on some classes of almost automorphic functions and applications to fractional differential equations abstract we study in this paper the properties of c n almost automorphic and asymptotically c n almost automorphic functions a new concept with values in a banach space we then give a new result related to the existence and uniqueness of an asymptotically almost automorphic solution of a semilinear fractional differential equation of the form d x t a x t f t x t b x t with t r 0 1 where a generates a family of resolvent family s t and f satisfies some lipschitz conditions

almost automorphic mild solutions to some partial neutral functional differential equations and applications abstract the paper considers the existence and uniqueness of almost automorphic mild solutions to some classes of first order partial neutral functional differential equations sufficient conditions for the existence and uniqueness of almost automorphic mild solutions to the above mentioned equations are obtained as an application a first order boundary value problem arising in control systems is considered

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

multiscale phenomena green s functions the dirichlet to neumann formulation subgrid scale models bubbles and the origins of stabilized methods abstract an approach is developed for deriving variational methods capable of representing multiscale phenomena the ideas are first illustrated on the exterior problem for the helmholtz equation this leads to the well known dirichlet to neumann formulation next a class of subgrid scale models is developed and the relationships to bubble function methods and stabilized methods are established it is shown that both the latter methods are approximate subgrid scale models the identification for stabilized methods leads to an analytical formula for the intrinsic time scale whose origins have been a mystery heretofore

finite calculus formulation for incompressible solids using linear triangles and tetrahedra summary many finite elements exhibit the so called volumetric locking in the analysis of incompressible or quasi incompressible problems in this paper a new approach is taken to overcome this undesirable effect the starting point is a new setting of the governing differential equations using a finite calculus fic formulation the basis of the fic method is the satisfaction of the standard equations for balance of momentum equilibrium of forces and mass conservation in a domain of finite size and retaining higher order terms in the taylor expansions used to express the different terms of the differential equations over the balance domain the modified differential equations contain additional terms which introduce the necessary stability in the equations to overcome the volumetric locking problem the fic approach has been successfully used for deriving stabilized finite element and meshless methods for a wide range of advective diffusive and fluid flow problems the same ideas are applied in this paper to derive a stabilized formulation for static and dynamic finite element analysis of incompressible solids using linear triangles and tetrahedra examples of application of the new stabilized formulation to linear static problems as well as to the semi implicit and explicit 2d and 3d non linear transient dynamic analysis of an impact problem and a bulk forming process are presented copyright 2004 john wiley sons ltd

higher differentiability for solutions of nonhomogeneous elliptic obstacle problems abstract this paper focuses on weak solutions to the following variational inequality a x d u d u d x f p 2 f d u d x for all a w w 1 p w a e in where the vector field a satisfies some growth and ellipticity conditions we derive that the higher differentiability property of the weak solution u is related to the regularity of the assigned obstacle and the nonhomogeneous term f under a suitable integer or fractional differentiability assumption on a x with respect to x

stability and convergence of a class of enhanced strain methods a stability and convergence analysis is presented of a recently proposed variational formulation and finite element method for elasticity which incorporates an enhanced strain field the analysis is carried out for problems posed on polygonal domains in r n the finite element meshes of which are generated by affine maps from a master element the formulation incorporates as a special case the classical method of incompatible modes the problem initially has three variables viz displacement stress and enhanced strain but the stress is later eliminated by imposing a condition of orthogonality with respect to the enhanced strains two other conditions on the choice of finite element spaces ensure that the approximations are stable and convergent some features of nearly incompressible and incompressible problems are also investigated for these cases it is possible to argue that locking will not occur and that the only spurious pressures present are the so called checkerboard modes it is shown th

a variational multiscale discontinuous galerkin formulation for both implicit and explicit dynamic modeling of interfacial fracture abstract a stabilized discontinuous galerkin method is presented for modeling interfacial debonding under dynamic conditions the method s distinctive feature is its treatment of the inelastic gap at the interface as an internal variable that is evolved through a traction separation constitutive model enabling initially perfect adhesion to be captured numerical stability is derived using variational multiscale ideas and comparisons are drawn with both the intrinsic cohesive zone method and hybrid discontinuous galerkin cohesive zone method to expose subtle differences the proposed formulation is applied to model the nonlinear response of a composite unit cell under impact loading both explicit and implicit time integration schemes provide similar accuracy and stability and the critical time step for explicit analyses is only slightly reduced below the value for the continuous galerkin mesh without an interface further studies of mesh refinement and adjustments to the initial elastic interface stiffness in the reference cohesive zone model reveal the improved accuracy of the variational multiscale discontinuous galerkin method on coarser grids

a primal formulation for imposing periodic boundary conditions on conforming and nonconforming meshes abstract a variational multiscale discontinuous galerkin vmdg method is developed for microscale modeling of domains containing conforming and non conforming meshes essentially the product of the applied volume average strain or macro strain and the domain diameter acts as an imposed displacement jump within the vmdg terms hence the method is suitable for modeling deformation of both block and truly self periodic representative volume elements rves the primal displacement field and macro strain are the only unknowns because the method eliminates the lagrange multiplier lm enforcement of the kinematic constraint rigorous derivation of the method provides a framework to accommodate either the macro stress or macro strain as the driver of the microscale boundary value problem the method is developed first for finite deformations and then specialized to small deformation kinematics algorithmic modifications to the method are also studied for their effects on tangent symmetry and convergence rate the results from numerical studies for isotropic and anisotropic materials show that the proposed method is robust accurate stable and variationally consistent for modeling complicated conforming and nonconforming rves

composition of pseudo almost automorphic and asymptotically almost automorphic functions this paper is concerned with pseudo almost automorphic functions which are more general and complicated than pseudo almost periodic functions and asymptotically almost automorphic functions new results concerning the composition of pseudo almost automorphic functions are established

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

mixed stabilized finite element methods in nonlinear solid mechanics part i formulation abstract this paper exploits the concept of stabilized finite element methods to formulate stable mixed stress displacement and strain displacement finite elements for the solution of nonlinear solid mechanics problems the different assumptions and approximations used to derive the methods are exposed the proposed procedure is very general applicable to 2d and 3d problems implementation and computational aspects are also discussed showing that a robust application of the proposed formulation is feasible numerical examples show that the results obtained compare favorably with those obtained with the corresponding irreducible formulation

a relationship between stabilized finite element methods and the galerkin method with bubble functions abstract a relation between stabilized finite element methods and the galerkin method employing interpolations with bubble functions is established for the advective diffusive model and for the linearized compressible navier stokes equations the bubble functions are shown to help in stabilizing the advective operator without recourse to upwinding or any other numerical strategy in particular for the advective diffusive model the galerkin method employing piecewise linears with bubble functions is shown to be equivalent to the streamline upwind petrov galerkin supg method in the diffusive limit

regularized solutions for abstract volterra equations abstract we introduce a two kernel dependent family of strong continuous operators defined in a banach space which allows us to consider in an unified treatment the notions of among others c 0 semigroups of operators cosine families n times integrated semigroups resolvent families and k generalized solutions the results are applied to the study of existence and uniqueness of solutions for the volterra equation of convolution type u f a au in the case a is not necessarily densely defined examples for equations defined in l p spaces are also given

bounded mild solutions of perturbed volterra equations with infinite delay abstract we study existence and regularity of bounded mild solutions on the real line to perturbed integral equations with infinite delay in the space of almost periodic functions in the bohr sense the space of compact almost automorphic functions the space of almost automorphic functions and the space of asymptotically almost automorphic functions

aspects of the formulation and finite element implementation of large strain isotropic elasticity the paper presents a formulation of isotropic large strain elasticity and addresses some computational aspects of its finite element implementation on the theoretical side an eulerian setting of isotropic elasticity is discussed exclusively in terms of the finger tensor as a strain measure noval aspects are a direct representation of the eulerian elastic moduli in terms of the finger tensor and their rigorous decomposition into decoupled volumetric and isochoric contributions based on a multiplicative split of the finger tensor into spherical and unimodular parts the isochoric stress response is formulated in terms of the eigenvalues of the unimodular part of the finger tensor a constitutive algorithm for the computation of the stresses and tangent moduli for plane problems is developed and applied to a model problem of rubber elasticity on the computational side the implementation of the constitutive model in three possible finite element formulations is discussed after pointing out algorithmic techniques for the treatment of incompressible elasticity several numerical simulations are presented which show the performance of the proposed constitutive algorithm and the convergence behaviour of the different finite element fomulations for compressible and incompressible elasticity

a stabilized mixed finite element method for finite elasticity formulation for linear displacement and pressure interpolation abstract a stabilized mixed finite element method for finite elasticity is presented the method circumvents the fulfillment of the ladyzenskaya babuska brezzi condition by adding mesh dependent terms which are functions of the residuals of the euler lagrange equations to the usual galerkin method the weak form and the linearized weak form are presented in terms of the reference and current configuration numerical experiments using a tetrahedral element with linear shape functions for the displacements and for the pressure show that the method successfully yields a stabilized element

a new boundary element technique without domain integrals for elastoplastic solids summary a simple idea is proposed to solve boundary value problems for elastoplastic solids via boundary elements namely to use the green s functions corresponding to both the loading and unloading branches of the tangent constitutive operator to solve for plastic and elastic regions respectively in this way domain integrals are completely avoided in the boundary integral equations though a discretization of the region where plastic flow occurs still remains necessary to account for the inhomogeneity of plastic deformation the elastoplastic analysis reduces in essence to a straightforward adaptation of techniques valid for anisotropic linear elastic constitutive equations the loading branch of the elastoplastic constitutive operator may be viewed formally as a type of anisotropic elastic law numerical examples using j2 flow theory with linear hardening demonstrate that the proposed method retains all the advantages related to boundary element formulations is stable and performs well the method presented is for simplicity developed for the associative flow rule however a full derivation of green s function and boundary integral equations is also given for the general case of non associative flow rule it is shown that in the non associative case a domain integral unavoidably arises in the formulation copyright 2005 john wiley sons ltd

size effect and localization in j2 plasticity this paper studies the phenomenon of structural size effect and strain localization in j2 plasticity size effect is here understood as the change in the response of a given structure when the spatial dimensions are scaled up or down while the geometry and other relevant properties of the structure are preserved the work exploits the advantages of the mixed displacement pressure formulation in incompressible or quasi incompressible situations elasto j2 plastic constitutive behaviour with regularized softening is considered stability issues are discussed to ensure existence and uniqueness of the solution of the corresponding discrete finite element formulation numerical examples show that the formulation derived is able to solve a wide range of structural scales including real life engineering applications the results obtained do not suffer from spurious mesh dependence furthermore the formulation includes the classical theories of perfect plasticity and linear fracture mechanics as limit cases

a finite element formulation for the stokes problem allowing equal velocity pressure interpolation abstract in this paper we study a variational formulation of the stokes problem that accommodates the use of equal velocity pressure finite element interpolations the motivation of this method relies on the analysis of a class of fractional step methods for the navier stokes equations for which it is known that equal interpolations yield good numerical results the reason for this turns out to be the difference between two discrete laplacian operators computed in a different manner the formulation of the stokes problem considered here aims to reproduce this effect from the analysis of the finite element approximation of the problem we obtain stability and optimal error estimates using velocity pressure interpolations satisfying a compatibility condition much weaker than the inf sup condition of the standard formulation in particular this condition is fulfilled by the most common equal order interpolations

the finite cell method for nearly incompressible finite strain plasticity problems with complex geometries abstract in this paper the performance of the finite cell method is studied for nearly incompressible finite strain plasticity problems the finite cell method is a combination of the fictitious domain approach with the high order finite element method it provides easy mesh generation capabilities for highly complex geometries moreover this method offers high convergence rates the possibility to overcome locking and robustness against high mesh distortions the performance of this method is numerically investigated based on computations of benchmark and applied problems the results are also verified with the h and p version finite element method it is demonstrated that the finite cell method is an appropriate simulation tool for large plastic deformations of structures with complex geometries and microstructured materials such as porous and cellular metals that are made up of ductile materials obeying nearly incompressible j 2 theory of plasticity

improved robustness for nearly incompressible large deformation meshfree simulations on delaunay tessellations abstract a displacement based galerkin meshfree method for large deformation analysis of nearly incompressible elastic solids is presented nodal discretization of the domain is defined by a delaunay tessellation three node triangles and four node tetrahedra which is used to form the meshfree basis functions and to numerically integrate the weak form integrals in the proposed approach for nearly incompressible solids a volume averaged nodal projection operator is constructed to average the dilatational constraint at a node from the displacement field of surrounding nodes the nodal dilatational constraint is then projected onto the linear approximation space the displacement field is constructed on the linear space and enriched with bubble like meshfree basis functions for stability the new procedure leads to a displacement based formulation that is similar to f bar methodologies in finite elements and isogeometric analysis we adopt maximum entropy meshfree basis functions and the performance of the meshfree method is demonstrated on benchmark problems using structured and unstructured background meshes in two and three dimensions the nonlinear simulations reveal that the proposed methodology provides improved robustness for nearly incompressible large deformation analysis on delaunay meshes

local kinetic energy and singularities of the incompressible navier stokes equations abstract we study the partial regularity problem of the incompressible navier stokes equations a reverse holder inequality of velocity gradient with increasing support is obtained under the condition that a scaled functional corresponding the local kinetic energy is uniformly bounded as an application we give a new bound for the hausdorff dimension and the minkowski dimension of singular set when weak solutions v belong to l 0 t l 3 w r 3 where l 3 w r 3 denotes the standard weak lebesgue space

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

implicit finite incompressible elastodynamics with linear finite elements a stabilized method in rate form abstract we propose a stabilization method for linear tetrahedral finite elements suitable for the implicit time integration of the equations of nearly and fully incompressible nonlinear elastodynamics in particular we derive and discuss a generalized framework for stabilization and implicit time integration that can comprehensively be applied to the class of all isotropic hyperelastic models in this sense the presented development can be considered an important extension and complement to the stabilization approach proposed by the authors in previous work which was instead focused on explicit time integration and simple neo hookean models for nearly incompressible elasticity with the goal of computational efficiency we also present a two step block gauss seidel strategy for the time update of displacements velocities and pressures specifically a mixed system of equations for the velocity and pressure is updated implicitly in a first stage and the displacements are updated explicitly in a second stage the proposed mixed formulation is then embedded in newton type strategies for the nonlinear solution of the equations of motion various implicit time integration strategies are considered and particularly we focus on high frequency dissipation time integrators which are preferable in transient mechanics applications an extensive set of numerical computations with linear tetrahedral elements is presented to demonstrate the performance of the proposed approach

a stabilized nodally integrated tetrahedral a stabilized nodally integrated linear tetrahedral is formulated and analysed it is well known that linear tetrahedral elements perform poorly in problems with plasticity nearly incompressible materials and acute bending for a variety of reasons low order tetrahedral elements are preferable to quadratic tetrahedral elements particularly for nonlinear problems but the severe locking problems of tetrahedrals have forced analysts to employ hexahedral formulations for most nonlinear problems on the other hand automatic mesh generation is often not feasible for building many 3d hexahedral meshes a stabilized nodally integrated linear tetrahedral is developed and shown to perform very well in problems with plasticity nearly incompressible materials and acute bending the formulation is analytically and numerically shown to be stable and optimally convergent for the compressible case provided sufficient smoothness of the exact solution u c2 h1 3 future work may extend the formulation to the incompressible regime and relax the regularity requirements nonetheless the results demonstrate that the method is not susceptible to locking and performs quite well in several standard linear and nonlinear benchmarks published in 2006 by john wiley sons ltd

mixed linear linear simplicial elements for incompressible elasticity and plasticity this paper exploits the concept of orthogonal sub grid scales to stabilize the behaviour of mixed linear linear simplicial elements triangles and tetrahedra in incompressible or nearly incompressible situations both incompressible elastic and j2 plastic constitutive behaviours have been considered the different assumptions and approximations used to derive the method are exposed implementation and computational aspects are also discussed showing that a robust application of the proposed formulation is feasible numerical examples show that the elements derived are free of volumetric locking and spurious oscillations of the pressure and that the results obtained compare favourably with those obtained with the q1p0 quadrilateral

on the orthogonal subgrid scale pressure stabilization of finite deformation j2 plasticity the use of stabilization methods is becoming an increasingly well accepted technique due to their success in dealing with numerous numerical pathologies that arise in a variety of applications in computational mechanics in this paper a multiscale finite element method technique to deal with pressure stabilization of nearly incompressibility problems in nonlinear solid mechanics at finite deformations is presented a j2 flow theory plasticity model at finite deformations is considered a mixed formulation involving pressure and displacement fields is used as starting point within the finite element discretization setting continuous linear interpolation for both fields is considered to overcome the babuska brezzi stability condition a multiscale stabilization method based on the orthogonal subgrid scale osgs technique is introduced a suitable nonlinear expression of the stabilization parameter is proposed the main advantage of the method is the possibility of using linear triangular or tetrahedral finite elements which are easy to generate and therefore very convenient for practical industrial applications numerical results obtained using the osgs stabilization technique are compared with results provided by the p1 standard galerkin displacements linear triangular tetrahedral element p1 p1 standard mixed linear displacements linear pressure triangular tetrahedral element and q1 p0 mixed bilinear trilinear displacements constant pressure quadrilateral hexahedral element for 2d 3d nearly incompressible problems in the context of a nonlinear finite deformation j2 plasticity model

stability and comparison of different linear tetrahedral formulations for nearly incompressible explicit dynamic applications this papers summarizes two linear tetrahedral fe formulations that have been recently proposed to overcome volumetric locking in nearly incompressible explicit dynamic applications in particular the average nodal pressure anp technique described by bonet and burton communications in numerical methods in engineering 1998 14 437 449 is briefly reviewed in addition the split based formulation proposed by zienkiewicz et al international journal for numerical methods in engineering 1998 43 565 583 is described here in terms of a time integration of the nodal jacobian this will make it simple to compare both techniques and will enable a new combined method to be presented the paper will then discuss the stability constraints that each technique places on the timestep size a von neuman stability analysis on simple 1 d uniform meshes will show that the anp element permits the use of much larger timesteps than the split based formulations finally numerical examples corroborating in 3 d this analytical conclusions will be presented copyright 2001 john wiley sons ltd

a mixed enhanced formulation tetrahedral finite elements this paper considers the solution of problems in three dimensional solid mechanics using tetrahedral finite elements a formulation based on a mixed enhanced treatment involving displacement pressure and volume effects is presented the displacement and pressure are used as nodal quantities while volume effects and enhanced modes belong to individual elements both small and finite deformation problems are addressed and sample solutions are given to illustrate the performance of the formulation copyright 2000 john wiley sons ltd

continuum damage model for orthotropic materials application to masonry this paper contributes to the formulation of continuum damage models for orthotropic materials under plane stress conditions two stress transformation tensors related to tensile and compressive stress states respectively are used to establish a one to one mapping relationship between the orthotropic behaviour and an auxiliary model this allows the consideration of two individual damage criteria according to different failure mechanisms i e cracking and crushing the constitutive model adopted in the mapped space makes use of two scalar variables which monitor the local damage under tension and compression respectively the model affords the simulation of orthotropic induced damage while also accounting for unilateral effects thanks to a stress tensor split into tensile and compressive contributions the fundamentals of the method are presented together with the procedure utilized to adjust the model in order to study the mechanical behaviour of masonry material the validation of the model is carried out by means of comparisons with experimental results on different types of orthotropic masonry at the material level

stabilization of bi linear mixed finite elements for tetrahedra with enhanced interpolation using volume and area bubble functions in order to overcome the oscillatory effects of the mixed bi linear galerkin formulation for tetrahedral elements a stabilization approach is presented to this end the mixed method of incompatible modes and the mixed method of enhanced strains are reformulated thus giving both the interpretation of a mixed finite element method with stabilization terms for non linear problems these are non linearly dependent on the current deformation state and therefore are replaced by linearly dependent stabilization terms the approach becomes most attractive for the numerical implementation since the use of quantities related to the previous newton iteration step typically arising for mixed enhanced elements is completely avoided the stabilization matrices for the mixed method of incompatible modes and the mixed method of enhanced strains are obtained with volume and area bubble functions various numerical examples are presented which illustrate successfully the stabilization effect for bi linear tetrahedral elements copyright 2007 john wiley sons ltd

almost automorphic mild solutions to fractional differential equations abstract we introduce the concept of resolvent families to prove the existence of almost automorphic mild solutions to the differential equation d t u t a u t t n f t 1 2 n z considered in a banach space x where f r x is almost automorphic we also prove the existence and uniqueness of an almost automorphic mild solution of the semilinear equation d t u t a u t f t u t 1 2 assuming f t x is almost automorphic in t for each x x satisfies a global lipschitz condition and takes values on x finally we prove also the existence and uniqueness of an almost automorphic mild solution of the semilinear equation d t u t a u t f t u t u t 1 2 under analogous conditions as in the previous case

a geometric structure preserving discretization scheme for incompressible linearized elasticity abstract in this paper we present a geometric discretization scheme for incompressible linearized elasticity we use ideas from discrete exterior calculus dec to write the action for a discretized elastic body modeled by a simplicial complex after characterizing the configuration manifold of volume preserving discrete deformations we use hamilton s principle on this configuration manifold the discrete euler lagrange equations are obtained without using lagrange multipliers the main difference between our approach and the mixed finite element formulations is that we simultaneously use three different discrete spaces for the displacement field we explicitly derive the governing equations for the two dimensional case where the discrete spaces for the displacement field are constructed by p 1 polynomials over primal meshes for incompressibility constraint p 0 polynomials over dual meshes for the kinetic energy and p 1 polynomials over support volumes for the elastic energy and the discrete space of the pressure field is constructed by p 0 polynomials over primal meshes we test the efficiency and robustness of this geometric scheme using some numerical examples in particular we do not see any volume locking and or checkerboarding of pressure in our numerical examples this suggests that our choice of discrete solution spaces is compatible

volume averaged nodal projection method for nearly incompressible elasticity using meshfree and bubble basis functions we present a displacement based galerkin meshfree method for the analysis of nearly incompressible linear elastic solids where low order simplicial tessellations i e 3 node triangular or 4 node tetrahedral meshes are used as a background structure for numerical integration of the weak form integrals and to get the nodal information for the computation of the meshfree basis functions in this approach a volume averaged nodal projection operator is constructed to project the dilatational strain into an approximation space of equal or lower order than the approximation space for the displacement field resulting in a locking free method the stability of the method is provided via bubble like basis functions because the notion of an element or cell is not present in the computation of the meshfree basis functions such low order tessellations can be used regardless of the order of the approximation spaces desired first and second order meshfree basis functions are chosen as a particular case in the proposed method numerical examples are provided in two and three dimensions to demonstrate the robustness of the method its ability to avoid volumetric locking in the nearly incompressible regime and its improved performance when compared to the mini finite element scheme on the simplicial mesh

reduction of excessive energy in the four noded membrane quadrilateral element part ii near incompressibility and j2 plasticity abstract the elemental formulation presented in part i of this study e paraskevopoulos d talaslidis reduction of excessive energy in the four noded membrane quadrilateral element part i linear theory compressible materials comput methods appl mech engrg 194 2005 3771 3796 is extended in a straightforward manner to problems with nearly incompressible materials and to j 2 plastic flow problems sources of excessive energy resulting from the incompressibility constraint as well as the coupling between the deviatoric components of strain are examined and conclusions are drawn concerning the selection of appropriate approximations for the field variables a modified version of the hu washizu principle is employed that utilizes the orthogonality between deviatoric and volumetric terms and incorporates part of the plane strain conditions furthermore satisfaction of the patch test is analytically verified in deriving the weak form of the equations governing the j 2 plasticity problem attention is focused on a straightforward extension of the linear problem without reference to additional postulates in case of j 2 plasticity the current formulation incorporates an important modification that leads to further simplifications the continuous linear functions employed for the approximations are replaced by the heaviside function finally results of numerical examples and comparisons with other formulations are presented

mixed stabilized finite element methods in nonlinear solid mechanics part ii strain localization this paper deals with the question of strain localization associated with materials which exhibit softening due to tensile straining a standard local isotropic rankine damage model with strain softening is used as exemplary constitutive model both the irreducible and mixed forms of the problem are examined and stability and solvability conditions are discussed lack of uniqueness and convergence difficulties related to the strong material nonlinearities involved are also treated from this analysis the issue of local discretization error in the pre localization regime is deemed as the main difficulty to be overcome in the discrete problem focus is placed on low order finite elements with continuous strain and displacement fields triangular p1p1 and quadrilateral q1q1 although the presented approach is very general numerical examples show that the resulting procedure is remarkably robust it does not require the use of auxiliary tracking techniques and the results obtained do not suffer from spurious mesh bias dependence

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

benchmarking on bifurcation and localization in j2 plasticity for plane stress and plane strain conditions this paper studies the phenomenon of strain bifurcation and localization in j2 plasticity under plane stress and plane strain conditions necessary conditions for the outcome of bifurcation localization stress boundedness and decohesion are analytically established it is shown that the explicit consideration of these conditions allows for the determination of localization angles in certain situations of interest that can be used to conduct benchmark tests on finite element formulations the relative merits of irreducible stabilized mixed and displacement and or strain enhanced formulations are discussed numerical examples show that the mixed displacement pressure formulation is to be preferred to the standard irreducible schemes in order to predict correct failure mechanisms with localized patterns of plastic deformation mixed elements are shown to be practically free from mesh directional bias dependence

virtual bubbles and galerkin least squares type methods ga l s abstract the equivalence between stabilized finite element methods or galerkin least squares tyoe methods ga l s and the standard galerkin method with bubble functions is established in an abstract framework the results are applicable to various finite element spaces including high order elements and applications to the advective diffusive model and to the stokes problem are presented illustrating the potential of the abstract theory introduced here

on multiplicative perturbation of integral resolvent families abstract in this paper we study multiplicative perturbations for the generator of a strongly continuous integral resolvent family of bounded linear operators defined on a banach space x assuming that a t is a creep function which satisfies a 0 0 we prove that if a a generates an integral resolvent then a i b a also generates an integral resolvent for all b b x z where z belongs to a class of admissible banach spaces in special instances of a t the space z is proved to be characterized by an extended class of favard spaces

a triangular finite element with local remeshing for the large strain analysis of axisymmetric solids in this work a three node triangular finite element with two degrees of freedom per node for the large strain elasto plastic analysis of axisymmetric solids is presented the formulation resorts to the adjacent elements to obtain a quadratic interpolation of the geometry over a patch of four elements from which an average deformation gradient is defined thus the element formulation falls within the framework of assumed strain elements or more precisely of f bar type formulations the in plane behavior of the element is similar to the linear strain triangle but without the drawbacks of the quadratic triangle e g contact or distortion sensitivity the element does not suffer of volumetric locking in problems with isochoric plastic flow and the implementation is simple it has been implemented in a finite element code with explicit time integration of the momentum equations and tools that allow the simulation of industrial processes the widely accepted multiplicative decomposition of the deformation gradient in elastic and plastic components is adopted here an isotropic material with non linear isotropic hardening has been considered two versions of the element have been implemented based on a total and an updated lagrangian formulation respectively some approximations have been considered in the latter formulation aimed to reduce the number of operations in order to increase numerical efficiency to consider bulk forming with large geometric changes an automatic local remeshing strategy has been developed several examples are considered to assess the element performance with and without remeshing

a velocity stress mixed stabilized nodal finite element for elastodynamics analysis and computations with strongly and weakly enforced boundary conditions abstract a new nodal mixed finite element is proposed for the simulation of linear elastodynamics and wave propagation problems in time domain our method is based on equal order interpolation discrete spaces for both the velocity or displacement and stress or strain tensor variables the mixed form is derived using either the velocity stress or velocity strain pair of unknowns the latter being instrumental in extensions of the method to nonlinear mechanics the proposed approach works equally well on hexahedral or tetrahedral grids and for this reason it is suitable for time domain engineering applications in complex geometry the peculiarity of the proposed approach is the use of the rate form of the stress update equation which yields a set of governing equations with the structure of a non dissipative space time friedrichs system we complement standard traction boundary conditions for the stress with strongly and weakly enforced boundary conditions for the velocity or displacement weakly enforced boundary conditions are particularly suitable when considering complex geometrical shapes because they do not require dedicated data structures for the imposition of the boundary degrees of freedom but rather they utilize the structure of the variational formulation we also show how the framework of weakly enforced boundary conditions can be used to develop variational forms for multi domain simulations of heterogeneous media a complete analysis including stability and convergence proofs is included in the case of a space time variational approach a series of computational tests are used to demonstrate and verify the performance of the proposed approach

compact almost automorphic solutions to integral equations with infinite delay abstract given a l 1 r and the generator a of an l 1 integrable resolvent family of linear bounded operators defined on a banach space x we prove the existence of compact almost automorphic solutions of the semilinear integral equation u t t a t s a u s f s u s d s for each f r x x compact almost automorphic in t for each x x and satisfying lipschitz and holder type conditions in the scalar linear case we prove that a l 1 r positive nonincreasing and log convex is sufficient to obtain the existence of compact almost automorphic solutions

almost automorphic solutions for abstract functional differential equations for abstract linear functional differential equations with an almost automorphic forcing term we establish a result on the existence of almost automorphic solutions which extends the classical theorem due to massera on the existence of periodic solutions for linear periodic ordinary differential equations

stabilized finite element approximation of transient incompressible flows using orthogonal subscales abstract in this paper we present a stabilized finite element method to solve the transient navier stokes equations based on the decomposition of the unknowns into resolvable and subgrid scales the latter are approximately accounted for so as to end up with a stable finite element problem which in particular allows to deal with convection dominated flows and the use of equal velocity pressure interpolations three main issues are addressed the first is a method to estimate the behavior of the stabilization parameters based on a fourier analysis of the problem for the subscales secondly the way to deal with transient problems discretized using a finite difference scheme is discussed finally the treatment of the nonlinear term is also analyzed a very important feature of this work is that the subgrid scales are taken as orthogonal to the finite element space in the transient case this simplifies considerably the numerical scheme

almost periodic and pseudo almost periodic solutions to fractional differential and integro differential equations abstract we study the existence of almost periodic resp pseudo almost periodic mild solutions for fractional differential and integro differential equations in the case when the forcing term belongs to the class of stepanov almost resp stepanov like pseudo almost periodic functions

stabilized finite element method for the transient navier stokes equations based on a pressure gradient projection abstract in this paper we present a stabilized finite element formulation for the transient incompressible navier stokes equations the main idea is to introduce as a new unknown of the problem the projection of the pressure gradient onto the velocity space and to add to the incompresibility equation the difference between the laplacian of the pressure and the divergence of this new vector field this leads to a pressure stabilization effect that allows the use of equal interpolation for both velocities and pressures in the case of the transient equations we consider the possibility of treating the pressure gradient projection either implicitly or explicity in the first case the number of unknowns of the problem is substantially increased with respect to the standard galerkin formulation nevertheless iterative techniques may be used in order to uncouple the calculation of the pressure gradient projection from the rest of unknowns velocity and pressure when this vector field is treated explicitly the increment of computational cost of the stabilized formulation with respect to the galerkin method is very low we provide a stability estimate for the case of the simple backward euler time integration scheme for both the implicit and the explicit treatment of the pressure gradient projection

a stabilized formulation for incompressible elasticity using linear displacement and pressure interpolations in this paper a stabilized finite element method to deal with incompressibility in solid mechanics is presented a mixed formulation involving pressure and displacement fields is used and a continuous linear interpolation is considered for both fields to overcome the babuska brezzi condition a stabilization technique based on the orthogonal sub scale method is introduced the main advantage of the method is the possibility of using linear triangular or tetrahedral finite elements which are easy to generate for real industrial applications results are compared with standard galerkin and q1p0 mixed formulations for nearly incompressible problems in the context of linear elasticity

stabilization of incompressibility and convection through orthogonal sub scales in finite element methods two apparently different forms of dealing with the numerical instability due to the incompressibility constraint of the stokes problem are analyzed in this paper the first of them is the stabilization through the pressure gradient projection which consists of adding a certain least squares form of the difference between the pressure gradient and its l2 projection onto the discrete velocity space in the variational equations of the problem the second is a sub grid scale method whose stabilization effect is very similar to that of the galerkin least squares gls method for the stokes problem it is shown here that the first method can also be recast in the framework of sub grid scale methods with a particular choice for the space of sub scales this leads to a new stabilization procedure whose applicability to stabilize convection is also studied in this paper

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

triangles and tetrahedra in explicit dynamic codes for solids explicit dynamic codes which are used currently for the study of plastic deformations in impact or with some modification for metal forming suffer two serious limitations first only quadrilateral or hexahedral linear elements can be used thus limiting the possibilities of adaptive refinement and adaptive meshing second even with the use of such elements special devices such as reduced integration must be introduced to avoid locking and reduce costs these necessitate complex hour glass control mending type procedures the main difficulties are those due to the need of treatment of almost incompressible deformation modes recently similar difficulties have been overcome in the context of fluid dynamics soil dynamics and we show here how the processes introduced there can be adopted effectively to the present problem thus allowing an almost unrestricted choice of element interpolations 1998 john wiley sons ltd

a mixed three field fe formulation for stress accurate analysis including the incompressible limit abstract in previous works the authors have presented the stabilized mixed displacement pressure formulation to deal with the incompressibility constraint more recently the authors have derived stable mixed stress displacement formulations using linear linear interpolations to enhance stress accuracy in both linear and non linear problems in both cases the variational multi scale vms stabilization technique and in particular the orthogonal subgrid scale oss method allows the use of linear linear interpolations for triangular and tetrahedral elements bypassing the strictness of the inf sup condition on the choice of the interpolation spaces these stabilization procedures lead to discrete problems which are fully stable free of volumetric locking or stress oscillations this work exploits the concept of mixed finite element methods to formulate stable displacement stress pressure finite elements aimed for the solution of nonlinear problems for both solid and fluid finite element fe analyses the final goal is to design a finite element technology able to tackle simultaneously problems which may involve isochoric behavior preserve the original volume of the strain field together with high degree of accuracy of the stress field these two features are crucial in nonlinear solid and fluid mechanics as used in most numerical simulations of industrial manufacturing processes numerical benchmarks show that the results obtained compare very favorably with those obtained with the corresponding mixed displacement pressure formulation