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

continuum approach to computational multiscale modeling of propagating fracture a new approach to two scale modeling of propagating fracture based on computational homogenization fe2 is presented the specific features of the approach are a a continuum setting for representation of the fracture at both scales based on the continuum strong discontinuity approach csda and b the use for the considered non smooth discontinuous problem of the same computational homogenization framework than for classical smooth cases as a key issue the approach retrieves a characteristic length computed at the lower scale which is exported to the upper one and used therein as a regularization parameter for a propagating strong discontinuity kinematics this guarantees the correct transfer of fracture energy between scales and the proper dissipation at the upper scale representative simulations show that the resulting formulation provides consistent results which are objective with respect to size and bias of the upper scale mesh and with respect to the size of the lower scale rve failure cell as well as the capability to model propagating cracks at the upper scale in combination with crack path field and strain injection techniques the continuum character of the approach confers to the formulation a minimal intrusive character with respect to standard procedures for multi scale computational homogenization

topology optimization of multiscale elastoviscoplastic structures in this chapter we take a step further toward the design of multiscale elastoviscoplastic structures using the multiscale design framework discussed in chapter 1 this subject is extremely challenging from both aspects of topology optimization and multiscale modeling first unlike linear designs topology optimization of elastovisoplastic structures encounters instability issues during the iterative solution process and the evaluation of sensitivities is more demanding second the consideration of path dependent plastic behavior at the microscopic scale results in significantly augmented computational burden in terms of computing time and storage requirement when using the fe 2 method

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

axisymmetric pressure boundary loading for finite deformation analysis using p fem follower loads i e loads which depend on the boundary displacements by definition frequently occur in finite deformation boundary value problems restricting to axisymmetrical applications we provide analytical and numerical solutions for a set of problems in compressible neo hookean materials so to serve as benchmark problems for verifying the accuracy and efficiency of various fe methods for follower load applications thereafter the weak formulation for the follower load in 3 d domain is reduced to an axisymmetrical setting and subsequently consistently linearized in the framework of p fems exploiting the blending function mapping techniques the set of axisymmetric benchmark solutions is compared to numerical experiments in which the results obtained by a p fem code are compared to these obtained by a state of the art commercial h fem code and to the exact results these demonstrate the efficiency and accuracy of p fems when applied to problems in finite deformations with follower loads 2006 elsevier b v all rights reserved

bandler kohout subproduct with yager s classes of fuzzy implications the bandler kohout subproduct bks inference mechanism is one of the two established fuzzy relational inference fri mechanisms the other one being zadeh s compositional rule of inference cri both these fris are known to possess many desirable properties it can be seen that many of these desirable properties are due to the rich underlying structure viz the residuated algebra from which the employed operations come in this study we discuss the bks relational inference system with the fuzzy implication interpreted as yager s classes of implications which do not form a residuated structure on 0 1 we show that many of the desirable properties viz interpolativity continuity robustness which are known for the bks with residuated implications are also available under this framework thus expanding the choice of operations available to practitioners note that to the best of the authors knowledge this is the first attempt at studying the suitability of an fri where the operations come from a nonresiduated structure

effective properties of composite materials with periodic microstructure a computational approach abstract this study reviews several problems which are specific of composites with periodic microstructure composed of linear or nonlinear constituents the theoretical background of the method is recalled first two different families of numerical methods are considered to solve the problem the first is based on the finite element method the concept of macroscopic degrees of freedom is presented the implementation of periodicity conditions is discussed a general framework permitting either a strain or stress control is proposed the second numerical method is based on fast fourier transforms it considers first the problem of a homogeneous linear reference material undergoing a nonhomogeneous periodic eigenstrain the solution of this problem is based on the explicit form of the periodic green s function of the reference medium the relative merits of the two methods are compared and several examples are discussed both methods give very comparable results on test examples and their domains of applications appear to be complementary

on generalized modus ponens with multiple rules and a residuated implication we consider a multiple rule generalized modus ponens inference scheme with an interpretation based on compositional rule of inference cri and a residuated implication we show that such a system is equivalent as far as cri is concerned to a system that satisfies the basic requirement for fuzzy reasoning proposed by turksen and tian fuzzy sets and systems 58 1993 3 40 we establish an analogous conclusion for an alternative interpretation due to magrez and smets of generalized modus ponens which we call consequent dilation rule cdr this method is computationally faster than cri but it produces less specific inference results

on transformation strains and uniform fields in multiphase elastic media the effect of local eigenstrain and eigenstress fields or transformation fields on the local strains and stresses is explored in multiphase elastic solids of arbitrary geometry and material symmetry the residual local fields caused by such transformation fields are sought in terms of certain transformation influence functions and transformation concentration factor tensors general properties of these functions and concentration factors and their relation to the analogous mechanical influence functions and concentration factors are established in part with the help of uniform strain fields in multiphase media specific estimates of the transformation concentration factor tensors are evaluated by the self consistent and mori tanaka methods it is found here that although the two methods use different constraint tensors in solutions of the respective dilute problems their estimates of the mechanical thermal and transformation concentration factor tensors and of the overall stiffness of multiphase media have a similar structure proofs that guarantee that these methods comply with the general properties of the transformation influence functions and provide diagonally symmetric estimates of the overall elastic stiffness are given for two phase and multiphase systems consisting of or reinforced by inclusions of similar shape and alignment one of the possible applications of the results in analysis of overall instantaneous properties and local fields in inelastic composite materials is described in the following paper

a new staggered algorithm for thermomechanical coupled problems the authors gratefully acknowledge the financial support of the portuguese foundation for science and technology fct under projects p2020 ptdc ems tec 0702 2014 poci 01 0145 feder 016779 and p2020 ptdc ems tec 6400 2014 poci 01 0145 feder 016876 by ue feder through the program compete 2020 the second author is also grateful to the fct for the postdoctoral grant sfrh bpd 101334 2014

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

checking the coherence and redundancy of fuzzy knowledge bases checking the coherence of a set of rules is an important step in knowledge base validation coherence is also needed in the field of fuzzy systems indeed rules are often used regardless of their semantics and it sometimes leads to sets of rules that make no sense avoiding redundancy is also of interest in real time systems for which the inference engine is time consuming a knowledge base is potentially inconsistent or incoherent if there exists a piece of input data that respects integrity constraints and that leads to logical inconsistency when added to the knowledge base we more particularly consider knowledge bases composed of parallel fuzzy rules then coherence means that the projection on the input variables of the conjunctive combination of the possibility distributions representing the fuzzy rules leaves these variables completely unrestricted i e any value for these variables is possible or at least not more restrictive than integrity constraints fuzzy rule representations can be implication based or conjunction based we show that only implication based models may lead to coherence problems however unlike conjunction based models they allow to design coherence checking processes some conditions that a set of parallel rules has to satisfy in order to avoid inconsistency problems are given for certainty or gradual rules the problem of redundancy which is also of interest for fuzzy knowledge bases validation is addressed for these two kinds of rules

a computational scheme for linear and non linear composites with arbitrary phase contrast a numerical method making use of fast fourier transforms has been proposed in moulinec and suquet 1994 1998 to investigate the effective properties of linear and non linear composites this method is based on an iterative scheme the rate of convergence of which is proportional to the contrast between the phases composites with high contrast typically above 104 or infinite contrast those containing voids or rigid inclusions or highly non linear materials cannot be handled by the method this paper presents two modified schemes the first one is an accelerated scheme for composites with high contrast which extends to elasticity a scheme initially proposed in eyre and milton 1999 its rate of convergence varies as the square root of the contrast the second scheme adequate for composites with infinite contrast is based on an augmented lagrangian method the resulting saddle point problem involves three steps the first step consists of solving a linear elastic problem using the fast fourier transform method in the second step a non linear problem is solved at each individual point in the volume element the third step consists of updating the lagrange multiplier applications of this scheme to rigidly reinforced and to voided composites are shown copyright 2001 john wiley sons ltd

applications of fuzzy relational equations for methods of reasoning in presence of fuzzy data the paper deals with implementation of a general scheme for fuzzy logic inference with the aid of fuzzy relational equations it is shown that antecedents and consequents are related in terms of a fuzzy relation various implementation methods of generalized modus ponens and modus tollens are put into extensive study it is pointed out that fuzzy relational equations form an effective and plausible tool for implementations of reasoning methods with fuzzy premises two examples of fuzzy controllers being a direct application of schemes of approximate reasoning are also discussed

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

on the law of importation x wedge y longrightarrow z equiv x longrightarrow y longrightarrow z in fuzzy logic the law of importation given by the equivalence x lambda y rarr z equiv xrarr y rarr z is a tautology in classical logic in a implications defined by turksen et al the above equivalence is taken as an axiom in this paper we investigate the general form of the law of importation j t x y z j x j y z where t is a t norm and j is a fuzzy implication for the three main classes of fuzzy implications i e r s and ql implications and also for the recently proposed yager s classes of fuzzy implications i e f and g implications we give necessary and sufficient conditions under which the law of importation holds for r s f and g implications in the case of ql implications we investigate some specific families of ql implications also we investigate the general form of the law of importation in the more general setting of uninorms and t operators for the above classes of fuzzy implications following this we propose a novel modified scheme of compositional rule of inference cri inferencing called the hierarchical cri which has some advantages over the classical cri following this we give some sufficient conditions on the operators employed under which the inference obtained from the classical cri and the hierarchical cri become identical highlighting the significant role played by the law of importation

a new 3 d numerical approach to the solution of pdes with optimal accuracy on irregular domains and cartesian meshes abstract a new 3 d numerical approach for the time dependent wave and heat equations as well as for the time independent laplace equation on irregular domains with the dirichlet boundary conditions has been developed trivial cartesian meshes and simple 27 point uniform and nonuniform stencil equations are used for 3 d irregular domains the calculation of the coefficients of the stencil equations is based on the minimization of the local truncation error of the stencil equations and yields the optimal order of accuracy of the new technique very small distances 0 1 h 1 0 9 h where h is the grid size between the grid points of a cartesian mesh and the boundary do not worsen the accuracy of the new technique at similar 27 point stencils the accuracy of the new approach is two orders higher than that for the linear finite elements the numerical results for irregular domains show that at the same number of degrees of freedom the new approach is even much more accurate than the high order up to the fifth order tetrahedral finite elements with much wider stencils the wave and heat equations can be uniformly treated with the new approach the order of the time derivative in these equations does not affect the coefficients of the stencil equations of the semi discrete systems the new approach can be directly applied to other partial differential equations

system of fuzzy relation equations with inf composition complete set of solutions the problem of solvability of a system of equations with inf composition is considered on finite universes equations are expressed using operations of a bl algebra we study complete set of solutions of the respective system in the particular case one equation and in the general case in both cases various conditions of solvability are found and proved we characterize all maximal solutions and prove that under certain conditions each solution of the system an equation is less than or equal to a respective maximal one as a result we are able to characterize the complete set of solutions examples of single equations and their systems are considered and complete sets of solutions are found for each

accelerated staggered coupling schemes for problems of thermoelasticity at finite strains this paper introduces a fully implicit partitioned coupling scheme for problems of thermoelasticity at finite strains utilizing the p version of the finite element method the mechanical and the thermal fields are partitioned into symmetric subproblems where algorithmic decoupling has been obtained by means of an isothermal operator split numerical relaxation methods have been implemented to accelerate the convergence of the algorithm such methods are well known from coupled fluid structure interaction problems leading to highly efficient algorithms having studied the influence of three different strategies polynomial prediction methods numerical relaxation with constant relaxation coefficients its dynamic variant with a residual based relaxation coefficient and a variant of a reduced order model quasi newton method we present several numerical simulations of quasi static problems investigating the performance of accelerated coupling schemes

finitary solvability conditions for systems of fuzzy relation equations in this paper we consider the problem of solving systems of fuzzy relation equations two types of these systems with different compositions are considered and processed simultaneously a new sufficient condition and new solvability criteria are proposed for systems of both types all these conditions are finitary and thus can be easily verified the sufficient condition and criteria of solvability characterize a relationship between a skeleton nxn matrix n is a number of equations and a vector of the right hand side

numerical model reduction with error control in computational homogenization of transient heat flow numerical model reduction nmr is exploited for solving the finite element problem on a representative volume element rve that arises from the computational homogenization of a model problem of transient heat flow since the problem is linear an orthogonal basis is obtained via the classical method of spectral decomposition a symmetrized version of the space time variational format is adopted for estimating the error from the model reduction in i energy norm and in ii given quantities of interest this technique which was recently developed in the context of the non selfadjoint stationary diffusion convection problem is novel in the present context of nmr by considering the discrete unreduced model as exact we are able to obtain guaranteed bounds on the error while using only the reduced basis and with minor computational effort the performance of the error estimates is demonstrated via numerical results where the subscale is modeled in both one and three spatial dimensions

homogenization of elastic viscoplastic composites by the mixed tfa abstract a new homogenization technique based on the transformation field analysis able to determine the overall behavior of viscoplastic heterogeneous materials is proposed this method is derived developing a variational formulation of the compatibility and evolution equations governing two classical elastic viscoplastic models i e perzyna and peric models a representation form for the stress field and the plastic multiplier is defined on the representative volume element rve of the composite material resulting in a significant reduction of the history variables ruling the evolution problem a numerical procedure is developed integrating the evolution equation by a backward euler algorithm and solving the single time step developing a specific form of the predictor corrector technique the accuracy of the proposed homogenization method is assessed through some numerical examples for elastic viscoplastic composites the applications aim to verify the effectiveness of the presented technique in modeling the elastic viscoplastic composite behavior adopting a reduced number of history variables the homogenization results are compared with the ones obtained by nonlinear finite element micromechanical analyses

approximation theory of fuzzy systems based upon genuine many valued implications siso cases it is proved that the single input and single output siso fuzzy systems based upon genuine many valued implications are universal approximators it is shown theoretically that fuzzy control systems based upon genuine many valued implications are equivalent to those based upon t norm implications the general approach to construct fuzzy systems is given it is also shown that defuzzifier based upon center of areas is not appropriate to the fuzzy systems based upon genuine many valued implications

fuzzy inference systems preserving moser navara axioms abstract satisfiability of three naturally proposed axioms which are desirable for fuzzy inference system was discussed by moser and navara in 36 the fuzzy rule base models considered in this study were mainly the mamdani assilian ones and partly also logically motivated implicative fuzzy systems the investigation leads to the fact that often none of these fuzzy systems do satisfy the given axioms simultaneously therefore moser and navara proposed so called conditionally firing rules and proved that the simultaneous satisfaction of the three axioms is feasible under very mild and practically non restrictive conditions note that the inference mechanism tailored to the fuzzy rules in the investigation was the compositional rule of inference abb cri and similarly the concept of conditionally firing rules were stemming from the cri and the mamdani assilian model of a fuzzy rule base for the implicative interpretation of fuzzy rules the original axioms proposed by moser and navara were later on re defined by st pnicka and mandal with the aim to express the meaning of the original axioms initially proposed for the mamdani assilian rules furthermore conditionally firing implicative rules were proposed based on the so called bandler kohout subproduct abb bks inference mechanism and a study similar to the one by moser and navara was undertaken for them the study encompasses the satisfaction of the modified axioms for the use of implicative rules and the bks furthermore some additional results confirming the applicability of the conditionally firing rules satisfying the moser navara axioms are also provided including the universal approximation ability however the solvability criterions for fuzzy relational equations give a strong preference to the usage of the other combinations namely to the combination of cri with the implicative interpretation of fuzzy rules and to the combination of bks with the mamdani assilian interpretation of fuzzy rules therefore also these combinations of fuzzy inference mechanisms and interpretations of fuzzy rules should be investigated with respect to the satisfaction of moser navara axioms the main purpose of this article which extends the short conference contribution 47 by st pnicka is to provide such an investigation jointly with the review on conditionally firing rules and supplementary results

an adaptive sub incremental strategy for the solution of homogenization based multi scale problems abstract in this contribution several schemes for the solution of homogenization based multi scale constitutive problems undergoing finite strains with inelastic material behavior are investigated these schemes are aimed at improving the robustness and efficiency of the newton raphson method in the multilevel finite element ml fem framework an adaptive sub incremental strategy is proposed for the discrete representative volume element rve boundary value problem the procedure is able to ensure the convergence of the solution algorithm in the presence of several sources of non linearity and obtains improved initial guesses for the newton raphson scheme in the ml fem framework the enlargement of the convergence bowl of the newton raphson procedure at the micro scale allows larger macroscopic deformation gradients to be prescribed and significantly reduces the overall computational cost of ml fem analyses the proposed strategy preserves the quadratic rates of asymptotic convergence that characterize the newton raphson scheme at the macroscopic level numerical examples of both micro scale and two scale finite element simulations are presented to demonstrate the improved robustness and efficiency of the solution procedures proposed

entropy elasticity of isotropic rubber like solids at finite strains abstract this paper presents a macroscopic continuum formulation and a numerical analysis of constitutive equations for stress entropy and heat flux describing the thermoelastic behavior of amorphous cross linked polymers above the glass transition temperature in which a specimen typically snap back with rubbery characteristics the introduced coupled thermomechanical functional extends the classical strain energy function proposed by ogden volume changes due to thermal expansion are regarded for a large temperature domain and play a remarkable role in thermoelastic materials the non linear thermoelastic problem is solved within a staggered fractional step method which is based on a two phase isentropic operator split each of the two symmetric sub problems retains the characteristic dissipative structure of the implicit monolithic scheme which consequently results to an unconditionally stable product formula algorithm the numerical analysis side shows in particular the capability of the theoretical framework reproducing the realistic physical stress deformation temperature relations of rubber distinctive attention is paid to the thermoelastic inversion phenomena a remarkable property governing the class of rubber like materials

correct models of fuzzy if then rules are continuous we show that a system of fuzzy if then rules being modeled correctly works as a partially given fuzzy function its behavior is determined by a chosen structure for if then rules which assigns meaning to fuzzy sets in the if and then parts as well as to basic connectives this partial function can be extended to a whole domain of fuzzy sets with the help of the compositional rule of inference which plays a role of a mechanism for computing the dependent functional values we investigate the question whether this function is continuous two new notions are introduced a correct model of fuzzy if then rules in a structure and a continuous model of fuzzy if then rules with respect to given data we prove that correctness of models of fuzzy if then rules is connected with the problem of solvability of the respective system of fuzzy relation equations in this and only this case a model of fuzzy if then rules is continuous as a side result we have established a new criterion of a solvability of a system of fuzzy relation equations with sup composition

fully implicit formulation of elastoplastic homogenization problem for two scale analysis abstract in this study using a virtual work equation a micro macro kinematic relation and a linearized constitutive relation a boundary value problem is fully implicitly formulated to determine perturbed displacement increment fields in elastoplastic unit cells for two scale analysis it is shown that this implicit homogenization problem can be iteratively solved with quadratic convergences by successively updating strain increment fields in unit cells and that the boundary value problem formulated provides a computational algorithm which is versatile for initial setting of strain increment fields the computational algorithm developed is then examined by performing a two scale analysis of a holed plate with an elastoplastic micro structure subjected to tensile loading this demonstrates that the convergence in iteratively solving the implicit homogenization problem strongly depends on the initial setting of strain increment fields in unit cells

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

computational analysis of nonlinear composite structures using the nonuniform transformation field analysis abstract a reduced model for the effective behavior of nonlinear composites such as metal matrix composite materials has been recently proposed by the authors 1 it extends and improves on the transformation field analysis of dvorak 2 by considering nonuniform transformation strains also called plastic modes and is referred to as the nonuniform transformation field analysis the present study is devoted to the implementation of this new homogenized model into a structural computation a brief account on the reduction procedure is given first then the time integration of the model which is required at each integration point of the structural problem is performed by means of an implicit scheme two examples are discussed the response of the homogenized structure is compared to the exact response of the actual heterogeneous structure computed with a very fine mesh it is seen that not only the structural response is accurately captured by the ntfa model but also the local stress field is correctly approximated

time discretization of parabolic problems by the hp version of the discontinuous galerkin finite element method the discontinuous galerkin finite element method dgfem for the time discretization of parabolic problems is analyzed in the context of the hp version of the galerkin method error bounds which are explicit in the time steps as well as in the approximation orders are derived and it is shown that the hp dgfem gives spectral convergence in problems with smooth time dependence in conjunction with geometric time partitions it is proved that the hp dgfem results in exponential rates of convergence for piecewise analytic solutions exhibiting singularities induced by incompatible initial data or piecewise analytic forcing terms for the h version dgfem algebraically graded time partitions are determined that give the optimal algebraic convergence rates a fully discrete hp scheme is discussed exemplarily for the heat equation the use of certain mesh design principles for the spatial discretizations yields exponential rates of convergence in time and space numerical examples confirm the theoretical results

formulation of geometrically non linear problems in the spatial reference frame this paper presents a new formulation for geometrically non linear problems and their numerical treatment by the p version of the finite element method the formulation is characterized by a weak form based on the spatial representation of the equilibrium equations a deformed geometry mapped by the displacement field a natural description for non conservative loads that keeps the symmetry of the equations and a direct non incremental iterative algorithm to solve the equations the paper is concerned only with problems for which the solution is unique i e the load displacement curves are single valued and the strains are small examples are presented 1997 by john wiley sons ltd

entropic thermoelasticity at finite strains aspects of the formulation and numerical implementation abstract this paper presents a formulation of isotropic finite strain thermoelasticity and addresses some aspects of its numerical implementation on the theoretical side a eulerian setting of isotropic thermoelasticity is discussed based on the finger tensor as a strain measure novel aspects are a direct representation of the eulerian thermoelastic moduli in terms of the finger tensor and a rigorous decomposition of the thermoelastic response functions into decoupled volumetric and isochoric contributions based on a multiplicative split of the finger tensor into spherical and unimodular parts an algorithmic procedure for the computation of the stress and thermoelastic moduli based on a representation of the free energy in terms of eigenvalues of the unimodular part of the finger tensor is developed and applied to model problems of strictly entropic and modified entropic thermoelasticity furthermore two algorithms for the solution of the coupled problem are discussed based on operator splits of the global field equations of thermoelasticity the paper concludes with some representative numerical simulations of thermoelastic processes in rubber like materials

a short note on fuzzy relational inference systems this paper is a short note contribution to the topic of fuzzy relational inference systems and the preservation of their desirable properties it addresses the two main fuzzy relational inferences compositional rule of inference cri and the bandler kohout subproduct bk subproduct and their combination with two fundamental fuzzy relational models of fuzzy rule bases namely the mamdani assilian and the implicative models the goal of this short note article is twofold firstly we show that the robustness related to the combination of bk subproduct and implicative fuzzy rule base model was not proven correctly in 24 however we will show that the result itself is still valid and a valid proof will be provided secondly we shortly discuss the preservation of desirable properties of fuzzy inference systems and conclude that neither the above mentioned robustness nor any other computational advantages should automatically lead to a preference of the combinations of cri with mamdani assilian models or of the bk subproduct with the implicative models

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

a new viscoelastic constitutive model for continuous media at finite thermomechanical changes abstract this paper is concerned with the continuum formulation of a fully coupled thermomechanical constitutive model for highly deformable bodies with viscous dissipation the threedimensional material law is applicable to the thermomechanical characterization of elastomeric high polymeric solids in the finite strain domain under varying temperature the description is based on the concept of internal state variables and rational thermodynamics the main goal of the presentation is to develop consistent constitutive equations for the stress entropy and independent internal variables such that the second law of thermodynamics in the form of the clausius duhem inequality issatisfied motivated by the significant difference in bulk and shear response of elastomers the model employs a local decomposition of the deformation into a dilatational and an isochoric part the framework of nonlinear thermoviscoelasticity presented herein is formulated entirely in the reference configuration and provides a sound continuum basis for approximation techniques such as the finite element method copyright 1996 elsevier science ltd

on error controlled numerical model reduction in fe2 analysis of transient heat flow numerical model reduction is exploited for solving the two scale problem that arises from the computational homogenization of a model problem of transient heat flow since the problem is linear an orthogonal basis is obtained via the method of spectral decomposition a key feature is the construction of a symmetrized version of the space time variational format by which it is possible to estimate the error from the model reduction in i energy norm and in ii a given quantity of interest in previous work by the authors this strategy has been applied to the solution of an individual representative volume element problem whereas the error transport to the macroscale problem in the finite element squared fe2 approach was ignored in this paper such transport of error is included in the error estimate it is remarkable that it is still possible to obtain guaranteed bounds on the error as compared to the fully resolved discrete finite element problem while using only the reduced basis and with minor extra computational effort the performance of the error estimates is demonstrated via numerical results whereby the subscale is modeled in three dimensions whereas the macroscale problem is either one or two dimensional

multisurface thermoplasticity for single crystals at large strains in terms of eulerian vector updates this paper presents a formulation of large strain rate independent multisurface thermoplasticity for single crystals and addresses aspects of its numerical implementation 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 key feature of the present paper 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 this observation is intrinsically exploited on the numerical side by formulating a new fully implicit stress update algorithm and the associated consistent elastoplastic moduli in terms of these eulerian vectors the proposed return mapping algorithm treats the possibly redundant constraints of large strain multisurface plasticity for single crystals by means of an active set search furthermore it satisfies in an algorithmically exact way the plastic incompressibility condition in situations of multislip the performance of the proposed formulation is demonstrated for two representative numerical simulations of thermoplastic deformation processes in single crystals with isotropic taylor type hardening

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

on the suitability of the bandler kohout subproduct as an inference mechanism fuzzy relational inference fri systems form an important part of approximate reasoning schemes using fuzzy sets the compositional rule of inference cri which was introduced by zadeh has attracted the most attention so far in this paper we show that the fri scheme that is based on the bandler kohout bk subproduct along with a suitable realization of the fuzzy rules possesses all the important properties that are cited in favor of using cri viz equivalent and reasonable conditions for their solvability their interpolative properties and the preservation of the indistinguishability that may be inherent in the input fuzzy sets moreover we show that under certain conditions the equivalence of first infer then aggregate fita and first aggregate then infer fati inference strategies can be shown for the bk subproduct much like in the case of cri finally by addressing the computational complexity that may exist in the bk subproduct we suggest a hierarchical inferencing scheme thus this paper shows that the bk subproduct based fri is as effective and efficient as the cri itself

monotonicity of siso fuzzy relational inference with an implicative rule base a fuzzy relational inference fri mechanism is appraised based on the different desirable properties it possesses among these properties monotonicity of an fri has not received much attention in this work we investigate the monotonicity of a single input single output fri with an implicative form of the rule base in all the previous works that deal with monotonicity of an fri with the implicative form of rule base the employed fuzzy implications come from a residuated lattice it can be noticed that this rich underlying structure plays a major role in proving the results further we also modify the given monotone rule base this work differs from the previous works in that 1 the fuzzy implications employed in it do not come from any known residuated structure on text 0 1 and 2 the original rule base is employed without any alteration we determine conditions under which monotonicity of an fri where the rule base is modeled by a strict fuzzy implication can be ensured without transforming the original rule base thus the results in this work further augment the case for considering fuzzy implications other than those from the residuated setting to be used in applications

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

monolithic and partitioned coupling schemes for thermo viscoplasticity in this article we investigate a fully thermo mechanically coupled viscoplasticity model in view of various numerical aspects first we develop the entire system of differential algebraic equations resulting from the spatially discretized principle of virtual displacements the principle of virtual temperatures and the evolution equations of the internal variables provided by the constitutive model in the time integration step this system is solved both using a fully monolithic approach based on a backward euler scheme in combination with the multilevel newton algorithm as well as a partitioned approach solving the fully coupled system the latter is treated by means of a combination of a backward euler method and an accelerated gauss seidel multilevel newton scheme to solve the resulting system of algebraic equations within each time integration step additionally we consider a specific treatment of the interpolation between different meshes within the partitioned approach this is shown for p version finite elements based on hierarchical shape functions finally it turns out that the specific constitutive model of small strain thermo viscoplasticity which is based on the decomposition into kinematic hardening and energy storing strains yields a problem adapted stress algorithm this allows to reduce the stress algorithm on gauss point level to the solution of one scalar equation numerical examples serve to elucidate the behavior and properties of the proposed methods

nonuniform transformation field analysis the exact description of the overall behavior of composites with nonlinear dissipative phases requires an infinity of internal variables approximate models involving only a finite number of those can be obtained by considering a decomposition of the microscopic anelastic strain field on a finite set of transformation fields the transformation field analysis of dvorak proc r soc lond a 437 1992 311 corresponds to piecewise uniform transformation fields the present theory considers nonuniform transformation fields comparison with numerical simulations shows the accuracy of the proposed model

p fem for finite deformation powder compaction the simulation of powder compaction problems die compaction and cold isostatic pressing is considered herein by an implicit high order p version finite element method in this class of problems use is made of a finite strain viscoplasticity model with evolution equations for internal variables developed for the highly compressible behavior in powder compaction processes the classical approach of implicit finite elements applies the combination of backward euler integration scheme and the multilevel newton algorithm to solve the system of differential algebraic equations resulting from the space discretized weak formulation by means of p version finite elements this approach requires on gauss point level a robust stress algorithm the challenging investigations are the incorporation of the applied highly non linear viscoplasticity model into a p version finite element formulation using follower load applications several axisymmetric numerical examples show the feasibility and good performance of this p version approach

high order fems for thermo hyperelasticity at finite strains thermo hyperelastic problems at finite strains belong to a category of non linear coupled problems that impose challenges on their numerical treatment we present the weak form for a 1 d coupled stationary thermo hyperelastic system with constant or temperature dependent material properties the coupled system is discretized by a monolithic high order finite element method p fem based on hierarchical shape functions to verify the accuracy and to investigate the convergence rates of the p fem for the non linear coupled problem exact solutions are derived that are compared to the numerical results these demonstrate the accuracy and efficiency of the applied p fems

on locking and robustness in the finite element method a numerical scheme for the approximation of a parameter dependent problem is said to exhibit locking if the accuracy of the approximations deteriorates as the parameter tends to a limiting value a robust numerical scheme for the problem is one that is essentially uniformly convergent for all values of the parameter precise mathematical definitions for these terms are developed their quantitative characterization is given and some general theorems involving locking and robustness are proven a model problem involving heat transfer is analyzed in detail using this mathematical framework and various related computational results are described applications to some different problems involving locking are presented

an analysis of thep version of the finite element method for nearly incompressible materials in this paper we analyze the behavior of the so calledp version of the finite element method when applied to the equations of plane strain linear elasticity we establish optimal rate error estimates that are uniformly valid independent of the value of the poisson ratio v in the interval 0 1 2 this shows that thep versiondoes not exhibit the degeneracy phenomenon which has led to the use of various only partially justified techniques of reduced integration or mixed formulations for more standard finite element schemes and the case of a nearly incompressible material

locking effects in the finite element approximation of plate models we analyze the robustness of various standard finite element schemes for a hierarchy of plate models and obtain asymptotic convergence estimates that are uniform in terms of the thickness d we identify h version schemes that show locking i e for which the asymptotic convergence rate deteriorates as d 0 and also show that the p version is free of locking in order to isolate locking erects from boundary layer erects which also arise as d 0 our analysis is carried out for the periodic case which is free of boundary layers we analyze in detail the lowest model of the hierarchy the well known reissner mindlin model and show that the locking and robustness of finite element schemes for higher models of the hierarchy are essentially identical to the riessner mindlin case