weak convergence of the variations iterated integrals and doleans dade exponentials of sequences of semimartingales abstract this document investigates the weak convergence of variations iterated integrals and doleans dade exponentials v sub k y i sub k y and e gamma y are called respectively the variations the iterated integrals and the doleans dade exponential of the semimartingale y

weak solutions of set valued stochastic differential equations abstract the paper is devoted to the existence of weak solutions of set valued stochastic differential equations such equations were considered in the authors paper 22 where existence and uniqueness of strong solutions have been investigated now apart from the existence of weak solutions the weak compactness in distribution of the set of all weak solutions of set valued stochastic differential equations is considered

on a class of quasilinear systems with sign changing nonlinearities abstract we prove existence and nonexistence of positive solutions for the quasilinear system p u a x f u v in q v b x g u v in u v 0 on where p u div u p 2 u q v div v q 2 v p q 1 is a bounded domain in r n and the coefficients a x and b x are allowed to change sign

elastic plastic analysis of arbitrary heterogeneous materials with the voronoi cell finite element method abstract in this paper a voronoi cell finite element method is developed to solve small deformation elastic plasticity problems for arbitrary heterogenous materials dirichlet tessellation of microstructural representative materials results in a network of arbitrary sided polygons called voronoi cells each voronoi cell encompasses one second phase heterogeneity at most these are natural elements for the microstructure representing the basic structural elements of the material in this paper formulations are developed for directly considering voronoi cells as elements in a finite element model without any further dissection furthermore a composite voronoi cell finite element method is developed to account for the presence of the second phase within each polygonal element various numerical elastic plastic examples are executed for validating the effectiveness of this formulation finally studies are conducted to understand the effect of size shape and distribution of second phase on the averaged and true local responses of representative material elements

reflected solutions of backward sde s and related obstacle problems for pde s we study reflected solutions of one dimensional backward stochastic differential equations the reflection keeps the solution above a given stochastic process we prove uniqueness and existence both by a fixed point argument and by approximation via penalization we show that when the coefficient has a special form then the solution of our problem is the value function of a mixed optimal stopping optimal stochastic control problem we finally show that when put in a markovian framework the solution of our reflected bsde provides a probabilistic formula for the unique viscosity solution of an obstacle problem for a parabolic partial differential equation

two scale analysis of heterogeneous elastic plastic materials with asymptotic homogenization and voronoi cell finite element model in this paper a multiple scale finite element model vcfem homo has been developed for elastic plastic analysis of heterogeneous porous and composite materials by combining asymptotic homogenization theory with the voronoi cell finite element model vcfem vcfem for microstructural modeling originates from dirichlet tessellation of representative material elements at sampling points in the structure structural modeling is done by the general purpose finite element code abaqus and interfacing with the microscale vcfem analysis is done through the user subroutine in abaqus for material constitutive relation umat asymptotic homogenization in umat generates macroscopic material parameters for abaqus following the macroscopic analysis a local vcfem analysis is invoked to depict the true evolution of microstructural state variables various numerical examples are executed for validating the effectiveness of vcfem homo and the effect of size shape and distribution of heterogeneities on local and global response is examined

voronoi cell finite element model based on micropolar theory of thermoelasticity for heterogeneous materials in this paper a new voronoi cell finite element model is developed for solving steady state heat conduction and micropolar thermoelastic stress analysis problems in arbitrary heterogeneous materials the method is based on the natural discretization of a multiple phase domain into basic structural elements by dirichlet tessellation tessellation process results in a network of polygons called voronoi polygons in this paper formulations are developed for treating these polygons as elements in a finite element mesh furthermore a composite voronoi cell finite element model is developed to account for the presence of a second phase inclusion within a polygonal element various numerical examples are executed for validating the effectiveness of this model in the analysis of the temperature and stress fields for micropolar elastic materials effective material properties are derived for microstructures containing different distributions of second phase

asymptotic properties of monte carlo estimators of diffusion processes abstract this paper studies the limit distributions of monte carlo estimators of diffusion processes we examine two types of estimators based on the euler scheme one applied to the original processes the other to a doss transformation of the processes we show that the transformation increases the speed of convergence of the euler scheme we also study estimators of conditional expectations of diffusions after characterizing expected approximation errors we construct second order bias corrected estimators we also derive new convergence results for the mihlstein scheme illustrations of the results are provided in the context of simulation based estimation of diffusion processes

a regularized phenomenological multiscale damage model summary we present a regularized phenomenological multiscale model where elastic properties are computed using direct homogenization and subsequently evolved using a simple three parameter orthotropic continuum damage model the salient feature of the model is a unified regularization framework based on the concept of effective softening strain the unified regularization scheme has been employed in the context of constitutive law rescaling and the staggered nonlocal approach we show that an element erosion technique for crack propagation when exercised with one of the two regularization schemes 1 possesses a characteristic length 2 is consistent with fracture mechanics approach and 3 does not suffer from pathological mesh sensitivity copyright 2014 john wiley sons ltd

interior penalty discontinuous galerkin method on very general polygonal and polyhedral meshes this paper provides a theoretical foundation for interior penalty discontinuous galerkin methods for second order elliptic equations on very general polygonal or polyhedral meshes the mesh can be composed of any polygons or polyhedra that satisfy certain shape regularity conditions characterized in a recent paper by two of the authors wang and ye 2012 11 the usual h 1 conforming finite element methods on such meshes are either very complicated or impossible to implement in practical computation the interior penalty discontinuous galerkin method provides a simple and effective alternative approach which is efficient and robust results with such general meshes have important application in computational sciences

numerical approximation of doubly reflected bsdes with jumps and rcll obstacles we study a discrete time approximation scheme for the solution of a doubly reflected backward stochastic differential equation dbbsde in short with jumps driven by a brownian motion and an independent compensated poisson process moreover we suppose that the obstacles are right continuous and left limited rcll processes with predictable and totally inaccessible jumps and satisfy mokobodski s condition our main contribution consists in the construction of an implementable numerical sheme based on two random binomial trees and the penalization method which is shown to converge to the solution of the dbbsde finally we illustrate the theoretical results with some numerical examples in the case of general jumps

hierarchical modeling of heterogeneous solids in this paper a methodology is introduced for the development of adaptive methods for hierarchical modeling of elastic heterogeneous bodies the approach is based on the idea of computing an estimate of the modeling error introduced by replacing the actual fine scale material tensor with that of a homogenized material and to adaptively refine the material description until a prespecified error tolerance is met this process generates a family of coarse scale solutions in which the solution corresponding to the fine scale model of the body which embodies the exact microstructure loading and boundary conditions represents the highest level of sophistication in a family of continuum models the adaptive strategy developed can lead to a new non uniform description of material properties which reflects the loading and boundary conditions a post processing technique is also introduced which endows the coarse scale solutions with fine scale information through a local solution process convergence of the adaptive algorithm is proven and modeling error estimates as a function of scale of material description are presented preliminary results of several numerical experiments are given to confirm estimates and to illustrate the promise of the approach in practical applications

on a class of quasilinear problems with sign changing nonlinearities abstract we prove existence and nonexistence of positive solutions for the quasilinear problem p u m p u a x f u in u 0 on where p u div u p 2 u p u u p 2 u p 1 m 0 is a bounded domain in r n and the coefficient a x is allowed to change sign

two scale kinematics and linearization for simultaneous two scale analysis of periodic heterogeneous solids at finite strain abstract we introduce the notion of two scale kinematics and the procedure of two scale linearization which are indispensable to the simultaneous two scale analysis method for the mechanical behavior of periodic heterogeneous solids at finite strain these are accomplished by formulating the two scale boundary value problem in both material and spatial descriptions with reference to the two scale modeling strategy developed in comput methods appl mech engrg 190 40 41 2001 5427 that utilized the convergence results of mathematical homogenization the formulation brings the intimate relationship between micro and macro scale kinematics in describing the micro macro coupling behavior inherent in heterogeneous media it is also shown that the two scale linearization necessitates the strict consistency with the micro scale equilibrated state and naturally invites the tangential homogenization process for both material and spatial descriptions several numerical examples of simultaneous two scale computations are presented to illustrate the two scale nature of the deformation of a heterogeneous solid at finite strain

determination of the size of the representative volume element for random composites statistical and numerical approach the representative volume element rve plays a central role in the mechanics and physics of random heterogeneous materials with a view to predicting their effective properties a quantitative definition of its size is proposed in this work a rve size can be associated with a given precision of the estimation of the wanted overall property and the number of realizations of a given volume v of microstructure that one is able to consider it is shown to depend on the investigated morphological or physical property the contrast in the properties of the constituents and their volume fractions the methodology is applied to a specific random microstructure namely a two phase three dimensional voronoi mosaic finite element simulations of volumes of different sizes are performed in the case of linear elasticity and thermal conductivity the volumes are subjected to homogeneous strain stress or periodic boundary conditions the effective properties can be determined for large volumes and a small number of realizations conversely smaller volumes can be used providing that a sufficient number of realizations are considered a bias in the estimation of the effective properties is observed for too small volumes for all types of boundary conditions the variance of computed apparent properties for each volume size is used to define the precision of the estimation the key notion of integral range is introduced to relate this error estimation and the definition of the rve size for given wanted precision and number of realizations one is able to provide a minimal volume size for the computation of effective properties the results can also be used to predict the minimal number of realizations that must be considered for a given volume size in order to estimate the effective property for a given precision the rve sizes found for elastic and thermal properties but also for a geometrical property like volume fraction are compared

a return mapping algorithm for plane stress elastoplasticity an unconditionally stable algorithm for plane stress elastoplasticity is developed based upon the notion of elastic predictor return mapping plastic corrector enforcement of the consistency condition is shown to reduce to the solution of a simple nonlinear equation consistent elastoplastic tangent moduli are obtained by exact linearization of the algorithm use of these moduli is essential in order to preserve the asymptotic rate of quadratic convergence of newton methods the accuracy of the algorithm is assessed by means of iso error maps the excellent performance of the algorithm for large time steps is illustrated in numerical experiments

differential equations driven by rough paths with jumps abstract we develop the rough path counterpart of ito stochastic integration and differential equations driven by general semimartingales this significantly enlarges the classes of ito forward stochastic differential equations treatable with pathwise methods a number of applications are discussed

a generalized finite element method for polycrystals with discontinuous grain boundaries summary we present a generalized finite element method for the analysis of polycrystals with explicit treatment of grain boundaries grain boundaries and junctions understood as loci of possible displacement discontinuity are inserted into finite elements by exploiting the partition of unity property of finite element shape functions consequently the finite element mesh does not need to conform to the polycrystal topology the formulation is outlined and a numerical example is presented to demonstrate the potential and accuracy of the approach the proposed methodology can also be used for branched and intersecting cohesive cracks and comparisons are made to a related approach int j numer meth engng 2000 48 1741 copyright 2006 john wiley sons ltd

on a finite element method with variable element topology a new finite element like approximation method for problems in solid mechanics here called the variable element topology finite element method vetfem is presented the displacement based variational basis of the conventional finite element method fem is retained in the vetfem as is the discretization of the problem into elements however vetfem elements are not subject to any of the geometric or topological restrictions of conventional elements they may contain any number of nodes in any arrangement the polynomial vetfem shape functions emerge from a constrained minimization process on each element instead of from an isoparametric transformation from a parent element as in the conventional fem all the powerful features normally associated with the conventional fem are exhibited by the new method in addition because of the absence of geometric and or topological restrictions on the elements automatic mesh generation is enormously simplified for this reason the vetfem is thought to be particularly useful for problems involving very complex geometry adaptive remeshing or crack extension

convergence in probability for perturbed stochastic integral equations in this work one considers two stochastic integral equations indexed by some parameter and one studies the contiguity of their solutions when the parameter converges to some e0 two types of behaviour are described they lead to the notion of regular and singular perturbations the method which is used also enables a study of the rate of convergence applications to time discretization of equations are given

necessary conditions for optimal control of stochastic systems with random jumps a maximum principle is proved for optimal controls of stochastic systems with random jumps the control is allowed to enter into both diffusion and jump terms the form of the maximum principle turns out to be quite different from the one corresponding to the pure diffusion system the word pure here means the absence of the jump term in calculating the first order coefficient for the cost variation only a property for lebesgue integrals of scalar valued functions in the real number space cal r is used this shows that there is no essential difference between deterministic and stochastic systems as far as the derivation of maximum principles is concerned

a class of general algorithms for multi scale analyses of heterogeneous media abstract a class of computational algorithms for multi scale analyses is developed in this paper the two scale modeling scheme for the analysis of heterogeneous media with fine periodic microstructures is generalized by using relevant variational statements instead of the method of two scale asymptotic expansion the mathematical results on the generalized convergence are utilized in the two scale variational descriptions accordingly the global local type computational schemes can be unified in association with the homogenization procedure for general nonlinear problems after formulating the problem in linear elastostatics that with local contact condition and the elastoplastic problem we present representative numerical examples along with the computational algorithm consistent with our two scale modeling strategy as well as some direct approaches

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

development and testing of stable invariant isoparametric curvilinear 2 and 3 d hybrid stress elements abstract linear and quadratic serendipity hybrid stress elements are examined in respect of stability coordinate invariance and optimality a formulation based upon symmetry group theory successfully addresses these issues in undistorted geometries and is fully detailed for plane elements the resulting least order stable invariant stress polynomials can be applied as astute approximations in distorted cases through a variety of tensor components and variational principles a distortion sensitivity study for two and three dimensional elements provides favourable numerical comparisons with the assumed displacement method

adapted solution of a backward stochastic differential equation abstract let wt t 0 1 be a standard k dimensional weiner process defined on a probability space f p and let ft denote its natural filtration given a f1 measurable d dimensional random vector x we look for an adapted pair of processes x t y t t 0 1 with values in rd and rd k respectively which solves an equation of the form x t t 1 f s x s y s ds t 1 g s x s y s dw s x a linearized version of that equation appears in stochastic control theory as the equation satisfied by the adjoint process we also generalize our results to the following equation x t t 1 f s x s y s ds t 1 g s x s y s dw s x under rather restrictive assumptions on g

martingale difference arrays and stochastic integrals consider mdas xni and yni and stopping times n t 0 t 1 denote s n t a 0 sum limits i 1 tau n t x ni text t n t b 0 sum limits i 1 tau n t y ni and let be a function if the common distribution converges and if st tt denote the corresponding limiting processes then we give conditions such that the martingale transforms sum limits i 1 tau n t varphi s n i 1 y ni converge weakly to the stochastic integral int limits 0 t varphi s dt this result has important consequences for functional central limit theorems 1 if the mdas are connected by a difference equation of the form x ni varphi left s n i 1 right y ni then weak convergence of tn t implies that of sn t and the limit satisfies the stochastic differential equation ds varphi left s right d t this observation leads to functional limit theorems for diffusion approximations e g we obtain easily a result of lindvall 4 on the diffusion approximation of branching processes 2 if the mda xni arises from a likelihood ratio martingale then the limit satisfies s t 1 int limits 0 t sdt which leads to the representation of the limiting likelihood ratios as exponential martingale s t exp t t frac 1 2 t t t this approximation by an exponential martingale has been proved previously by swensen 9 using a taylor expansion of the log likelihood ratio 3 as a consequence we obtain a general functional central limit theorem if left sum limits i 1 tau n t x ni 2 right converges weakly to s s t then left sum limits i 1 tau n t x ni right converges weakly to st provided that the distribution of st is uniquely determined by that of s s t this assertion embraces previous central limit theorems dealing with cases where the increasing process s s t is deterministic

backward stochastic differential equations with reflection and dynkin games we establish existence and uniqueness results for adapted solutions of backward stochastic differential equations bsde s with two reflecting barriers generalizing the work of el karoui kapoudjian pardoux peng and quenez existence is proved first by solving a related pair of coupled optimal stopping problems and then under different conditions via a penalization method it is also shown that the solution coincides with the value of a certain dynkin game a stochastic game of optimal stopping moreover the connection with the backward sde enables us to provide a pathwise deterministic approach to the game

convergence en loi des suites d integrales stochastiques sur l espace mathbb d 1 de skorokhod for sequences of stochastic integrals k n x n functional limit theorems are presented these results hold under simple natural conditions

two level multiscale enrichment methodology for modeling of heterogeneous plates a new two level multiscale enrichment methodology for analysis of heterogeneous plates is presented the enrichments are applied in the displacement and strain levels the displacement field of a reissner mindlin plate is enriched using the multiscale enrichment functions based on the partition of unity principle the strain field is enriched using the mathematical homogenization theory the proposed methodology is implemented for linear and failure analysis of brittle heterogeneous plates the eigendeformation based model reduction approach is employed to efficiently evaluate the non linear processes in case of failure the capabilities of the proposed methodology are verified against direct three dimensional finite element models with full resolution of the microstructure copyright 2009 john wiley sons ltd

conforming polygonal finite elements summary in this paper conforming finite elements on polygon meshes are developed polygonal finite elements provide greater flexibility in mesh generation and are better suited for applications in solid mechanics which involve a significant change in the topology of the material domain in this study recent advances in meshfree approximations computational geometry and computer graphics are used to construct different trial and test approximations on polygonal elements a particular and notable contribution is the use of meshfree natural neighbour nn basis functions on a canonical element combined with an affine map to construct conforming approximations on convex polygons this numerical formulation enables the construction of conforming approximation on n gons n 3 and hence extends the potential applications of finite elements to convex polygons of arbitrary order numerical experiments on second order elliptic boundary value problems are presented to demonstrate the accuracy and convergence of the proposed method copyright 2004 john wiley sons ltd

a generalized space time mathematical homogenization theory for bridging atomistic and continuum scales a generalized space time mathematical homogenization theory which constructs an equivalent continuum description directly from molecular dynamics md equations is developed the noteworthy theoretical findings of this work are i the coarse scale continuum equations pdes obtained from the homogenization of md equations are identical to those obtained from the classical homogenization of the fine scale continuum ii the lower order effective continuum properties such as the fourth order elasticity tensor have similar characteristics to those resulting from the homogenization of fine scale continuum iii the higher order effective properties such as polarization and dispersion tensors substantially differ from those of continuum due to the discreteness effect both the heterogeneous continuum and discrete media possess the size effect but only atomistic medium has the discreteness effect some demonstrative numerical examples are presented to verify the formulation copyright 2005 john wiley sons ltd

analyses of large quasistatic deformations of inelastic bodies by a new hybrid stress finite element algorithm abstract a new hybrid stress finite element algorithm suitable for analyses of large quasistatic inelastic deformations is presented the algorithm is based upon a generalization of de veubeke s complementary energy principle the principal variables in the formulation are the nominal stress rate and spin and the resulting finite element equations are discrete versions of the equations of compatibility and angular momentum balance the algorithm produces true rates time derivatives as opposed to increments there results a complete separation of the boundary value problem for stress rate and velocity and the initial value problem for total stress and deformation hence their numerical treatments are essentially independent after a fairly comprehensive discussion of the numerical treatment of the boundary value problem we launch into a detailed examination of the numerical treatment of the initial value problem covering the topics of efficiency stability and objectivity the paper is closed with a set of examples finite homogeneous deformation problems which serve to bring out important aspects of the algorithm

cadlag skorokhod problem driven by a maximal monotone operator abstract the article deals with the existence and uniqueness of the solution of the following differential equation a cadlag skorokhod problem driven by a maximal monotone operator and with singular input generated by the cadlag function m d x t a x t d t d k t d d m t t 0 x 0 m 0 where k d is a pure jump function the jumps outside of the constrained domain d a are counteracted through the generalized projection by taking x t x t m t whenever x t m t d a approximations of the solution based on discretization and yosida penalization are also considered

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

multiple scale analysis of heterogeneous elastic structures using homogenization theory and voronoi cell finite element method abstract this paper deals with the development of a multiple scale finite element method by combining the asymptotic homogenization theory with voronoi cell vcfem for microstructural modeling the voronoi cell finite element model originates from dirichlet tessellation of a representative material element or a base cell in the microstructure homogenized material coefficients for a global displacement finite element model are generated by vcfem analysis using periodic boundary conditions on the base cell following the macroscopic analysis the local vcfem analysis is implemented to depict the true evolution of microstructural stresses and strains various numerical examples are executed for validating the effectiveness of vcfem macro micro modeling of elastic materials the effect of size shape orientation and distribution of heterogeneities on the local and global response are examined

scaled boundary polygons with application to fracture analysis of functionally graded materials summary this study presents a framework for the development of polygon elements based on the scaled boundary fem underpinning this study is the development of generalized scaled boundary shape functions valid for any n sided polygon these shape functions are continuous inside each polygon and across adjacent polygons for uncracked polygons the shape functions are linearly complete for cracked polygons the shape functions reproduce the square root singularity and the higher order terms in the williams eigenfunction expansion this allows the singular stress field in the vicinity of the crack tip to be represented accurately using these shape functions a novel scaled boundary polygon formulation that captures the heterogeneous material response observed in functionally graded materials is developed the stiffness matrix in each polygon is derived from the principle of virtual work using the scaled boundary shape functions the material heterogeneity is approximated in each polygon by a polynomial surface in scaled boundary coordinates the intrinsic properties of the scaled boundary shape functions enable accurate computation of stress intensity factors in cracked functionally graded materials directly from their definitions the new formulation is validated and its salient features are demonstrated using five numerical benchmarks copyright 2014 john wiley sons ltd

polygon scaled boundary finite elements for crack propagation modelling summary an automatic crack propagation modelling technique using polygon elements is presented a simple algorithm to generate a polygon mesh from a delaunay triangulated mesh is implemented the polygon element formulation is constructed from the scaled boundary finite element method sbfem treating each polygon as a sbfem subdomain and is very efficient in modelling singular stress fields in the vicinity of cracks stress intensity factors are computed directly from their definitions without any nodal enrichment functions an automatic remeshing algorithm capable of handling any n sided polygon is developed to accommodate crack propagation the algorithm is simple yet flexible because remeshing involves minimal changes to the global mesh and is limited to only polygons on the crack paths the efficiency of the polygon sbfem in computing accurate stress intensity factors is first demonstrated for a problem with a stationary crack four crack propagation benchmarks are then modelled to validate the developed technique and demonstrate its salient features the predicted crack paths show good agreement with experimental observations and numerical simulations reported in the literature copyright 2012 john wiley sons ltd

a positive solution branch for nonlinear eigenvalue problems in rn abstract in this note we give sufficient conditions for the existence of a positive solution branch for the problem u a x f u in r n u x 0 as x with sign changing weight a where n 3 and f is a smooth nonlinearity with f 0 0

existence and multiplicity of positive solutions of a nonlinear eigenvalue problem with indefinite weight function this paper is concerned with the existence multiplicity and stability of positive solutions of an indefinite weight boundary value problemu email protected t f u 0 0

voronoi cell finite difference method for the diffusion operator on arbitrary unstructured grids voronoi cells and the notion of natural neighbours are used to develop a finite difference method for the diffusion operator on arbitrary unstructured grids natural neighbours are based on the voronoi diagram which partitions space into closest point regions the sibson and the laplace non sibsonian interpolants which are based on natural neighbours have shown promise within a galerkin framework for the solution of partial differential equations in this paper we focus on the laplace interpolant with a two fold objective first to unify the previous developments related to the laplace interpolant and to indicate its ties to some well known numerical methods and secondly to propose a voronoi cell finite difference scheme for the diffusion operator on arbitrary unstructured grids a conservation law in integral form is discretized on voronoi cells to derive a finite difference scheme for the diffusion operator on irregular grids the proposed scheme can also be viewed as a point collocation technique a detailed study on consistency is conducted and the satisfaction of the discrete maximum principle stability is established owing to symmetry of the laplace weight a symmetric positive definite stiffness matrix is realized which permits the use of efficient linear solvers on a regular rectangular or hexagonal grid the difference scheme reduces to the classical finite difference method numerical examples for the poisson equation with dirichlet boundary conditions are presented to demonstrate the accuracy and convergence of the finite difference scheme copyright 2003 john wiley sons ltd

eigendeformation based reduced order homogenization for failure analysis of heterogeneous materials the manuscript presents a novel model reduction approach for periodic heterogeneous media which combines the multiple scale asymptotic msa expansion method with the transformation field analysis tfa to reduce the computational cost of a direct homogenization approach without significantly compromising on solution accuracy the evolution of failure in micro phases and interfaces is modeled using eigendeformation adaptive model improvement strategy incorporating a hierarchical sequence of computational homogenization models is employed to control the accuracy of the model we present the model formulation and the computational details along with verification with respect to direct homogenization and validation with respect to physical experiments studies

finite deformation plasticity for composite structures computational models and adaptive strategies abstract we develop computational models and adaptive modeling strategies for obtaining an approximate solution to a boundary value problem describing the finite deformation plasticity of heterogeneous structures a nearly optimal mathematical model consists of an averaging scheme based on approximating eigenstrains and elastic concentration factors in each micro phase by a constant in the portion of the macro domain where modeling errors are small whereas elsewhere a more detailed mathematical model based on a piecewise constant approximation of eigenstrains and elastic concentration factors is utilized the methodology is developed within the framework of statistically homogeneous composite material and local periodicity assumptions

smooth approximation of stochastic differential equations consider an ito process x satisfying the stochastic differential equation dx a x dt b x dw where a b are smooth and w is a multidimensional brownian motion suppose that wn has smooth sample paths and that wn converges weakly to w a central question in stochastic analysis is to understand the limiting behavior of solutions xn to the ordinary differential equation dxn a xn dt b xn dwn the classical wong zakai theorem gives sufficient conditions under which xn converges weakly to x provided that the stochastic integral b x dw is given the stratonovich interpretation the sufficient conditions are automatic in one dimension but in higher dimensions the correct interpretation of b x dw depends sensitively on how the smooth approximation wnis chosen in applications a natural class of smooth approximations arise by setting wn t n 1 2 nt0v sds where t is a flow generated e g by an ordinary differential equation and v is a mean zero observable under mild conditions on t we give a definitive answer to the interpretation question for the stochastic integral b x dw our theory applies to anosov or axiom a flows t as well as to a large class of nonuniformly hyperbolic flows including the one defined by the well known lorenz equations and our main results do not require any mixing assumptions on t the methods used in this paper are a combination of rough path theory and smooth ergodic theory

unstructured grid method for stress wave propagation in elastic media a new numerical method named unstructured grid method is presented to calculate two dimensional stress wave propagation problems in elastic media this method is based on the dynamic equilibrium equations of the investigated lumps that are formed among the auxiliary unstructured grids the approach to the solution is obtained by calculating the node displacements and the central point stresses of the spatial grids alternately the stability criterion of the method is given and tested numerically analysis of dispersion for numerical phase velocity is studied the rule is provided to determine the spatial step size of discretization mesh so as to ensure the numerical accuracy of the unstructured grid method numerical results are compared with the available exact solutions and with the solutions of central difference method for demonstrating the good accuracy of the new method the unstructured grid method possesses higher calculating speed than the central difference method finally the dynamic behavior of a square plate with a hole under an impact loading is researched

numerical algorithms and simulations for reflected backward stochastic differential equations with two continuous barriers in this paper we study different algorithms for reflected backward stochastic differential equations bsde in short with two continuous barriers based on the framework of using a binomial tree to simulate 1 d brownian motion we introduce numerical algorithms by the penalization method and the reflected method respectively in the end simulation results are also presented

high order polygonal discontinuous petrov galerkin polydpg methods using ultraweak formulations abstract this work represents the first endeavor in using ultraweak formulations to implement high order polygonal finite element methods via the discontinuous petrov galerkin dpg methodology ultraweak variational formulations are nonstandard in that all the weight of the derivatives lies in the test space while most of the trial space can be chosen as copies of l 2 discretizations that have no need to be continuous across adjacent elements additionally the test spaces are broken along the mesh interfaces this allows one to construct conforming polygonal finite element methods termed here as polydpg methods by defining most spaces by restriction of a bounding triangle or box to the polygonal element the only variables that require nontrivial compatibility across elements are the so called interface or skeleton variables which can be defined directly on the element boundaries unlike other high order polygonal methods polydpg methods do not require ad hoc stabilization terms thanks to the crafted stability of the dpg methodology a proof of convergence of the form h p is provided and corroborated through several illustrative numerical examples these include polygonal meshes with n sided convex elements and with highly distorted concave elements as well as the modeling of discontinuous material properties along an arbitrary interface that cuts a uniform grid since polydpg methods have a natural a posteriori error estimator a polygonal adaptive strategy is developed and compared to standard adaptivity schemes based on constrained hanging nodes this work is also accompanied by an open source polydpg software supporting polygonal and conventional elements

a scaled boundary polygon formulation for elasto plastic analyses this study presents a novel scaled boundary polygon formulation to model elasto plastic material responses in structures the polygons have flexible mesh generation capabilities and are more accurate than standard finite elements especially for problems with cracks and notches shape functions of arbitrary n sided polygons are constructed using the scaled boundary finite element method these shape functions are conforming and linearly complete when modeling a crack strain singularities are analytically modeled without enrichment standard finite element procedures are used to formulate the stiffness matrix and residual load vector the nonlinear material constitutive matrix and the internal stresses are approximated locally in each polygon by a polynomial function the stiffness matrix and the residual load vector are matrix power integrals that can be evaluated analytically even when a strain singularity is present standard nonlinear equation solvers e g the modified newton raphson algorithm are used to obtain the nonlinear response of the structure the proposed formulation is validated using several numerical benchmarks

numerical integration over arbitrary polygonal domains based on schwarz christoffel conformal mapping this paper presents a new numerical integration technique oil arbitrary polygonal domains the polygonal domain is mapped conformally to the unit disk using schwarz christoffel mapping and a midpoint quadrature rule defined oil this unit disk is used this method eliminates the need for a two level isoparametric mapping usually required moreover the positivity of the jacobian is guaranteed numerical results presented for a few benchmark problems in the context of polygonal finite elements show that the proposed method yields accurate results

a material based finite element analysis of heterogeneous media involving dirichlet tessellations abstract in this paper a new finite element formulation has been developed for analysis of heterogeneous media in which the second phase is randomly dispersed within the matrix it introduces a tessellation based mesh generation technique to account for the arbitrariness in location shape and size of the second phase an assumed stress hybrid formulation has been implemented to utilize the resulting voronoi polygons as elements in a finite element model the effect of the second phase has been accounted for by introducing a transformation strain based constitutive formulation numerical examples have been conducted to validate the model

computational continua revisited summary in the recent paper fish and kuznetsov introduced the so called computational continua c2 approach which is a variant of the higher order computational homogenization that does not require higher order continuity introduces no new degrees of freedom and is free of higher order boundary conditions in a follow up paper on reduced order computational continua the c2 formulation has been enhanced with a model reduction scheme based on construction of residual free fields to yield a computationally efficient framework coined as rc2 the original c2 formulations were limited to rectangular and box elements the primary objectives of the present manuscript is to revisit the original formulation in three respects i consistent formulation of boundary conditions for unit cells subjected to higher order coarse scale fields ii effective solution of the unit cell problem for lower order approximation of eigenstrains and iii development of nonlocal quadrature schemes for general two dimensional quad and triangle and three dimensional hexahedral and tetrahedral elements copyright 2014 john wiley sons ltd

simulation of the multi scale convergence in computational homogenization approaches although the asymptotic homogenization is known to explicitly predict the thermo mechanical behaviors of an overall structure as well as the microstructures the current developments in engineering fields introduce some kinds of approximation about the microstructural geometry in order for the homogenization method for periodic media to apply for general heterogeneous ones the problems arising from mathematical modeling are examined in the framework of representative volume element rve analyses here the notion of homogenization convergence allows us to eliminate the geometrical periodicity requirement when the size of rve is sufficiently large then the numerical studies in this paper realize the multi scale nature of the convergence of overall material properties as the unit cell size is increased in addition to such dependency of the macroscopic field variables on the selected size of unit cells the convergence nature of microscopic stress values is also studied quantitatively via the computational homogenization method similar discussions are made for the elastoplastic mechanical responses in both macro and microscopic levels in these multi scale numerical analyses the specific effects of the microstructural morphology are reflected by using the digital image based dib finite element fe modeling technique which enables the construction of accurate microstructural models

adaptivity and convergence in the voronoi cell finite element model for analyzing heterogeneous materials in this paper an adaptive voronoi cell finite element model is presented for analyzing micromechanical response of composites and porous materials both elastic and elastic plastic materials are considered two error measures viz a traction reciprocity error and an error in the kinematic relation are formulated as indicators of the quality of vcfem solutions based on a posteriori evaluation of these error measures element adaptation is executed in two consecutive stages in the first stage displacement function adaptations on the element boundaries and matrix inclusion void interfaces are carried out to minimize the corresponding traction reciprocity errors this is accomplished through a sequence of h refinement and spectral p enrichment strategy in an optimal displacement direction following this an enrichment of matrix and inclusion stress functions or enrp adaptation is conducted to reduce the error in kinematic relations the complete process improves convergence characteristics of the vcfem solution numerical analysis is conducted to examine the potential of the resulting vcfem code in analyzing microstructures with different distributions sizes and shapes of heterogeneities the method is seen to perform very well for the wide variety of problems solved

global local analysis of granular media in quasi static equilibrium abstract a method of global local analysis is developed for quasi static equilibrium problems for granular media the two scale modeling based on mathematical homogenization theory enables us to formulate two separate boundary value problems in terms of macro and microscales the macroscale problem governs the equilibrium of a global structure composed of granular assemblies while the microscale one is posed for the particulate nature of a local structure with the friction contact mechanism between particles the local structure is identified with a periodic representative volume element or equivalently a unit cell over which averaging is performed the mechanical behavior of unit cells is analyzed by a discrete numerical model in which spring and friction devices connect rigid particles whereas the continuum based finite element method is used for the macroscopic one representative numerical examples are presented to demonstrate the capability of the proposed two scale analysis method for granular materials