenomenological approach a nonlocal feature is incorporated into the constitutive model through the gradient of a scalar measure of damage and a symmetry boundary condition is invoked for the nonlocal governing differential equation in numerical calculations the gradient is evaluated through a simple difference scheme for applications to the interface problems with geologic media the proposed procedure is verified with analytical solutions for one dimensional cases and illustrated with two dimensional cases for which experimental observations are available some important theoretical and computational issues associated with nonlocal models are then discussed based on the results obtained

stochastic bifurcations in the nonlinear parallel ising model we investigate the phase transitions of a nonlinear parallel version of the ising model characterized by an antiferromagnetic linear coupling and ferromagnetic nonlinear one this model arises in problems of opinion formation the mean field approximation shows chaotic oscillations by changing the couplings or the connectivity the spatial model shows bifurcations in the average magnetization similar to that seen in the mean field approximation induced by the change of the topology after rewiring short range to long range connection as predicted by the small world effect these coherent periodic and chaotic oscillations of the magnetization reflect a certain degree of synchronization of the spins induced by long range couplings similar bifurcations may be induced in the randomly connected model by changing the couplings or the connectivity and also the dilution degree of asynchronism of the updating we also examined the effects of inhomogeneity mixing ferromagnetic and antiferromagnetic coupling which induces an unexpected bifurcation diagram with a bubbling behavior as also happens for dilution

border collision bifurcations including period two to period three for piecewise smooth systems abstract we examine bifurcation phenomena for maps that are piecewise smooth and depend continuously on a parameter in the simplest case there is a surface in phase space along which the map has no derivative or has two one sided derivatives is the border of two regions in which the map is smooth as the parameter is varied a fixed point e may collide with the border and we may assume that this collision occurs at 0 a variety of bifurcations occur frequently in such situations but never or almost never occur in smooth systems in particular e may cross the border and so will exist for 0 but it may be a saddle in one case say 0 for 0 there may be a stable period 3 orbit which similarly shrinks to e0 as 0 hence one observes the following stable periodic orbits a stable period 2 orbit collapses to a point and is reborn as a stable period 3 orbit we also see analogously stable period 2 to stable period p orbit bifurcations with p 5 11 52 or period 2 to quasi periodic or even to a chaotic attractor we believe this phenomenon will be seen in many applications

the superconvergent patch recovery and a posteriori error estimates part 1 the recovery technique this is the first of two papers concerning superconvergent recovery techniques and a posteriori error estimation in this paper a general recovery technique is developed for determining the derivatives stresses of the finite element solutions at nodes the implementation of the recovery technique is simple and cost effective the technique has been tested for a group of widely used linear quadratic and cubic elements for both one and two dimensional problems numerical experiments demonstrate that the recovered nodal values of the derivatives with linear and cubic elements are superconvergent one order higher accuracy is achieved by the procedure with linear and cubic elements but two order higher accuracy is achieved for the derivatives with quadratic elements in particular an o h4 convergence of the nodal values of the derivatives for a quadratic triangular element is reported for the first time the performance of the proposed technique is compared with the widely used smoothing procedure of global l2 projection and other methods it is found that the derivatives recovered at interelement nodes by using l2 projection are also superconvergent for linear elements but not for quadratic elements numerical experiments on the convergence of the recovered solutions in the energy norm are also presented higher rates of convergence are again observed the results presented in this part of the paper indicate clearly that a new powerful and economical process is now available which should supersede the currently used post processing procedures applied in most codes

using the refinement equation for evaluating integrals of wavelets the wavelet galerkin method for solving partial differential equations leads to the problem of computing integrals of products of derivatives of wavelets this paper studies the problem from the point of view of stationary subdivision schemes one of the main results is to identify these integrals as components of the unique solution of a certain eigenvector moment problem associated with the coefficients of the refinement equation asymptotic expansions for the corresponding subdivision schemes form an important ingredient of our approach

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

secant structural solution strategies under element constraint for incremental damage abstract two major difficulties in the nonlinear analysis of post peak structural behavior are the occurrence of an ill conditioned tangent stiffness matrix around critical points namely limit and bifurcation points and the selection of a suitable constrain on the solution path as an attempt to make failure prediction available in a routine manner new solution strategies are proposed in which a secant structural stiffness matrix is formulated for incremental damage models and the solution path is controlled through a suitable measure of failure at the most severely damaged point in the body numerical solutions are given for plane strain and plane stress problems to show that snap back and snap through associated with shear band formation can be inexpensively predicted

the noisy voter model under the influence of contrarians abstract the influence of contrarians on the noisy voter model is studied at the mean field level the noisy voter model is a variant of the voter model where agents can adopt two opinions optimistic or pessimistic and can change them by means of an imitation herding and an intrinsic noise mechanisms an ensemble of noisy voters undergoes a finite size phase transition upon increasing the relative importance of the noise to the herding form a bimodal phase where most of the agents share the same opinion to a unimodal phase where almost the same fraction of agent are in opposite states by the inclusion of contrarians we allow for some voters to adopt the opposite opinion of other agents anti herding we first consider the case of only contrarians and show that the only possible steady state is the unimodal one more generally when voters and contrarians are present we show that the bimodal unimodal transition of the noisy voter model prevails only if the number of contrarians in the system is smaller than four and their characteristic rates are small enough for the number of contrarians bigger or equal to four the voters and the contrarians can be seen only in the unimodal phase moreover if the number of voters and contrarians as well as the noise and herding rates are of the same order then the probability functions of the steady state are very well approximated by the gaussian distribution

coupled damage and plasticity models derived from energy and dissipation potentials a theoretical framework is defined that allows plasticity and damage models of inelastic behaviour to be combined within a consistent approach much emphasis is placed on the fact that within this framework the entire constitutive response is specified through two potential functions with no additional assumptions or evolution equations being necessary both plastic strain and damage parameter have roles as internal variables within the theory two classes of models are derived involving respectively uncoupled and coupled plasticity and damage examples of application of the theory are presented

disorder induced phase transition in kinetic models of opinion dynamics abstract we propose a model of continuous opinion dynamics where mutual interactions can be both positive and negative different types of distributions for the interactions all characterized by a single parameter p denoting the fraction of negative interactions are considered results from exact calculation of a discrete version and numerical simulations of the continuous version of the model indicate the existence of a universal continuous phase transition at p p c below which a consensus is reached although the order disorder transition is analogous to a ferromagnetic paramagnetic phase transition with comparable critical exponents the model is characterized by some distinctive features relevant to a social system

coupled creep elastoplastic damage analysis for isotropic and anisotropic nonlinear materials abstract this paper deals with the computational aspects of a coupled creep elastoplastic damage analysis for anisotropic and as a special case isotropic nonlinear materials a three phase backward euler integration algorithm for stress update is proposed for anisotropic nonlinear materials a general direct stress return mapping algorithm utilising newton raphson iteration is derived the stress vector and scalar variables quantifying the incremental creep plasticity and damage are updated simultaneously for isotropic materials the elasto plastic stress update algorithm for plane stress by jetteur 1986 engng camp 3 251 253 is extended to include creep and damage in addition a simple stress algorithm for the general three dimensional isotropic case is also presented the resulting algorithms are suitable for inclusion in general structural analysis codes the consistent tangent matrix is also formulated for use in a global newton iterative procedure in which structural displacements are sought as the problem unknowns examples are given using the general purpose code lusas in which the algorithms have been implemented

a new variational theory and a computational algorithm for coupled elastoplastic damage models a model of elastoplasticity with hardening coupled with ductile damage which allows anisotropic change of the shape of the damage domain is presented the assumption for the development of the constitutive model consists in assigning the elastic and damage domains and the free energy the general variational formulation for the elastoplastic model coupled with damage is derived as well as a mixed principle which is useful from the computational standpoint accordingly a solution algorithm is then derived and examples are presented

a thermodynamically consistent plastic damage framework for localized failure in quasi brittle solids material model and strain localization analysis aiming for the modeling of localized failure in quasi brittle solids this paper addresses a thermodynamically consistent plastic damage framework and the corresponding strain localization analysis a unified elastoplastic damage model is first presented based on two alternative kinematic decompositions assuming infinitesimal deformations with the evolution laws of involved internal variables characterized by a dissipative flow tensor for the strong or regularized discontinuity to form in such inelastic quasi brittle solids and to evolve eventually into a fully softened one a novel strain localization analysis is then suggested a kinematic constraint more demanding than the classical discontinuous bifurcation condition is derived by accounting for the traction continuity and the loading unloading states consistent with the kinematics of a strong or regularized discontinuity more specifically the strain jumps characterized by maxwell s kinematic condition have to be completely inelastic energy dissipative reproduction of this kinematics implies vanishing of the aforesaid dissipative flow tensorial components in the directions orthogonal to the discontinuity orientation this property allows naturally developing a localized plastic damage model for the discontinuity band with its orientation and the traction based failure criterion consistently determined a posteriori from the given stress based counterpart the general results are then particularized to the 2d conditions of plane stress and plane strain it is found that in the case of plane stress strain localization into a strong or regularized discontinuity can occur at the onset of strain softening contrariwise owing to an extra kinematic constraint in the condition of plane strain some continuous inelastic deformations and substantial re orientation of principal strain directions in general have to take place in the softening regime prior to strain localization the classical rankine mohr coulomb von mises j2 and drucker prager criteria are analyzed as illustrative examples in particular both the closed form solutions for the discontinuity angles validated by numerical simulations and the corresponding traction based failure criteria are obtained

quantum field theory in ninety minutes on presente divers aspects de la theorie quantique des champs la theorie p 2 a 2 dimensions la theorie 3 4 a 3 dimensions la theorie de yang mills a 4 dimensions

adaptive meshing for dynamic strain localization a mesh enrichment procedure is developed to capture the shear band for strain localization in elasto visco plastic solids the enriched mesh comprises four and five noded quadrilateral elements which can be adaptively refined in the localized zone the criterion for mesh adaption combines three well known localization characteristics to predict the onset of localization in individual elements a modified procedure for transferring state variables between two successive refined meshes is proposed the procedure is tested by solving several sample problems consistent and stable solutions are obtained in particular shear band widths and plastic strains are found to converge to stable values the results are compared with solutions using the enriched displacement procedure defined in l the efficiency of the global adaptive scheme is tested on initial and boundary value problems that involve different material properties and geometries

nonequilibrium transitions in complex networks a model of social interaction we analyze the nonequilibrium order disorder transition of axelrod s model of social interaction in several complex networks in a small world network we find a transition between an ordered homogeneous state and a disordered state the transition point is shifted by the degree of spatial disorder of the underlying network the network disorder favoring ordered configurations in random scale free networks the transition is only observed for finite size systems showing system size scaling while in the thermodynamic limit only ordered configurations are always obtained thus in the thermodynamic limit the transition disappears however in structured scale free networks the phase transition between an ordered and a disordered phase is restored

wavelet galerkin method for one dimensional elastoplasticity and damage problems constitutive modeling and computational aspects abstract this work presents an analysis of the wavelet galerkin method for one dimensional elastoplastic damage problems time stepping algorithm for non linear dynamics is presented numerical treatment of the constitutive models is developed by the use of return mapping algorithm for spacial discretization we can use wavelet galerkin method instead of standard finite element method this approach allows to locate singularities the discrete formulation developed can be applied to the simulation of one dimensional problems for elastic plastic damage models

pseudo potential of elastoplastic damage constitutive model and its application damage pseudo potentials from which the damage evolution equations can be acquired are usually expressed as scalar functions of irreversible thermodynamic variables a lower potential for an action with the dissipation property corresponds to a helmholtz free energy function in classical mechanics therefore pseudo potential acts as a cornerstone of the damage constitutive relationship according to the analysis on state and process of a damage system the authors study the connection between damage action pseudo potential and free energy function next a general method to define the pseudo potential of damage process is discussed the discrete elementary equations of continuum damage mechanics are derived from the action functional subsequently the numerical implementation of the aforementioned damage model is given comparison between experimental evidences and numerical results verifies the soundness of the theoretical model and the numerical framework

universality of weak selection weak selection which means a phenotype is slightly advantageous over another is an important limiting case in evolutionary biology recently it has been introduced into evolutionary game theory in evolutionary game dynamics the probability to be imitated or to reproduce depends on the performance in a game the influence of the game on the stochastic dynamics in finite populations is governed by the intensity of selection in many models of both unstructured and structured populations a key assumption allowing analytical calculations is weak selection which means that all individuals perform approximately equally well in the weak selection limit many different microscopic evolutionary models have the same or similar properties how universal is weak selection for those microscopic evolutionary processes we answer this question by investigating the fixation probability and the average fixation time not only up to linear but also up to higher orders in selection intensity we find universal higher order expansions which allow a rescaling of the selection intensity with this we can identify specific models which violate linear weak selection results such as the one third rule of coordination games in finite but large populations

ondelettes and phase cell cluster expansions a vindication y meyer has recently developed a particularly useful o n basis forl2 r d expansions using this basis i e expansions into ondelettes or wavelets have yielded important new results in soft and hard analysis the expansion into ondelettes of a boson scalar field naturally leads to phase cell cluster expansions a formalism already developed by the authors using other related bases adoption of ondelettes expansions into the phase cell program gives improvements of some extant results and excises an early error

a block spin construction of ondelettes part i lemarie functions using block spin assignments we construct anl2 orthonormal basis consisting of dyadic scalings and translates of just a finite number of functions these functions have exponential localization and for even values of a construction parameterm one can make them classcm 1 with vanishing moments up to orderm inclusive such a basis has an important application to phase cell cluster expansions in quantum field theory

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

phase space localization theorem for ondelettes it is proven that an orthonormal basis of ondelettes can never have exponential localization in both position space and momentum space

computational damage mechanics for composite materials based on mathematical homogenization this paper is aimed at developing a non local theory for obtaining numerical approximation to a boundary value problem describing damage phenomena in a brittle composite material the mathematical homogenization method based on double scale asymptotic expansion is generalized to account for damage effects in heterogeneous media a closed form expression relating local fields to the overall strain and damage is derived non local damage theory is developed by introducing the concept of non local phase fields stress strain free energy density damage release rate etc in a manner analogous to that currently practiced in concrete 1 2 with the only exception being that the weight functions are taken to be c0 continuous over a single phase and zero elsewhere numerical results of our model were found to be in good agreement with experimental data of 4 point bend test conducted on composite beam made of blackglas nextel 5 harness satin weave copyright 1999 john wiley sons ltd

on the localization of topological invariants the approach of formal differential geometry to the topological invariants which can be localized is developed the universal space and universal characteristic forms are constructed they give rise to primary and secondary characteristic forms

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

an adaptive wavelet galerkin method for an elastic plastic damage constitutive model 1d problem we present a wavelet galerkin method for the analysis of elastic plastic damage systems ju s model j w ju int j solids struct 25 1989 803 is explicitly considered and numerically tested but the method applies equally well to a broad range of damage mechanics models a three step elastic predictor plastic corrector damage corrector strategy is the core of the proposed approach we use a displacement approach with wavelet interpolating functions instead of classical polynomials this allows to clearly locate those sites in the system where damage is taking place thanks to the high pass filtering action operated by the wavelets this opens the way to inexpensive self adaptive strategies that are introduced and preliminary tested herein

gradient dependent plasticity formulation and algorithmic aspects a plasticity theory is proposed in which the yield strength not only depends on an equivalent plastic strain measure hardening parameter but also on the laplacian thereof the consistency condition now results in a differential equation instead of an algebraic equation as in conventional plasticity to properly solve the set of non linear differential equations the plastic multiplier is discretized in addition to the usual discretization of the displacements for appropriate boundary conditions this formulation can also be derived from a variational principle accordingly the theory is complete

a pgd based multiscale formulation for non linear solid mechanics under small deformations abstract model reduction techniques have became an attractive and a promising field to be applied in multiscale methods the main objective of this work is to formulate a multiscale procedure for non linear problems based on parametrized microscale models the novelty of this work relies in the implementation of the model reduction technique known as proper generalized decomposition for solving the high dimensional parametrized problem resulting from the microscale model the multiscale framework here proposed is formulated to non linear problems specifically to material non linearities where material response is governed by a strain dependent evolution law two strategies to deal with this kind of problem under small deformations are detailed in this work both strategies based on parametrized microscale models solved by pgd have been applied to a problem with a rate dependent isotropic damage model first a procedure where the problem is solved by uncoupling the equilibrium equation to the state variable expression has been explored in order to alleviate the parametrized microscale problem a second strategy for problems with material non linearity has been proposed incorporating a parametrized microscale problem at each macroscale increment fe pgd the basis of those procedures are described and compared highlighting the solution accuracy and computer time consumption in comparison to a traditional finite element analysis

lattice structures for optimal design and robust implementation of two channel perfect reconstruction qmf banks a lattice structure and an algorithm are presented for the design of two channel qmf quadrature mirror filter banks satisfying a sufficient condition for perfect reconstruction the structure inherently has the perfect reconstruction property while the algorithm ensures a good stopband attenuation for each of the analysis filters implementations of such lattice structures are robust in the sense that the perfect reconstruction property is preserved in spite of coefficient quantization the lattice structure has the hierarchical property that a higher order perfect reconstruction qmf bank can be obtained from a lower order perfect reconstruction qmf bank simply by adding more lattice sections several numerical examples are provided in the form of design tables

random graphs with arbitrary degree distributions and their applications recent work on the structure of social networks and the internet has focused attention on graphs with distributions of vertex degree that are significantly different from the poisson degree distributions that have been widely studied in the past in this paper we develop in detail the theory of random graphs with arbitrary degree distributions in addition to simple undirected unipartite graphs we examine the properties of directed and bipartite graphs among other results we derive exact expressions for the position of the phase transition at which a giant component first forms the mean component size the size of the giant component if there is one the mean number of vertices a certain distance away from a randomly chosen vertex and the average vertex vertex distance within a graph we apply our theory to some real world graphs including the worldwide web and collaboration graphs of scientists and fortune 1000 company directors we demonstrate that in some cases random graphs with appropriate distributions of vertex degree predict with surprising accuracy the behavior of the real world while in others there is a measurable discrepancy between theory and reality perhaps indicating the presence of additional social structure in the network that is not captured by the random graph

a study of strain localization in a multiple scale framework the one dimensional problem abstract this work approaches strain localization by recognizing the multiple scales inherent in the problem a component associated with the region of localized strain typically one with high gradient is referred to as the fine scale it represents the microstructure the field obtained by removing the fine scale from the total solution is referred to as the coarse scale the aim of the multiple scale method advanced here is to derive a model for the coarse scale field that accounts for the finite scale this process eliminates the fine scale from the problem yet retains its effect in applying this framework to the nonlinear problems with which localized strains are associated a crucial step is a first order approximation of the relevant relations the fully nonlinear problem is solved by an iterative scheme by accounting directly for the microstructure the multiple scale model recovers the regularizing effects of various alternative formulations for softening strain localization it thus presents itself as a unifying framework for such models numerical solutions are shown to be invariant with respect to the discretization furthermore for cases in which the displacements assume a distinct profile within the localization band the multiple scale model provides a resolution that can be made as accurate as desired even with the coarsest mesh possible the model is applied to strain localization problems that arise in inviscid and viscoplastic solids numerical simulations are presented that demonstrate the efficacy of the approach

clusters and the entropy in opinion dynamics on complex networks abstract in this work we investigate a heterogeneous population in the modified hegselmann krause opinion model on complex networks we introduce the shannon information entropy about all relative opinion clusters to characterize the cluster profile in the final configuration independent of network structures there exists the optimal stubbornness of one subpopulation for the largest number of clusters and the highest entropy besides there is the optimal bounded confidence or subpopulation ratio of one subpopulation for the smallest number of clusters and the lowest entropy however network structures affect cluster profiles indeed a large average degree favors consensus for making different networks more similar with complete graphs the network size has limited impact on cluster profiles of heterogeneous populations on scale free networks but has significant effects upon those on small world networks

nature of phase transitions in a probabilistic cellular automaton with two absorbing states we present a probabilistic cellular automaton with two absorbing states which can be considered a natural extension of the domany kinzel model despite its simplicity it shows a very rich phase diagram with two second order and one first order transition lines that meet at a bicritical point we study the phase transitions and the critical behavior of the model using mean field approximations direct numerical simulations and field theory the second order critical curves and the kink critical dynamics are found to be in the directed percolation and parity conservation universality classes respectively the first char21 order phase transition is put in evidence by examining the hysteresis cycle we also study the chaotic phase in which two replicas evolving with the same noise diverge using mean field and numerical techniques finally we show how the shape of the potential of the field theoretic formulation of the problem can be obtained by direct numerical simulations

phase transitions of extended range probabilistic cellular automata with two absorbing states we study phase transitions in a long range one dimensional cellular automaton with two symmetric absorbing states it includes and extends several other models like the ising and domany kinzel ones it is characterized by competing ferromagnetic linear and antiferromagnetic nonlinear couplings despite its simplicity this model exhibits an extremely rich phase diagram we present numerical results and mean field approximations

finite element simulation of dynamic strain localization a multi scale problem abstract a finite element procedure for the post localization analysis of elasto plastic solids is developed to ensure unique solutions the duvaut lions visco plastic regularization procedure 1 is implemented a bifurcation analysis of the underlying backbone elasto plastic material is performed to locate the shear band and to define its orientation the width of the shear band is assumed to be much smaller than the characteristic element size h to capture the structure of the shear band the kinematics is enriched by incorporating additional degrees of freedom in a patch within the element and overlying the shear band within each localized element compatibility is ensured between the strain fields inside and outside the patch a petrov galerkin type procedure to account for the narrow width of the patch is implemented the results indicate formation of mesh and patch invariant shear bands finally the effects of varying material parameters are studied the results are found to be consistent with known localization characteristics

shear band localization via local j2 continuum damage mechanics this paper describes a novel formulation for the solution of problems involving shear band localization using a local isotropic j2 continuum damage model and mixed linear simplex triangles and tetrahedra stabilization methods are used to ensure existence and uniqueness of the solution attaining global and local stability of the corresponding discrete finite element formulation consistent residual viscosity is used to enhance robustness and convergence of the formulation implementation and computational aspects are also discussed a simple isotropic local j2 damage constitutive model is considered either with linear or exponential softening the softening modulus is regularized according to the material mode ii fracture energy and the element size numerical examples show that the formulation derived is fully stable and remarkably robust totally free of volumetric locking and spurious oscillations of the pressure as a consequence the results obtained do not suffer from spurious mesh size or mesh bias dependence comparing very favourably with those obtained with the ill posed standard approaches 2004 elsevier b v all rights reserved

topological bifurcations in a model society of reasonable contrarians people are often divided into conformists and contrarians the former tending to align to the majority opinion in their neighborhood and the latter tending to disagree with that majority in practice however the contrarian tendency is rarely followed when there is an overwhelming majority with a given opinion which denotes a social norm such reasonable contrarian behavior is often considered a mark of independent thought and can be a useful strategy in financial markets we present the opinion dynamics of a society of reasonable contrarian agents the model is a cellular automaton of ising type with antiferromagnetic pair interactions modeling contrarianism and plaquette terms modeling social norms we introduce the entropy of the collective variable as a way of comparing deterministic mean field and probabilistic simulations bifurcation diagrams in the mean field approximation the model exhibits bifurcations and a chaotic phase interpreted as coherent oscillations of the whole society however in a one dimensional spatial arrangement one observes incoherent oscillations and a constant average in simulations on watts strogatz networks with a small world effect the mean field behavior is recovered with a bifurcation diagram that resembles the mean field one but where the rewiring probability is used as the control parameter similar bifurcation diagrams are found for scale free networks and we are able to compute an effective connectivity for such networks

solving the 2 d heat equations using wavelet galerkin method with variable time step a wavelet galerkin method to solve nonhomogenous 2 d heat equations in finite rectangular domains is presented integrals involving nonhomogenity terms with scaling function are evaluated based on available connection coefficients variable time step technique is used to delay the error blow up hence obtaining better results for solutions that reach steady state

multi scale methods in this paper four multiple scale methods are proposed the meshless hierarchical partition of unity is used as a multiple scale basis the multiple scale analysis with the introduction of a dilation parameter to perform multiresolution analysis is discussed the multiple field based on a 1 d gradient plasticity theory with material length scale is also proposed to remove the mesh dependency difficulty in softening localization problems a non local smoothing particle integration procedure with its multiple scale analysis are then developed these techniques are described in the context of the reproducing kernel particle method results are presented for elastic plastic one dimensional problems and 2 d large deformation strain localization problems to illustrate the effectiveness of these methods copyright 2000 john wiley sons ltd