rosenbrock type methods applied to finite element computations within finite strain viscoelasticity abstract in this article time adaptive high order rosenbrock type methods are applied to the system of differential algebraic equations which results from the space discretization using finite elements based on a constitutive model of finite strain viscoelasticity it is shown that in this smooth problem more efficient finite element computations result in comparison to classical finite element approaches since the time integration on the basis of rosenbrock type methods does not lead to a system of non linear equations in other words all aspects of implicit finite elements as local iterations on gauss point level and global equilibrium iterations do not occur the first introduction to this approach proposed by hartmann and wensch 22 is extended here to the case of finite strain applications where the geometrical non linear deformation has an essential contribution to the non linearities additionally a clear decomposition into local element or gauss point work and global computational work using the schur complement is introduced to exploit the classical finite element character moreover the extension to the reaction force computation which is different to the classical approach and the influence to mixed element formulations here the three field formulation for displacements pressure and dilatation are discussed the performance of various rosenbrock type methods is investigated and shows that for low accuracy requirements as in order one methods the proposal yields a drastic reduction of the computational time

on plastic incompressibility within time adaptive finite elements combined with projection techniques abstract this article treats the interpretation of quasi static finite elements applied to constitutive equations of evolutionary type as a solution scheme to solve globally differential algebraic equations this concept is applied to finite strain viscoplasticity based on a model with non linear kinematic hardening under the assumption of plastic incompressibility the model is based on multiple multiplicative decomposition both for the deformation gradient into an elastic and an inelastic part as well as for the inelastic part into a kinematic hardening energy storage and a dissipative part both intermediate configurations are described by inelastic right cauchy green tensors satisfying inelastic incompressibility in the theoretical context the attention in view of the numerical treatment within finite elements is focused on diagonally implicit runge kutta methods which destroy the assumption of plastic incompressibility during the time integration due to an additive structure of the integration step in combination with a multilevel newton algorithm these algorithms embed the classical strain driven radial return method to this end a concept of geometric numerical integration is applied where the plastic incompressibility condition is taken into account as an additional side condition since the literature states large integration errors if the side condition is not taken into account a particular focus lies on the application of a time adaptive procedure accordingly the article investigates i the algorithmic treatment of kinematic hardening within time adaptive finite elements ii the influence of the perzyna type viscoplasticity approach in view of an order reduction phenomenon and iii the influence of taking into account the exact fulfillment of plastic incompressibility using a projection method having the advantage of simple implementation

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

variational and projection methods for the volume constraint in finite deformation elasto plasticity this paper focuses on the treatment of volume constraints which in the context of elasto plasticity typically arise as a result of assuming volume preserving plastic flow projection methods based on the modification of the discrete gradient operator b often proposed on an ad hoc basis are systematically obtained in the variational context furnished by a three field hu washizu principle the fully nonlinear formulation proposed here is based on a local multiplicative split of the deformation gradient into volume preserving and dilatational parts without relying on rate forms of the weak form of momentum balance this approach fits naturally in a formulation of plasticity based on the multiplicative decomposition of the deformation gradient and enables one to exactly enforce the condition of volume preserving plastic flow within the framework proposed in this paper rate forms and incrementally objective algorithms are entirely bypassed

an efficient stress algorithm with applications in viscoplasticity and plasticity this paper deals with two main topics the first one concerns the equivalence of stress algorithms based on a backward euler step applied on viscoplastic models of chaboche type and their elastoplastic counterpart generally the stress algorithm yields a system of non linear algebraic equations and the corresponding consistent tangent operator occurring in the principle of virtual displacements leads to a system of linear equations this procedure can be obtained utilizing only numerical methods the second topic concerns a special constitutive relation based on a kinematic hardening model using a sum of armstrong frederick terms which is equivalent to a multi surface plasticity model applying this model a so called problem adapted stress algorithm is derived where only one non linear equation must be solved this result is independent of the number of terms in the hardening model furthermore only the viscoplastic algorithm must be implemented since it includes the elastoplastic constitutive model as a special case 1997 by john wiley sons ltd

finite strain viscoplasticity with nonlinear kinematic hardening phenomenological modeling and time integration abstract this article deals with a viscoplastic material model of overstress type the model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part an additional multiplicative decomposition of inelastic part is used to describe a nonlinear kinematic hardening of armstrong frederick type two implicit time stepping methods are adopted for numerical integration of evolution equations such that the plastic incompressibility constraint is exactly satisfied the first method is based on the tensor exponential the second method is a modified euler backward method special numerical tests show that both approaches yield similar results even for finite inelastic increments the basic features of the material response predicted by the material model are illustrated with a series of numerical simulations

an analysis of a new class of integration algorithms for elastoplastic constitutive relations an accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors is carried out in this paper for simplicity attention is confined to infinitesimal deformations the integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations general rate independent and rate dependent behaviour with plastic hardening or softening associated or non associated flow rules and nonlinear elastic response can be efficiently treated within the present framework isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding

on a superconvergent lattice boltzmann boundary scheme in a seminal paper 20 ginzburg and adler 1994 analyzed the bounce back boundary conditions for the lattice boltzmann scheme and showed that it could be made exact to second order for the poiseuille flow if some expressions depending upon the parameters of the method were satisfied thus defining so called magic parameters using the taylor expansion method that one of us developed we analyze a series of simple situations 1d and 2d for diffusion and for linear fluid problems using bounce back and anti bounce back numerical boundary conditions the result is that magic parameters depend upon the detailed choice of the moments and of their equilibrium values they may also depend upon the way the flow is driven

efficient implicit integration for finite strain viscoplasticity with a nested multiplicative split abstract an efficient and reliable stress computation algorithm is presented which is based on implicit integration of the local evolution equations of multiplicative finite strain plasticity viscoplasticity the algorithm is illustrated by an example involving a combined nonlinear isotropic kinematic hardening numerous backstress tensors are employed for a better description of the material behavior the considered material model exhibits the so called weak invariance under arbitrary isochoric changes of the reference configuration and the presented algorithm retains this useful property even more the weak invariance serves as a guide in constructing this algorithm the constraint of inelastic incompressibility is exactly preserved as well the proposed method is first order accurate concerning the accuracy of the stress computation the new algorithm is comparable to the euler backward method with a subsequent correction of incompressibility ebmsc and the classical exponential method em regarding the computational efficiency the new algorithm is superior to the ebmsc and em some accuracy tests are presented using parameters of the aluminum alloy 5754 o and the 42crmo4 steel fem solutions of two boundary value problems using msc marc are presented to show the correctness of the numerical implementation

a newton schur alternative to the consistent tangent approach in computational plasticity we introduce a newton schur alternative to the consistent tangent approach in plasticity computations and show that the structure of the consistent tangent approach is preserved in the new newton schur approach however the local constitutive iterations used in the conventional computational plasticity analyses are eliminated when using the newton schur approach two numerical examples are presented which illustrate the efficiencies gained by the new approach

high order quasi static finite element computations in space and time with application to finite strain viscoelasticity on the one hand high order quasi static finite elements have been developed on the basis of isogeometric analysis or hierarchical shape functions based on integrated legendre polynomials which display favorable behavior in comparison to linear element formulations if we consider constitutive models of evolutionary type such as elastoplasticity viscoplasticity or viscoelasticity only first order methods are employed to integrate the ordinary differential equations at the gauss point level leading to errors caused by the time integration on the other hand high order time integration methods have been devised to treat the resulting system of differential algebraic equations dae system following the spatial discretization this however is only done using spatial discretizations with linear or quadratic h elements based on lagrange polynomials or related mixed element formulations in this article both approaches are combined using a p version finite element approach on the basis of hierarchical shape functions and the resulting dae system is solved by means of high order one step methods the first step in this treatise is to apply stiffly accurate diagonally implicit runge kutta methods combined with the multilevel newton algorithm since the computational outlay for computing the tangential stiffness matrix is very high in the case of p version finite elements rosenbrock type methods are applied as well which lead to a completely iteration free technique we then compare the two approaches the next step is to investigate three dimensional examples showing the properties on the basis of a constitutive model in finite strain viscoelasticity

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

remarks on the interpretation of current non linear finite element analyses as differential algebraic equations for the numerical solution of materially non linear problems like in computational plasticity or viscoplasticity the finite element discretization in space is usually coupled with point wise defined evolution equations characterizing the material behaviour the interpretation of such systems as differential algebraic equations dae allows modern day integration algorithms from numerical mathematics to be efficiently applied especially the application of diagonally implicit runge kutta methods dirk together with a multilevel newton method preserves the algorithmic structure of current finite element implementations which are based on the principle of virtual displacements and on backward euler schemes for the local time integration moreover the notion of the consistent tangent operator becomes more obvious in this context the quadratical order of convergence of the multilevel newton algorithm is usually validated by numerical studies however an analytical proof of this second order convergence has already been given by authors in the field of non linear electrical networks we show that this proof can be applied in the current context based on the dae interpretation mentioned above we finally compare the proposed procedure to several well known stress algorithms and show that the inclusion of a step size control based on local error estimations merely requires a small extra time investment copyright 2001 john wiley sons ltd

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

on the formulation of closest point projection algorithms in elastoplasticity part ii globally convergent schemes this paper presents the formulation of numerical algorithms for the solution of the closest point projection equations that appear in typical implementations of return mapping algorithms in elastoplasticity the main motivation behind this work is to avoid the poor global convergence properties of a straight application of a newton scheme in the solution of these equations the so called newton cppm the mathematical structure behind the closest point projection equations identified in part i of this work delineates clearly different strategies for the successful solution of these equations in particular primal and dual closest point projection algorithms are proposed in non augmented and augmented lagrangian versions for the imposition of the consistency condition the primal algorithms involve a direct solution of the original closest point projection equations whereas the dual schemes involve a two level structure by which the original system of equations is staggered with the imposition of the consistency condition driving alone the iterative process newton schemes in combination with appropriate line search strategies are considered resulting in the desired asymptotically quadratic local rate of convergence and the sought global convergence character of the iterative schemes these properties together with the computational performance of the different schemes are evaluated through representative numerical examples involving different models of finite strain plasticity in particular the avoidance of the large regions of no convergence in the trial state observed in the standard newton cppm is clearly illustrated

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

time integration of the dual problem of elastoplasticity by runge kutta methods implicit runge kutta methods for the dual problem of elastoplasticity are analyzed and classified the choice of runge kutta time integration is inspired by the problem structure which consists of a coupled system of balance equations and unilaterally constrained evolution equations and which can be viewed as an infinite dimensional differential algebraic equation focussing on the time axis and leaving the space variables continuous a grid independent existence and uniqueness result is given for the class of coercive runge kutta methods moreover contractivity preservation and convergence are shown for methods that are also algebraically stable

convergence of lattice boltzmann methods for stokes flows in periodic and bounded domains combining an asymptotic analysis of the lattice boltzmann method m junk z yang asymptotic analysis of lattice boltzmann boundary conditions j stat phys 121 2005 3 35 with the stability estimate presented in m junk w a yong weighted l 2 stability of the lattice boltzmann equation preprint we are able to prove some strict convergence results the proof applies to the lattice boltzmann method with linear collision operator both in the case of periodic domains and bounded domains if the dirichlet boundary condition is realized with the bounce back rule

a higher order time integration method for viscoplasticity time integration in viscoplasticity is discussed from both engineering and mathematical points of view a second order integration scheme is presented and combined with an adaptive time stepping algorithm which utilizes local error estimates for the choice of time steps and a closed form expression for the consistent tangent operator is derived the algorithm is applied to the viscoplastic model by choi and krempl

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

an onsager like relation for the lattice boltzmann method an onsager like relation is proposed as a new criterion for constructing and analyzing the lattice boltzmann lb method for lb models obeying the relation we analyze their linearized stability establish their diffusive limit and find new constraints for those with free parameters the new relation seems of fundamental importance for the lb method

effective permeability of multifractal porous media abstract we show how the real space renormalization group method can be used to calculate analytically the scaling exponents of the effective absolute permeability in multifractal porous media the permeability fields considered are deterministic and random multifractals constructed with multiplicative processes we discuss the implications of the results on the understanding of fluid flow in oil reservoirs

exponential map algorithm for stress updates in anisotropic multiplicative elastoplasticity for single crystals this paper presents a new stress update algorithm for large strain rate independent single crystal plasticity the theoretical frame is the well established continuum slip theory based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts a distinct feature of the present formulation is the introduction and computational exploitation of a particularly simple hyperelastic stress response function based on a further multiplicative decomposition of the elastic deformation gradient into spherical and unimodular parts resulting in a very convenient representation of the schmid resolved shear stresses on the crystallographic slip systems in terms of a simple inner product of eulerian vectors the key contribution of this paper is an algorithmic formulation of the exponential map exp sl 3 sl 3 for updating the special linear group sl 3 of unimodular plastic deformation maps this update preserves exactly the plastic incompressibility condition of the anisotropic plasticity model under consideration the resulting fully implicit stress update algorithm treats the possibly redundant constraints of single crystal plasticity by means of an active set search it exploits intrinsically the simple representation of the schmid stresses by formulating the return algorithm and the associated consistent elastoplastic moduli in terms of eulerian vectors updates the performance of the proposed algorithm is demonstrated by means of a representative numerical example

conservation laws and the numerical solution of odes ii abstract many physical systems described by an initial value problem for a system of ordinary differential equations odes conserve physical quantities such as the net charge or total energy as the system evolves typical codes for the numerical solution of the odes will not conserve these quantities and this can lead to solutions which are not even qualitatively correct one way to impose conservation laws is to perturb the numerical solution at each step of the integration a simple theory is developed in this paper which tells how this should be done so as to guarantee convergence of codes based on one step methods it is also easy to interpret the effect on the accuracy of the perturbations

geometric integrators for multiplicative viscoplasticity analysis of error accumulation abstract the inelastic incompressibility is a typical feature of metal plasticity viscoplasticity over the last decade there has been a great amount of research related to construction of numerical integration algorithms which exactly preserve this property in this paper we examine both numerically and mathematically the excellent accuracy and convergence characteristics of such integrators in order to simplify the considerations we consider strain driven processes without hardening effects in terms of a classical model of multiplicative viscoplasticity we illustrate the notion of exponential stability of the exact solution we show that this property enables the construction of effective and stable numerical algorithms if the incompressibility is exactly satisfied on the other hand if the incompressibility constraint is violated spurious degrees of freedom are introduced in general this results in the loss of the exponential stability and a dramatic deterioration of convergence of numerical methods

a monolithic finite element approach using high order schemes in time and space applied to finite strain thermo viscoelasticity this article addresses a thermo mechanically coupled problem of thermo viscoelasticity at finite strains using a monolithic approach the underlying equations are based on the non linear transient heat equation the local equilibrium conditions and the evolution equations of the internal variables the latter describe the hardening behavior of the material if the method of vertical lines is applied its first step namely the spatial discretization yields a system of differential algebraic equations dae system here we employ the p version of the finite element method based on integrated legendre polynomials this can lead to very precise solutions in the spatial domain in order to be accurate in the time domain as well stiffly accurate diagonally implicit runge kutta methods are applied to solve the dae system yielding a coupled system of non linear algebraic equations in this article the system is solved monolithically by employing the multilevel newton algorithm accordingly a high order result is obtained in the space and the time domain the numerical concept is applied to a constitutive model of finite strain thermo viscoelasticity several examples are applied to demonstrate the efficiency and applicability of the numerical scheme it is especially the transient problems that call for time adaptive schemes which are naturally embedded in the concept

an explicit solution for implicit time stepping in multiplicative finite strain viscoelasticity abstract we consider the numerical treatment of one of the most popular finite strain models of the viscoelastic maxwell body this model is based on the multiplicative decomposition of the deformation gradient combined with neo hookean hyperelastic relations between stresses and elastic strains the evolution equation is six dimensional and describes an incompressible flow such that the volume changes are purely elastic for the corresponding local initial value problem a fully implicit integration procedure is considered and a simple explicit update formula is derived thus no local iterative procedure is required which makes the numerical scheme more robust and efficient the resulting integration algorithm is unconditionally stable and first order accurate the incompressibility constraint of the inelastic flow is exactly preserved a rigorous proof of the symmetry of the consistent tangent operator is provided moreover some properties of the numerical solution like invariance under the change of the reference configuration and positive energy dissipation within a time step are discussed numerical tests show that in terms of accuracy the proposed integration algorithm is equivalent to the classical implicit scheme based on the exponential mapping finally in order to check the stability of the algorithm numerically a representative initial boundary value problem involving finite viscoelastic deformations is considered a fem solution of the representative problem using msc marc is presented

weighted mathbb l 2 stability of the lattice boltzmann method this article is concerned with the linearized stability of the lattice boltzmann method both on periodic domains and on bounded domains with the bounce back rule used at the boundaries under a structural hypothesis we prove that a weighted mathbb l 2 norm of the solutions to the linearized lattice boltzmann method is decreasing with time moreover we show that the structural hypothesis holds true for many lattice boltzmann models

scaling properties of disordered multifractals abstract in turbulence the simplest phenomenological models of the energy cascade are multiplicative processes constructed on a regular grid in short m p g they have been used mostly for their simplicity allowing many of their properties to be derived analytically and their capacity to reproduce the scale invariance properties of various geophysical fields however these m p g s suffer from the drawback of lacking translation invariance in their spatial statistics spatial homogeneity and therefore they cannot be fully satisfactory models for geophysical fields in this paper we are interested in finding new construction methods for spatially homogeneous random multifractals we investigate the scaling properties of a new family of gridless models of multifractals

volume preserving energy momentum schemes for isochoric multiplicative plasticity abstract this paper presents a new energy dissipative momentum conserving algorithm for multiplicative finite strain plasticity f f e f p that also preserves exactly the plastic volume for isochoric plastic models the new algorithm exhibits exactly the conservation laws of linear and angular momentum of the underlying physical problem as well as its energy evolution a strictly positive energy dissipation in fact the exact energy dissipation is obtained by design during plastic steps while enforcing the plastic consistency i e the yield condition on the final stress appearing in the equations of motion exact energy conservation is attained in particular during elastic steps the aforementioned preservation of the plastic volume is obtained by a new treatment of the geometric structure behind the considered multiplicative models of finite strain plasticity namely we present a new approximation of the reference and elastic metrics whose contractions with the incremental total and elastic strains lead exactly to the increment of the total and elastic natural volumetric strains respectively the elastic metric is defined in the intermediate configuration defined itself by the proper discrete approximation in time of the plastic deformation gradient f p the new algorithm extends to the plastic range existing energy momentum conserving schemes for nonlinear elastic problems but incorporating a new modified elastic stress formula consistent with this new geometric setting the inherited conservation laws of momenta and especially the non negative character of the energy dissipation leads to an improved performance over existing more classical schemes showing numerical instabilities in the considered highly nonlinear geometric setting of large deformations and strains several numerical simulations are presented illustrating these properties

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

convergence results for a coordinate projection method applied to mechanical systems with algebraic constraints the equations of motion of mechanical multibody systems with algebraic constraints are of index 3 and therefore not directly solvable by standard ode or dae methods reducing the index by different

polyconvexity of generalized polynomial type hyperelastic strain energy functions for near incompressibility abstract in this article we investigate several models contained in the literature in the case of near incompressibility based on invariants in terms of polyconvexity and coerciveness inequality which are sufficient to guarantee the existence of a solution these models are due to rivlin and saunders namely the generalized polynomial type elasticity and arruda and boyce the extension to near incompressibility is usually carried out by an additive decomposition of the strain energy into a volume changing and a volume preserving part where the volume changing part depends on the determinant of the deformation gradient and the volume preserving part on the invariants of the unimodular right cauchy green tensor it will be shown that the arruda boyce model satisfies the polyconvexity condition whereas the polynomial type elasticity does not therefore we propose a new class of strain energy functions depending on invariants moreover we focus our attention on the structure of further isotropic strain energy functions

on the stability structure for lattice boltzmann schemes the stability structure for lattice boltzmann schemes has been introduced in banda et al 2006 16 junk and yong 2007 14 to analyze the stability of numerical algorithms the first purpose of this paper is to discuss the stability structure from the perspective of matrix analysis its second goal is to illustrate and apply the results to different classes of lattice boltzmann collision operators in particular we formulate an equivalence condition just recently also reported in yong 2008 18 that guarantees the existence of a pre stability structure it is then illustrated by several examples how this equivalence condition can be effectively employed for the systematic verification and construction of stable collision operators finally we point out some shortcomings of the stability structure approach arising in certain cases

a fast algorithm for the estimation of the equivalent hydraulic conductivity of heterogeneous media fast upscaling of hydraulic conductivity is a recurrent problem in modeling flow through heterogeneous porous media we propose a new renormalization technique it is based on the iterative application of the cardwell and parsons 1945 bounds on elementary groups of cells the combination of the bounds with a heuristic formula allows anisotropy to be taken into account the new technique is tested and compared with other fast techniques among the tested techniques the two most reliable ones are the tensorial renormalization and the new simplified renormalization the numerical efficiency of the simplified renormalization leads us to recommend it when a diagonal tensor of equivalent conductivity is sufficient

scaling of the effective permeability in multifractal porous media abstract the real space renormalization group method is used to calculate analytically the scaling exponents of the effective absolute permeability in multifractal porous media

on the application of multi step integration methods to infinitesimal elastoplasticity this article proposes an implicit algorithm for time integration of the differential algebraic equations of small deformation elastoplasticity in strain space the algorithm employs a two step backwards differentiation formula and a standard operator split procedure second order accuracy and non linear stability are established under appropriate constitutive restrictions the algorithm is implemented for the model of j2 plasticity and numerical simulations are conducted that illustrate its applicability and accuracy

computation in finite strain viscoelasticity finite elements based on the interpretation as differential algebraic equations abstract in this article the interpretation of current non linear finite element calculations applied to constitutive equations of evolutionary type as a system of differential algebraic equations is continued p ellsiepen s hartmann int j numer methods engrg 51 2001 679 this procedure is applied to a model of finite strain viscoelasticity which incorporates a particular model of non linear rate dependence three specific topics are studied firstly we investigate a possible treatment of the interpretation in view of mixed finite elements secondly the application of stiffly accurate diagonally implicit runge kutta methods which yield on element level the same structure as a backward euler based integration step is analysed it is shown that the resulting stress algorithm is reducible to the solution of only three non linear equations at each gauss point one maxwell element lastly the effect with respect to expense and achievable accuracy of a time adaptive procedure is focused which is necessary in the case of different time scales such as relaxation or creep dominated processes

single node second order boundary schemes for the lattice boltzmann method abstract based on our recently developed maxwell iteration for the lattice boltzmann method we propose a class of single node boundary schemes for dirichlet boundary conditions of the navier stokes equations the schemes all have second order accuracy for both straight and curved boundaries the accuracy and stability of two specific schemes are examined through several numerical experiments the results validate the second order accuracy and show that a boundary scheme with a convex combination of distribution functions has better stability

convergence of lattice boltzmann methods for navier stokes flows in periodic and bounded domains combining an asymptotic analysis of the lattice boltzmann method with a stability estimate we are able to prove some convergence results which establish a strict relation to the incompressible navier stokes equation the proof applies to the lattice boltzmann method in the case of periodic domains and for specific bounded domains if the dirichlet boundary condition is realized with the bounce back rule

derivation and analysis of lattice boltzmann schemes for the linearized euler equations we derive lattice boltzmann lbm schemes to solve the linearized euler equations in 1d 2d and 3d with the future goal of coupling them to an lbm scheme for navier stokes equations and a finite volume scheme for linearized euler equations the derivation uses the analytical maxwellian in a bgk model in this way we are able to obtain second order schemes in addition we perform an l 2 stability analysis numerical results validate the approach

seven velocity three dimensional vectorial lattice boltzmann method including various types of approximations to the pressure and two parameterized second order boundary treatments abstract in this paper we present a seven velocity three dimensional d3n7 vectorial lattice boltzmann method lbm including various types of approximations to the pressure and propose a family of two parameterized second order boundary schemes with accuracy independent of the boundary location in order to show the numerical stability of the d3n7 model we construct a symmetrizer to handle the nonlinear approximations to the pressure in the meantime we relate the stability based on the vectorial model to that based on the conventional scalar model through an orthogonal similarity transformation finally two 3 d examples with straight and curved boundaries numerically validate the d3n7 model including linear and nonlinear approximations to the pressure together with the proposed boundary schemes

a structured approach to the construction of stable linear lattice boltzmann collision operator abstract we introduce a structured approach to the construction of linear bgk type collision operators ensuring that the resulting lattice boltzmann methods are stable with respect to a weighted l 2 norm the results hold for particular boundary conditions including periodic bounce back and bounce back with flipping of sign boundary conditions this construction uses the equivalent moment space definition of bgk type collision operators and the notion of stability structures as guiding principle for the choice of the equilibrium moments for those moments influencing the error term only but not the order of consistency the presented structured approach is then applied to the 3d isothermal linearized euler equations with non vanishing background velocity finally convergence results in the strong discrete l norm highlight the suitability of the structured approach introduced in this manuscript

effective saturated hydraulic conductivity of two dimensional random multifractal fields 0 991 p 0 0001 thisrelationship indicates that hkidecreases with increasing long range spatial correlation among the k values in the field furthermore as hki decreases it becomes increasingly dominated by flow channeling this is because high values of k become more and more clustered as p decreases this approach may prove useful for the prediction of hki from generalized dimensions estimated by multifractal analysis of field measurements of k the results may also be applicable to the design of sampling strategies for multiple small scale slug tests at a given resolution citation koirala s r e perfect r w gentry and j w kim 2008 effective saturated hydraulic conductivity of two dimensional random multifractal fields water resour res 44 w08410 doi 10 1029 2007wr006199

consistent integration of the constitutive equations of gurson materials under adiabatic conditions in this paper a consistent integration procedure for the thermoviscoplastic version of the complete gurson model is proposed with adiabatic conditions considered and with the use of the backward euler integration scheme a numerical algorithm implicit in all variables as well as the corresponding algorithmic operator have been developed the proposed algorithm was implemented in a finite element code and its performance is demonstrated with the numerical simulation of different examples

weighted l2 stability of a discrete kinetic approximation for the incompressible navier stokes equations on bounded domains abstract this paper is concerned with the stability of a discrete kinetic approximation with a boundary scheme introduced by the authors in a previous work we prove the weighted l 2 stability of the approximation by using an identity on three point difference schemes for convection equations with the weighted l 2 stability the convergence of the discrete kinetic approximation can be directly established moreover the present stability analysis particularly the identity on three point difference schemes may be adapted to other kinetic methods numerical experiments are conducted to verify our stability results

finite element analysis of internally balanced elastic materials abstract this paper provides a finite element treatment for a generalized hyperelastic theory in which the deformation gradient is subject to the multiplicative two factor decomposition that is commonly used in large strain plasticity the multiplicative decomposition in the present context is motivated by a theory of balanced internal variables one of which is the first factor in the decomposition previous studies have shown how the associated continuum mechanical formulation then leads not only to the stress equations of equilibrium but also to an additional tensor balance equation that serves to determine the individual factors in the decomposition such a theory has been shown to predict loading thresholds associated with the emergence of slip surfaces at grip locations in well posed boundary value problems however previous numerical treatments focused on shooting method procedures that failed to resolve loading plateaus and other key features associated with the emergence of such singular surfaces in the present work we describe a finite element treatment that resolves such previously obscure details additional finite element simulations illustrate new aspects of singular surface emergence in this type of theory including the emergence of singular surfaces in the interior of the computational domain

on the modelling of non linear kinematic hardening at finite strains with application to springback comparison of time integration algorithms the paper discusses the derivation and the numerical implementation of a finite strain material model for non linear kinematic and isotropic hardening the kinematic hardening component represents a continuum extension of the classical rheological model of armstrong frederick kinematic hardening in addition a comparison between several numerical algorithms for the integration of the evolution equations is conducted in particular a new form of the exponential map that preserves the plastic volume and the symmetry of the internal variables as well as two modifications of the backward euler scheme are discussed finally the applicability of the model for springback prediction is demonstrated by performing simulations of the draw bending process and a comparison with experiments the results show an excellent agreement between simulation and experiment copyright 2007 john wiley sons ltd

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