a free boundary problem for the laplacian with a constant bernoulli type boundary condition we study a free boundary problem for the laplace operator where we impose a bernoulli type boundary condition we show that there exists a solution to this problem we use a beurling s technique by defining two classes of sub and supersolutions and a perron argument we try to generalize here a previous work of a henrot and h shahgholian we extend these results in different directions

computational plasticity for composite structures based on mathematical homogenization theory and practice abstract this paper generalizes the classical mathematical homogenization theory for heterogeneous medium to account for eigenstrains starting from the double scale asymptotic expansion for the displacement and eigenstrain fields we derive a close form expression relating arbitrary eigenstrains to the mechanical fields in the phases the overall structural response is computed using an averaging scheme by which phase concentration factors are computed in the average sense for each micro constituent and history data is updated at two points reinforcement and matrix in the microstructure one for each phase macroscopic history data is stored in the database and then subjected in the post processing stage onto the unit cell in the critical locations for numerical examples considered the cpu time obtained by means of the two point averaging scheme with variational micro history recovery with 30 seconds on sparc 10 51 as opposed to 7 hours using classical mathematical homogenization theory at the same time the maximum error in the microstress field in the critical unit cell was only 3 5 in comparison with the classical mathematical homogenization theory

standard staggered and staggered newton schemes in thermo hydro mechanical problems the aim of the paper is to compare the rates of iteration convergence of two staggered numerical schemes one using successive substitutions and the other the newton method in the case of very weakly coupled problems the newton method is one order faster but there are specific cases when it is slower than the standard staggered algorithm in both cases a convergence condition must be verified the behaviour of the investigated staggered procedures in case of thermo hydro mechanical problems are shown on examples

quadrature formulae and asymptotic error expansions for wavelet approximations of smooth functions this paper deals with typical problems that arise when using wavelets in numerical analysis applications the first part involves the construction of quadrature formulae for the calculation of inner products of smooth functions and scaling functions several types of quadratures are discussed and compared for different classes of wavelets since their construction using monomials is ill conditioned also a modified well conditioned construction using chebyshev polynomials is presented the second part of the paper deals with pointwise asymptotic error expansions of wavelet approximations of smooth functions they are used to derive asymptotic interpolating properties of the wavelet approximation and to construct a convergence acceleration algorithm this is illustrated with numerical examples

modeling and simulation of piezocomposites solution procedures for large scale transient analysis of piezocomposites are developed computational efficiency of unconditionally stable and conditionally stable implicit partitioned schemes as well as explicit partitioned schemes is investigated in the context of multilevel solution methods applied to separate field equations

multigrid method for periodic heterogeneous media part 1 convergence studies for one dimensional case abstract a multi grid method for a periodic heterogeneous medium in 1 d is presented based on the homogenization theory special integrid transfer operators have been developed to simulate a low frequency response of the differential equations with oscillatory coefficients the proposed multi grid method has been proved to have a fast rate of convergence governed by the ratio q 4 q where 0

algorithms for strong coupling procedures abstract this paper considers algorithms for computing the response of a coupled problem with a partitioned approach one important example treated here is fluid structure interaction fsi often procedures or even software exists to solve each sub problem separately and one wants to couple both this setting seems to allow only the so called weak coupling which is not sufficient for some problems the so called strong coupling is often a totally implicit formulation where the system components are evaluated at the same time level this usually requires an iterative procedure the fsi problem is cast as an abstract differential algebraic equation dae for which the coupling procedures are developed with the partitioned approach one simple and frequently used computational procedure is similar to a block gauss seidel iteration it is shown why this approach may experience difficulties and how they may be circumvented with newton like methods still staying in the partitioned framework the functional and software engineering requirements for the simulation interface are described and analysed some simple coupled example problems demonstrate how the proposed procedures work

unconditionally stable staggered solution procedure for soil pore fluid interaction problems this paper presents a simple procedure for modifying the dynamic coupled soil pore fluid equations in a manner which allows a stable and efficient staggered solution procedure to be used the solution method is simpler than an alternative suggested by park15 and has a direct physical interpretation this stabilized procedure is efficient in numerical time domain analysis of soil pore fluid occurring in earthquake and consolidation problems numerical examples of one and two dimensional saturated poroelastic media demonstrate the procedure

evaluation of three and two field finite element methods for the dynamic response of saturated soil the three field formulation u p u is presented and is applied to solve dynamic equations for saturated porous media in order to evaluate the accuracy and the performance of this three field approximation the u u and the u w formulations are also considered and a few one and two dimensional examples are solved using the three methods problems for which both the pore fluid and the solid grains are incompressible are also considered and are solved using the u p u approximation accuracy was determined by a comparison of the finite element results with the analytical solution given by gajo and mongiovi 19 for a wide range of permeability

a dynamically adaptive multilevel wavelet collocation method for solving partial differential equations in a finite domain a dynamically adaptive multilevel wavelet collocation method is developed for the solution of partial differential equations the multilevel structure of the algorithm provides a simple way to adapt computational refinements to local demands of the solution high resolution computations are performed only in regions where sharp transitions occur the scheme handles general boundary conditions the method is applied to the solution of the one dimensional burgers equation with small viscosity a moving shock problem and a nonlinear thermoacoustic wave problem the results indicate that the method is very accurate and efficient

discrete to continuum bridging based on multigrid principles abstract the paper presents a new concurrent multiscale approach based on multigrid principles with intent of solving large molecular statics and molecular dynamics systems we show that the coarse model effective stiffness matrix obtained by variational restriction of the atomistic model effective stiffness matrix coincides with the effective stiffness matrix of the equivalent continuum scale model the equivalent continuum model is defined for both molecular statics and molecular dynamics cases and theoretical estimates of the rate of convergence for the proposed concurrent multiscale approach are obtained

multi grid method for periodic heterogeneous media part 2 multiscale modeling and quality control in multidimensional case abstract a multi grid method for a periodic heterogeneous medium in multidimensions is developed based on the homogenization theory special intergrid transfer operators have been developed to stimulate a low frequency response of the boundary value problem with oscillatory coefficients an adaptive strategy is developed to form a nearly optimal two scale computational model consisting of the finite element mesh entirely constructed on the microscale in the regions identified by the idealization error indicators while elsewhere the modeling level is only sufficient to capture the response of homogenized medium numerical experiments show the usefulness of the proposed adaptive multi level procedure for predicting a detailed response of composite specimens

wavelet galerkin method in multi scale homogenization of heterogeneous media the hierarchical properties of scaling functions and wavelets can be utilized as effective means for multi scale homogenization of heterogeneous materials under galerkin framework it is shown in this work however when the scaling functions are used as the shape functions in the multi scale wavelet galerkin approximation the linear dependency in the scaling functions renders improper zero energy modes in the discrete differential operator stiffness matrix if integration by parts is invoked in the galerkin weak form an effort is made to obtain the analytical expression of the improper zero energy modes in the wavelet galerkin differential operator and the improper nullity of the discrete differential operator is then removed by an eigenvalue shifting approach a unique property of multi scale wavelet galerkin approximation is that the discrete differential operator at any scale can be effectively obtained this property is particularly useful in problems where the multi scale solution cannot be obtained simply by a wavelet projection of the finest scale solution without utilizing the multi scale discrete differential operator for example the multi scale analysis of an eigenvalue problem with oscillating coefficients copyright 2005 john wiley sons ltd

stable element free galerkin solution procedures for the coupled soil pore fluid problem it is always difficult to solve the coupled soil pore fluid problem when the soil is saturated and impermeable because this situation often results in intensive oscillations of the solutions this topic has been discussed widely in the field of the finite element method but rarely by meshless methods the element free galerkin efg method has outstanding advantages of solving this problem based on the fact that its interpolation function can be constructed flexibly by the nodes in the compact domain in this study an efg numerical model together with a stabilization technique is proposed to obtain stable solutions especially for the saturated and impermeable soil close agreement between computational results and analytical solutions for one and two dimensional examples shows that the proposed numerical model not only provides highly accurate solutions for the saturated soil with relatively high permeability but also eliminates the oscillations of the solutions very effectively for the saturated and impermeable soil furthermore the influences of the hydraulic anisotropy a typical property of two dimensional problems on the proposed stabilization technique are discussed it is suggested that the optimal distribution of the nodes of essential variables can be designed according to the relative importance of the permeability in different directions copyright c 2010 john wiley sons ltd

numerical methods for multiscale elliptic problems we present an overview of the recent development on numerical methods for elliptic problems with multiscale coefficients we carry out a thorough study of two representative techniques the heterogeneous multiscale method hmm and the multiscale finite element method msfem for problems with scale separation but without specific assumptions on the particular form of the coefficients analytical and numerical results show that hmm gives comparable accuracy as msfem with much less cost for problems without scale separation our numerical results suggest that hmm performs at least as well as msfem in terms of accuracy and cost even though in this case both methods may fail to converge since the cost of msfem is comparable to that of solving the full fine scale problem one might expect that it does not need scale separation and still retains some accuracy we show that this is not the case specifically we give an example showing that if there exists an intermediate scale comparable to h the size of the macroscale mesh then msfem commits a finite error even with overlapping

a short and versatile finite element multiscale code for homogenization problems we describe a multiscale finite element fe solver for elliptic or parabolic problems with highly oscillating coefficients based on recent developments of the so called heterogeneous multiscale method hmm the algorithm relies on coupled macro and microsolvers the framework of the hmm allows to design a code whose structure follows the classical finite elements implementation at the macro level to account for the fine scales of the problem elementwise numerical integration is replaced by micro fe methods on sampling domains we discuss a short and flexible fe implementation of the multiscale algorithm which can accommodate simplicial or quadrilateral fe and various coupling conditions for the constrained micro simulations extensive numerical examples including three dimensional and time dependent problems are presented illustrating the efficiency and the versatility of the computational strategy

a multi level computational model for multi scale damage analysis in composite and porous materials abstract an adaptive multi level methodology is developed in this paper to create a hierarchy of computational sub domains with varying resolution for multiple scale problems it is intended to concurrently predict evolution of variables at the structural and microstructural scales as well as to track the incidence and propagation of microstructural damage in composite and porous materials the microstructural analysis is conducted with the voronoi cell finite element model vcfem while a conventional displacement based fem code executes the macroscopic analysis the model introduces three levels in the computational domain which include macro macro micro and microscopic analysis it differentiates between non critical and critical regions and ranges from macroscopic computations using continuum constitutive relations to zooming in at hotspots for pure microscopic simulations coupling between the scales in regions of periodic microstructure is accomplished through asymptotic homogenization an adaptive process significantly increases the efficiency while retaining appropriate level of accuracy for each region numerical examples are conducted for composite and porous materials with a variety of microscopic architectures to demonstrate the potential of the model

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

multi time step and two scale domain decomposition method for non linear structural dynamics in this paper we propose a method to improve the means of taking into account the specific time scale and space scale characteristics in time dependent non linear problems this method enables the use of arbitrary time steps in each subdomain these can be coupled by prescribing continuous velocities at the interfaces which are modelled using a dual schur formulation for certain subdomains in space we adopt a two scale resolution technique inspired by the multigrid methods in order to obtain the part of the solution related to small variation lengths on a refined scale and the part corresponding to large variation lengths on a coarse scale for non linear problems we propose an algorithm with a single iteration level to deal with both the non linear equilibrium and the two space scales thanks to a two grid method in which the relaxation steps are performed using a non linear preconditioned conjugate gradient algorithm finally we present an example which demonstrates the feasibility of the method copyright 2003 john wiley sons ltd

a spline wavelet finite element method in structural mechanics the wavelet based methods are powerful to analyse the field problems with changes in gradients and singularities due to the excellent multi resolution properties of wavelet functions wavelet based finite elements are often constructed in the wavelet space where field displacements are expressed as a product of wavelet functions and wavelet coefficients when a complex structural problem is analysed the interface between different elements and boundary conditions cannot be easily treated as in the case of conventional finite element methods fems a new wavelet based fem in structural mechanics is proposed in the paper by using the spline wavelets in which the formulation is developed in a similar way of conventional displacement based fem the spline wavelet functions are used as the element displacement interpolation functions and the shape functions are expressed by wavelets the detailed formulations of typical spline wavelet elements such as plane beam element in plane triangular element in plane rectangular element tetrahedral solid element and hexahedral solid element are derived the numerical examples have illustrated that the proposed spline wavelet finite element formulation achieves a high numerical accuracy and fast convergence rate copyright 2005 john wiley sons ltd

fixed point convergence of modular steady state heat transfer models coupling multiple scales and phenomena for melt crystal growth a block gauss seidel iteration procedure is employed to couple two independent heat transfer codes representing different scales and phenomena in a melt crystal growth system via shared domain boundaries in general such strategies are attractive because of their simplicity for solving problems that may be represented by linking via shared boundary conditions existing codes using a modular design however these approaches often meet with limited success due to convergence difficulties associated with the overall model the mathematical framework of fixed point iterations is employed to assess convergence behaviour for steady state non linear heat transfer models analytical forms describe the convergence of one dimensional problems and provide insight to the behaviour of more complicated two dimensional models certain implementations that are physically reasonable result in algorithms that will never converge demonstrating that notions based on physical intuition may not be useful for predicting algorithm performance a mixing of flux and temperature information along the shared model boundary leads to successful iterative strategies under many conditions

the fast adaptive composite grid fac method for elliptic equation the fast adaptive composite grid fag method is a systematic process for solving differential boundary value problems fac uses global and local uniform grids both to define the composite grid problem and to interact for its fast solution it can with little added cost substantially improve accuracy of the coarse grid solution and is very suitable for vector and parallel computation this paper develops both the theoretical and practical aspects of fac as it applies to elliptic problems 1 introduction the need for local resolution in physical models occurs frequently in practice special local features of the forcing function operator coefficients boundary and boundary conditions can demand resolution in restricted regions of the domain that is much finer than the required global resolution it is important that the discretization and solution processes account for this locally that is that the local phenomena do not precipitate a dramatic increase in the overall computation unfortunately this objective of efficiently adapting to local features is often in conflict with the solution process equation solvers can degrade or even fail to apply in the presence of varying discretization scales data structures that account for irregular grids can be cumbersome the computer architecture may not be able to effectively account for grid irregularity e g vectorizability may be inhibited etc in fact even the discretization process itself may find difficulty with this objective for finite differences it is problematic to develop accurate difference formulae for irregular grids for finite elements this objective is reflected in the substantial overhead costs needed to automate the discretization the fast adaptive composite grid method fac 11 is a discretization and solution method designed to achieve efficient local resolution by constructing the

on the generalized wavelet galerkin method abstract in the frame of the traditional wavelet galerkin method based on the compactly supported wavelets it is important to calculate the so called connection coefficients that are some integrals whose integrands involve products of wavelets their derivatives as well as some known coefficients in considered differential equations however even for linear differential equations with non constant coefficient the computation of connect coefficients becomes rather time consuming and often even impossible in this paper we propose a generalized wavelet galerkin method based on the compactly supported wavelets which is computationally very efficient even for differential equations with non constant coefficients no matter linear or nonlinear problems some related mathematical theorems are proved based on which the basic ideas of the generalized wavelet galerkin method are described in details in addition some examples are used to illustrate its validity and high efficiency a nonlinear example shows that the generalized wavelet galerkin method is not only valid to solve nonlinear problems but also possesses the ability to find new solutions of multi solution problems this method can be widely applied to various types of both linear and nonlinear differential equations in science and engineering

wavelet galerkin solutions for one dimensional partial differential equations in this paper we describe how wavelets may be used to solve partial differential equations these problems are currently solved by techniques such as finite differences finite elements and multi grid the wavelet method however offers several advantages over traditional methods wavelets have the ability to represent functions at different levels of resolution thereby providing a logical means of developing a hierarchy of solutions furthermore compactly supported wavelets such as those due to daubechies1 are localized in space which means that the solution can be refined in regions of high gradient e g stress concentrations without having to regenerate the mesh for the entire problem in order to demonstrate the wavelet technique we consider the one dimensional counterpart of helmholtz s equation by comparison with a simple finite difference solution to this problem with periodic boundary conditions we show how a wavelet technique may be efficiently developed dirichlet boundary conditions are then imposed using the capacitance matrix method described by proskurowski and widlund2 and others the convergence rates of the wavelet solutions are examined and they are found to compare extremely favourably to the finite difference solutions preliminary investigations also indicate that the wavelet technique is a strong contender to the finite element method at least for problems with simple geometries

fractional step methods for index 1 differential algebraic equations in the numerical solution of ordinary differential systems the method of fractional steps also known as operator splitting yields high order accurate schemes based on separate computationally convenient treatments of distinct physical effects such schemes are equally desirable but much less accurate for semi explicit index 1 differential algebraic equations daes in the first half of this note it is shown that email protected ve application to daes of standard splitting schemes suffers from order reduction both first and second order schemes are only first order accurate for daes in the second half of this note a new family of higher order splitting schemes for semi explicit index 1 daes is developed the new schemes are based on a deferred correction paradigm in which an error equation is solved numerically and therefore inherit a simple computationally convenient structure higher order convergence of the new schemes is proved and numerical results confirm the expected order of accuracy in addition to establishing efficiency

stability analysis of finite difference schemes revisited a study of decoupled solution strategies for coupled multifield problems summary many problems in engineering physics or other disciplines require an integrated treatment of coupled heterogeneous fields the mathematical models of such problems commonly consist of a coupled pde system considerable progress has been made in the development of schemes to solve such systems resulting in a wide spectrum of monolithic and decoupled numerical solution approaches in particular the flexibility offered by the decoupled strategies in choosing appropriate solution methods and adjustable time step sizes has motivated the elaboration of these schemes however the way of decoupling can influence the stability of the resulting solution algorithm and hence urges a comprehensive stability analysis the purpose of this contribution is to elucidate the salient points in the stability analysis of the numerical solution schemes to this end we introduce a general framework for the stability analysis of solution strategies and provide an easy to use procedure to find the necessary stability condition the procedure is tested against decoupled solution strategies for volume and surface coupled problems namely thermoelastodynamics porous media dynamics and fluid and structure structure interaction in this context the influence of explicit and implicit predictors and the sequence of the time integration on the stability condition is carefully examined copyright 2013 john wiley sons ltd

unconditionally stable sequential schemes for all way coupled thermoporomechanics undrained adiabatic and extended fixed stress splits abstract we propose two sequential methods for the all way coupled thermoporomechanical problems the undrained adiabatic split that combines together the undrained and adiabatic methods of poromechanics and thermomechanics respectively and the extended fixed stress split we perform nonlinear stability analysis for the two sequential methods introducing a new extended norm that can encompass the all way coupled thermoporomechanical problems we find that the two sequential methods are unconditionally stable if 0 5 where is the parameter of time discretization for the generalized midpoint rule at t n we also perform the spectral analysis in order to further investigate stability and convergence of the two methods the spectral analysis shows unconditional stability of the two sequential methods which yields the magnitudes of the amplification factor less than unity we then show numerical examples which support the a priori stability and convergence estimates

on convergence conditions of partitioned solution procedures for consolidation problems abstract a systematic approach to determine conditions for convergence of partitioned staggered procedures for consolidation problems is presented consistency convergence and stability is investigated for linear and nonlinear problems and a comparison of the partitioned and direct method is made conclusions based also on numerical evidence are drawn the significance of the ratio of the time step length to the square of the finite element mesh length is shown

comments on the computation of wavelet galerkin approximation on a bounded interval in this letter we identify and correct the errors in int j numer meth eng 1996 39 2921 2944 and we also develop clearer procedures for the computation of the connection coefficients from the wavelet galerkin scheme

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

variational multiscale methods to embed the macromechanical continuum formulation with fine scale strain gradient theories a variational basis is presented to link fine scale theories of material behaviour with the classical macromechanical continuum theory the approach is based on the weak form of the linear momentum balance equations and a separation of the weighting function and displacement fields into coarse and fine scale components coarse and fine scale weak forms are defined the latter is used to introduce a strain gradient theory that operates at finer scales of deformation attention is focused upon applications requiring the enhanced physical accuracy of the fine scale strain gradient theory without the computational cost of discretization that spans the range from coarse to fine scales a variationally consistent method is developed to embed the fine scale strain gradient theory in the macromechanical formulation the embedding is achieved by eliminating the fine scale displacement field from the problem two examples demonstrate the numerical efficiency of the method while retaining physical and mathematical properties of the fine scale strain gradient theory copyright 2003 john wiley sons ltd

a two scale approximation of the schur complement and its use for non intrusive coupling this paper presents a two scale approximation of the schur complement of a subdomain s stiffness matrix obtained by combining local ie element strips and global ie homogenized contributions this approximation is used in the context of a coupling strategy that is designed to embed local plasticity and geometric details into a small region of a large linear elastic structure the strategy consists in creating a local model which contains the desired features of the concerned region and then substituting it into the global problem by the means of a non intrusive solver coupling technique adapted from domain decomposition methods using the two scale approximation of the schur complement as a robin condition on the local model enables to reach high efficiency examples include a large 3d problem provided by our industrial partner snecma

the one phase free boundary problem for the p laplacian with non constant bernoulli boundary condition our objective here is to generalize our earlier results on the existence of classical convex solution to a free boundary problem with a bernoulli type boundary gradient condition and with the p laplacian as the governing operator the main theorems of this paper assert that the exterior and the interior free boundary problem with a bernoulli law i e with a prescribed pressure a x on the free streamline of the flow have convex solutions provided the initial domains are convex the continuous function a x is subject to certain convexity properties in our earlier results we have considered the case of constant a x in the lines of the proof of the main results we also prove the semi continuity up to the boundary of the gradient of the p capacitary potentials in convex rings with c 1 boundaries

a unified set of single step algorithms part 1 general formulation and applications a general algorithm for a single step time marching scheme for use in dynamic or diffusion equations is presented this algorithm is easily programmed in its universal form for all orders of approximation and covers most of the currently used schemes as well as presenting many new possibilities in many cases it presents a computationally advantageous form over conventional procedures this is particularly so when compared with the newmark algorighm and its variants

existence of classical solutions to a free boundary problem for the p laplace operator i the exterior convex case in this paper we prove under convexity assumptions for the data the existence of classical solutions for a bernoulli type free boundary problem with the p laplacian as the governing operator the method employed here originates from a pioneering work of a beurling where he proves the existence for the harmonic case in the plane though with no geometrical restrictions

multiscale enrichment based on partition of unity a new multiscale enrichment method based on the partition of unity mepu method is presented it is a synthesis of mathematical homogenization theory and the partition of unity method its primary objective is to extend the range of applicability of mathematical homogenization theory to problems where scale separation may not be possible mepu is perfectly suited for enriching the coarse scale continuum descriptions pdes with fine scale features and the quasi continuum formulations with relevant atomistic data numerical results show that it provides a considerable improvement over classical mathematical homogenization theory and quasi continuum formulations copyright 2005 john wiley sons ltd

multiscale asymptotic homogenization for multiphysics problems with multiple spatial and temporal scales a coupled thermo viscoelastic example problem abstract a systematic approach for analyzing multiple physical processes interacting at multiple spatial and temporal scales is developed the proposed computational framework is applied to the coupled thermo viscoelastic composites with microscopically periodic mechanical and thermal properties a rapidly varying spatial and temporal scales are introduced to capture the effects of spatial and temporal fluctuations induced by spatial heterogeneities at diverse time scales the initial boundary value problem on the macroscale is derived by using the double scale asymptotic analysis in space and time it is shown that an extra history dependent long term memory term introduced by the homogenization process in space and time can be obtained by solving a first order initial value problem this is in contrast to the long term memory term obtained by the classical spatial homogenization which requires solutions of the initial boundary value problem in the unit cell domain the validity limits of the proposed spatial temporal homogenized solution are established numerical example shows a good agreement between the proposed model and the reference solution obtained by using a finite element mesh with element size comparable to that of material heterogeneity

on multiscale fe analyses of heterogeneous structures from homogenization to multigrid solvers heterogeneous structures like composites often need a fine scale resolution of micro effects which influence the macroscopic overall response this is of particular relevance in the fully non linear range of large strains and inelastic material response of the constituents suitable solution methods introduce a multifield scenario of hierarchically superimposed states on different length scales for big differences of micro and macro scales the argument of scale separation induces the application of homogenization methods such types of physical multiscale approaches can be treated by nested multilevel finite element analyses that discretize both the fine scale micro structure as well as the macroscopic boundary value problem in contrast small scale differences require full resolution of the heterogeneous structure effective solution methods for the resulting large scale problems with strongly oscillating properties are suitably designed geometric multigrid techniques which may be considered as numerical multiscale approaches in both scenarios a key ingredient is the suitable formulation of scale bridging algorithms that govern the transfer between different scales the paper outlines new mesh bridging techniques in a deformation driven context for fully non linear response which exploit in a non trivial manner weak constraints on the average deformation in typical finite element patches the framework is based on an incremental variational structure of finite inelasticity the proposed new formulations provide variational based homogenization algorithms for physical multiscale scenarios and problem dependent optimal finite element grid transfers for numerical multiscale scenarios of heterogeneous materials copyright 2007 john wiley sons ltd

fdm solutions to linear dynamics of porous media efficiency stability and parallel solution strategy summary this paper presents a strategy to improve the efficiency of simulations involving porous materials with linear behaviour and full saturation the method is named parallel lines finite difference and uses a method to decouple a discretised version of the governing equations allowing parallel computations as a result the complexity and the bandwidth of the global matrix are significantly reduced and hence the efficiency is improved the other advantage of the scheme is the fulfilment of the inf sup stability condition the scheme is developed to solve porous media formulations derived from the theory of porous media both the u p and u v p formulations are considered u displacement of solid p pressure of liquid and v velocity of liquid several simulations are performed to demonstrate the capabilities of the method

laser induced heating of dynamic particulate depositions in additive manufacturing abstract many applications in additive manufacturing involve the dynamic deposition of powders and the in flight heating of such material by a laser in order to characterize such systems the discrete element method dem is employed specifically this paper focuses on the initial stages of this process by developing a modular discrete element type multiphysics simulation method for the particle dynamics and heating by a laser and detailed thermal behavior the objective is to provide researchers with a framework to construct computational tools for this growing industry in order to achieve this from a simulation standpoint the overall particle mixture system is constructed by coupling submodels for each primary physical process dynamics and heating together an iterative staggering scheme is developed whereby within every time step each individual particle is solved freezing the state of the remaining multiparticle system the state of the particle is then updated and the algorithm moves to the next particle in the system and the process is repeated the overall process sweeps through the entire system repeatedly until convergence is achieved in an appropriate norm as the system evolves an error estimate dictates the time step size that is needed to induce convergence to below an appropriate error level thus the process can be considered as an implicit time stepping scheme which is combined with an internal iterative staggering process in order to control rates of convergence within a time step the algorithm adjusts the time step size if the iterative process does not converge within a desired number of iterations below an error tolerance the time step is reduced the degree of time step reduction is determined by utilizing an estimate of the spectral radius of the coupled system since the construction of model and solution process is modular one can easily replace physical submodels with other choices making it easy to numerically experiment with a variety of models qualitative and quantitative analyses are provided as well as three dimensional numerical examples this paper addresses the first of two overall macrostages of a complex manufacturing process with dem the first stage addressed in this paper concentrates on dry powder materials which are of a discrete particulate character using dem to characterize the deposition and in flight particle heating other papers of the author zohdi 2010 2013 2014 2015 81 82 2008 have addressed stage two namely phase transformations curing cooling and stress analysis using more appropriate continuum and hybrid dem continuum approaches

stability and convergence of sequential methods for coupled flow and geomechanics fixed stress and fixed strain splits abstract we analyze stability and convergence of sequential implicit methods for coupled flow and geomechanics in which the flow problem is solved first we employ the von neumann and energy methods for linear and nonlinear problems respectively we consider two sequential methods with the generalized midpoint rule for tn where is the parameter of time discretization namely the fixed strain and fixed stress splits the von neumann method indicates that the fixed strain split is only conditionally stable and that its stability limit is a coupling strength less than unity if 0 5 on the other hand the fixed stress split is unconditionally stable when 0 5 the amplification factors of the fixed stress split are different from those of the undrained split and are identical to the fully coupled method unconditional stability of the fixed stress split is also obtained from the energy method for poroelastoplasticity we show that the fixed stress split is contractive and b stable when 0 5 we also estimate the convergence behaviors for the two sequential methods by the matrix based and spectral analyses for the backward euler method in time from the estimates the fixed strain split may not be convergent with a fixed number of iterations particularly around the stability limit even though it is stable the fixed stress split however is convergent for a fixed number of iterations showing better accuracy than the undrained split even when we cannot obtain the exact local bulk modulus or exact rock compressibility at the flow step a priori due to complex boundary conditions or the nonlinearity of the materials the fixed stress split can still provide stability and convergence by an appropriate estimation of the local bulk modulus such as the dimension based estimation by which the employed local bulk modulus is less stiff than the exact local bulk modulus we provide numerical examples supporting all the estimates of stability and convergence for the fixed strain and fixed stress splits

unconditionally convergent partitioned solution procedure for dynamic coupled mechanical systems a new partitioned solution procedure for the direct time integration of second order coupled field systems is presented and it is applied to the problem of soil pore fluid interaction the necessary convergence analysis for the iterative method is carried out and the fulfilment of the convergence condition is achieved with the introduction of two suitable auxiliary matrices in the basic equations governing the dynamic phenomena numerical examples are presented to demonstrate the effectiveness and the versatility of the proposed solution procedure

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

an iterative stabilized fractional step algorithm for finite element analysis in saturated soil dynamics abstract the discretization of the u p model for saturated porous media results in the semi discrete system of mixed type in displacements and pressures the babuska brezzi condition or the simpler patch test proposed by zienkiewicz and taylor precludes the use of elements with the equal low order of interpolation for u and p unless special stabilization techniques such as the fractional step algorithms are used the purpose of this paper is to present a modified version of the fractional step algorithm which allows much larger time step sizes than those for the existing ones the method is based on introducing an iteration algorithm the numerical experiments demonstrate the effectiveness and improved performance of the proposed modified version of the fractional step algorithm

a space time multilevel method for molecular dynamics simulations we present a novel multiscale approach for molecular dynamics simulations it is aimed at bridging discrete scales with either coarse grained discrete or continuum scales the method consists of the waveform relaxation scheme aimed at capturing the high frequency response of atomistic vibrations and a coarse scale solution in space and time aimed at resolving smooth features in both space and time domains of the discrete medium the method is implicit in space and time possesses superior stability properties and consequently enables larger time steps governed by accuracy considerations of coarse scale quantities of interest performance studies on polymer melts have shown significant speed up compared to the classical explicit methods in particular on parallel machines

an adaptive multilevel wavelet collocation method for elliptic problems an adaptive multilevel wavelet collocation method for solving multi dimensional elliptic problems with localized structures is described the method is based on multi dimensional second generation wavelets and is an extension of the dynamically adaptive second generation wavelet collocation method for evolution problems int j comp fluid dyn 17 2003 151 wavelet decomposition is used for grid adaptation and interpolation while a hierarchical finite difference scheme which takes advantage of wavelet multilevel decomposition is used for derivative calculations the multilevel structure of the wavelet approximation provides a natural way to obtain the solution on a near optimal grid in order to accelerate the convergence of the solver an iterative procedure analogous to the multigrid algorithm is developed the overall computational complexity of the solver is o n where n is the number of adapted grid points the accuracy and computational efficiency of the method are demonstrated for the solution of two and three dimensional elliptic test problems

a new numerically stable sequential algorithm for coupled finite strain elastoplastic geomechanics and flow abstract we propose a new numerically stable sequential implicit method for coupled flow and finite strain multiplicative elastoplastic geomechanics we find from stability analysis that the sequential method that solves the flow problem first by fixing the first piola kirchhoff total stress solving the geomechanics solid deformation problem at the next step is unconditionally stable contractive and b stable in this sense this method named the fixed first piola kirchhoff stress method is an extension of the fixed stress method in coupled flow and infinitesimal geomechanics we also study the fixed second piola kirchhoff stress method comparing it with the fixed first piola kirchhoff stress method because the constitutive relations are formulated by the second piola kirchhoff total stress although fixing the second piola kirchhoff total stress field does not provide theoretical unconditional stability in space discretization we use the finite element method for the geomechanics problem with the total lagrangian approach while employing the finite volume method for the flow problem geometrical nonlinearity from the total lagrangian approach results in full tensor permeability even if the initial permeability is isotropic to consider the full tensor permeability accurately we employ the multipoint flux approximation in solving the flow problem in time discretization the backward euler method is used then we perform numerical experiments of the two fixed stress sequential methods with various scenarios and find superiority of their numerical stability specifically the two fixed stress sequential methods provide almost identical results for elasticity for j 2 plasticity the two sequential methods yield slightly different numerical results although the trends of the results are similar for the drucker prager plasticity we find that the results from the two methods are almost identical for all the test cases the two sequential methods are numerically stable

direct estimation of generalized stress intensity factors using a three scale concurrent multigrid x fem a concurrent multigrid method is devised for the direct estimation of stress intensity factors and higher order coefficients of the elastic crack tip asymptotic field the proposed method bridges three characteristic length scales that can be present in fracture mechanics the structure the crack and the singularity at the crack tip for each of them a relevant model is proposed first a truncated analytical reduced order model based on williams expansion is used to describe the singularity at the tip then it is coupled with a standard extended finite element fe method model which is known to be suitable for the scale of the crack a multigrid solver finally bridges the scale of the crack to that of the structure for which a standard fe model is often accurate enough dedicated coupling algorithms are presented and the effects of their parameters are discussed the efficiency and accuracy of this new approach are exemplified using three benchmarks

stability and convergence of sequential methods for coupled flow and geomechanics drained and undrained splits abstract we perform a stability and convergence analysis of sequential methods for coupled flow and geomechanics in which the mechanics sub problem is solved first we consider slow deformations so that inertia is negligible and the mechanical problem is governed by an elliptic equation we use biot s self consistent theory to obtain the classical parabolic type flow problem we use a generalized midpoint rule parameter between 0 and 1 time discretization and consider two classical sequential methods the drained and undrained splits the von neumann method provides sharp stability estimates for the linear poroelasticity problem the drained split with backward euler time discretization 1 is conditionally stable and its stability depends only on the coupling strength and it is independent of time step size the drained split with the midpoint rule 0 5 is unconditionally unstable the mixed time discretization with 1 0 for mechanics and 0 5 for flow has the same stability properties as the backward euler scheme the von neumann method indicates that the undrained split is unconditionally stable when 0 5 we extend the stability analysis to the nonlinear regime poro elastoplasticity via the energy method it is well known that the drained split does not inherit the contractivity property of the continuum problem thereby precluding unconditional stability for the undrained split we show that it is b stable therefore unconditionally stable at the algorithmic level when 0 5 we also analyze convergence of the drained and undrained splits and derive the a priori error estimates from matrix algebra and spectral analysis we show that the drained split with a fixed number of iterations is not convergent even when it is stable the undrained split with a fixed number of iterations is convergent for a compressible system i e finite biot modulus for a nearly incompressible system i e very large biot modulus the undrained split loses first order accuracy and becomes non convergent in time we also study the rate of convergence of both splits when they are used in a fully iterated sequential scheme when the medium permeability is high or the time step size is large which corresponds to a high diffusion of pressure the error amplification of the drained split is lower and therefore converges faster than the undrained split the situation is reversed in the case of low permeability and small time step size we provide numerical experiments supporting all the stability and convergence estimates of the drained and undrained splits in the linear and nonlinear regimes we also show that our spatial discretization finite volumes for flow and finite elements for mechanics removes the well documented spurious instability in consolidation problems at early times

an adaptive multiscale resolution strategy for the finite deformation analysis of microheterogeneous structures abstract standard homogenized formulations of problems posed on microheterogeneous domains provide a lower order of accuracy in regions where highly localized variations are observed in the solution fields in order to account for this loss of accuracy for the finite deformation analysis of generally inelastic macrostructures a scale adaptation strategy is developed where a transition from a homogenized description to an explicit microstructural resolution is pursued in designated zones of interest motivated by higher order homogenization techniques the adaptation zones are identified based on a post processing step on the homogenized solution and correspond to regions with high strain gradients in order to avoid modeling errors emanating from the use of approximate explicit macroscale constitutive formulations an exact homogenization procedure based on databased and direct multilevel finite element computations is employed the overall methodology is investigated in a two dimensional setting where special attention is paid to the underlying multiscale mesh resolution and additionally demonstrated with a three dimensional problem numerical observations suggest the concept of a representative adaptation zone within which scale adaptation effects can be assessed

some inverse problems around the tokamak tore supra we consider two inverse problems related to the tokamak textsl tore supra through the study of the magnetostatic equation for the poloidal flux the first one deals with the cauchy issue of recovering in a two dimensional annular domain boundary magnetic values on the inner boundary namely the limiter from available overdetermined data on the outer boundary using tools from complex analysis and properties of genereralized hardy spaces we establish stability and existence properties secondly the inverse problem of recovering the shape of the plasma is addressed thank tools of shape optimization again results about existence and optimality are provided they give rise to a fast algorithm of identification which is applied to several numerical simulations computing good results either for the classical harmonic case or for the data coming from textsl tore supra

global basis two level method for indefinite systems part 1 convergence studies a robust two level solver for high indefinite system of equations arising from the finite element discretization is developed it is shown that the optimal coarse model is spanned by the spectrum of the highest eigenmodes of the smoothing iteration matrix convergence studies conducted on a model prolongation operator reveal pathological sensitivity to any deviation from the optimal coarse model copyright 2000 john wiley sons ltd

an energetically consistent concurrent multiscale method for heterogeneous heat transfer and phase transition applications abstract a concurrent multiscale method is developed to model time dependent heat transfer and phase transitions in heterogeneous media and is formulated in a way such that the energy being exchanged between scales is conserved ensuring this energetic consistency among scales enables the implementation of high fidelity physics based models at critical locations within the coarse scale to temporally and spatially resolve highly complex and localized phenomena to achieve this only neumann boundary conditions are applied over the fine scale domain ensuring a conservative formulation the coarse scale solution is used to reconstruct these neumann boundary conditions on the fine scale which are then used to evolve a separate system of governing equations the results on the fine scale are then sent back to the coarse scale through an energy based homogenization scheme transient simulations for the heat equation are implemented with the proposed method to demonstrate its accuracy in energy conservation and effectiveness including the coupling of a phase field model at the fine scale to a coarse scale heat equation

the computation of wavelet galerkin approximation on a bounded interval this paper describes exact evaluations of various finite integrals whose integrands involve products of daubechies compactly supported wavelets and their derivatives and or integrals these finite integrals play an essential role in the wavelet galerkin approximation of differential or integral equations on a bounded interval

the discontinuous petrov galerkin methodology for the mixed multiscale finite element method abstract we present the application of the discontinuous petrov galerkin dpg methodology for the mixed multiscale finite element method msfem the msfem upscaling technique relies on incorporating fine scale features through special in a sense optimized for approximability trial functions while the dpg methodology allows for the selection of the optimal test functions to provide stability of the fem approximation the special trial functions are computed online by the solution of local boundary value problems we improved this process using the static condensation that restricted the construction of the functions to the coarse mesh skeleton element interfaces only we have verified by numerical tests that the proposed improvement of msfem reduced both the approximation error and computational cost moreover it simplified the algorithm significantly the key component of this prolongation construction is our novel method for prolongation of both traction and displacement vectors on element edges of arbitrary shape the proposed prolongation operator may be also used in the multigrid solver for direct analysis of composites with varying material parameters using an arbitrary well posed functional setting with or without the dpg methodology

a multiscale finite element method for optimal control problems governed by the elliptic homogenization equations in this article we develop and analyze a priori estimates for optimal control problems with multiscale governed by the elliptic homogenization equations the multiscale finite element is applied to capture the effect of microscale through modification of finite element basis functions without resolving all the small scale features the optimal estimate is derived for elliptic homogenization problems without resonance effect o e h by using an over sampling technique and the boundary layer assumption furthermore the a priori estimate is obtained for the optimal control problems governed by the elliptic homogenization equations

an analytical coarse grid operator applied to a multiscale multigrid method equations describing flow through heterogeneous porous media are often difficult to solve by direct numerical simulation given their expensive computational requirement in this paper numerical convergence is achieved for solving the flow equation with high contrast variable coefficients using two low computational methods that incorporate analytical approximations into the geometric multigrid the methods are inheritably fast and easily implementable with coefficients describing general non periodic media the first method named here as analytical coarse operator aco defines the operator at each coarse scale of the v cycle using an analytical approximation of the upscale tensor it works in the same way as iterative homogenization its efficiency and reliability are measured by comparing with similar algorithms using arithmetic and harmonic averages of the coefficient since they are widely used in the literature the second method called analytical prolongation operator apo may be termed as aggressive coarsening because it obtains the solution by skipping few levels in the v cycle it is an extension of the first approach where a multiscale prolongation operator is defined using an analytical approximation of the solution of the cell problem from homogenization theory the efficiency and reliability of this method are measured by comparing the number of v cycles with the full numerical implementation various test cases demonstrated that convergence can be achieved using typical implementation procedures of the geometric multigrid method therefore it highlights the low cost and easy implementation features of the methods the examples include media having separable and non separable scales periodic or not in the case of non periodic medium the problem of determining coarse grids that are representative element volume rev is also addressed the medium from the spe10 benchmark project is an application of the method for non separable scale

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

convergence estimates for the wavelet galerkin method this paper presents an analysis of the galerkin approximation of a time dependent initial value problem correctly posed in the petrovskii sense the approximating spaces mathcal v h are spanned by translations and dilations of a single function phi and fourier techniques are used to analyze the accuracy of the method this kind of procedure has already been applied in the literature for spline approximations our purpose here is to point out that the same methodology can be used for wavelet based methods since the hypotheses required are automatically satisfied in the context of wavelet analysis for instance the basic function phi is supposed to be regular which means that phi and all its derivatives up to a certain order should have fast decay at infinity phi also must satisfy the so called strang and fix condition which guarantees that smooth functions can be approximated from mathcal v h with good accuracy this class of functions includes not only the b splines but al

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

adaptive s method for linear elastostatics abstract a methodology has been developed to simultaneously treat phenomena at several scales the key features of the method are i a detailed error diagnosis which identifies critical regions and ii a feedback procedure which overlays portions of the finite element mesh where unacceptable errors have been identified by local finite element mesh es and then subsequently improves the quality of the solution in the global and local response until the desired level of accuracy is achieved the method can be routinely used as a global local method and or as an adaptive technique which provides a measure of reliability of global and local computations numerical experiments for problems in homogeneous and heterogeneous laminated composites media are presented to validate the present formulation

unstructured multigrid method for shells summary an accelerated multigrid method which exploits shell element formulation to speed up the iterative process is developed for inherently poor conditioned thin domain problems on unstructured grids its building blocks are i intergrid transfer operators based on the shell element shape functions ii heavy smoothing procedures in the form of modified incomplete cholesky factorization and iii various two and threeparameter acceleration schemes both the flat shell triangular element and the assumed strain degenerated solid shell element are considered numerical results show a remarkable robustness for a wide spectrum of span thickness ratios encountered in practical applications

on the homotopy analysis method for nonlinear problems a powerful easy to use analytic tool for nonlinear problems in general namely the homotopy analysis method is further improved and systematically described through a typical nonlinear problem i e the algebraically decaying viscous boundary layer flow due to a moving sheet two rules the rule of solution expression and the rule of coefficient ergodicity are proposed which play important roles in the frame of the homotopy analysis method and simplify its applications in science and engineering an explicit analytic solution is given for the first time with recursive formulas for coefficients this analytic solution agrees well with numerical results and can be regarded as a definition of the solution of the considered nonlinear problem

error propagation of staggered solution procedures for transient problems abstract closed formulas for the error of staggered and simultaneous procedures are derived and compared conditions of global convergence are determined it is shown that in some cases a complicated condition for stability of the staggered scheme can be replaced by a simpler one the simultaneous stability condition for one iteration step a counterexample for global convergence of the staggered method with a constant number of iterations is presented

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

a new unconditionally stable fractional step method for non linear coupled thermomechanical problems a new class of time stepping algorithms for strongly coupled thermomechanical problems is presented which retains the computational convenience of traditional staggered algorithms without upsetting the unconditional stability property characteristic of fully implicit monolithic schemes 11 the proposed schemes are fractional step methods associated with a two phase operator split of the full non linear system of thermoelasticity into an adiabatic elastodynamics phase followed by a heat conduction phase at fixed configuration this operator split is shown to inherit the contractivity property of the full problem of evolution thus leading to unconditionally b stable product formula algorithms in sharp contrast with this stability result traditional staggered algorithms based on an isothermal mechanical phase followed by a heat conduction phase with an effective heat source are shown to lead at best to conditionally stable schemes it is further shown that the actual implementation of these two classes of schemes is essentially identical the numerical simulations presented include both dynamic and quasi static problems and are shown to closely replicate the stability estimates and non linear stability results derived for these two classes of staggered schemes

multigrid methods for variational problems further results in an earlier paper siam j numer anal 19 1982 pp 924 929 we developed a convergence theory for a class of multigrid methods applied to positive definite self adjoint differential boundary value problems where the multigrid process used w cycling and richardson s iteration in the present paper we extend this theory to include v cycling and more general relaxation schemes such as jacobi and arbitrarily ordered gauss seidel

numerical analysis of the stress concentration near holes originating in previously loaded viscoelastic bodies at finite strains abstract the state of stress and strain of previously loaded viscoelastic bodies with holes originating in them successively or simultaneously is analyzed under finite plane deformations the problem statement and solution are based on the theory of repeatedly superimposed large deformations the material mechanical properties are described using integral relations of the convolution type over time with a weakly singular kernel the problem solving is based on the finite element method to calculate the integral of the convolution type a recurrence formula is used that can be obtained by approximating the initial kernel with a linear combination of exponential functions the truncated prony s series the nonlinear effects and the effect of the interaction between holes on the stress concentration are analyzed for the dynamic problems the results for incompressible and weakly compressible materials are compared

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