finite element formulation for modeling nonlinear viscoelastic elastomers nonlinear viscoelastic response of reinforced elastomers is modeled using a three dimensional mixed finite element method with a nonlocal pressure field a general second order unconditionally stable exponential integrator based on a diagonal pade approximation is developed and the bergstrom boyce nonlinear viscoelastic law is employed as a prototype model an implicit finite element scheme with consistent linearization is used and the novel integrator is successfully implemented finally several viscoelastic examples including a study of the unit cell for a solid propellant are solved to demonstrate the computational algorithm and relevant underlying physics

forced vibrations of superquadratic hamiltonian systems on etudie l existence des solutions t periodiques ter t 0 du systeme hamiltonien suivant z gh z f t ou g est la matrice asymetrique standard

a discrete differential sequence for elasticity based upon continuous displacements the present paper introduces a mixed stress displacement method for linear elasticity as an extension of the work performed by christiansen numer math 119 2011 pp 613 640 for computational relativity moreover we establish self adjointness in a special sense and perform numerical simulations to assess the relevance of the method including comparison with the recent tdnns a sinwel a new family of mixed finite elements for elasticity ph d thesis linz university 2009 a pechstein and j schoberl math models methods appl sci 21 2011 pp 1761 1782 mixed formulation extensions to higher order approximations and nonlinear elasticity are also introduced

iteration inequalities of the maslov type index theory with applications abstract in this paper by using the index theory introduced by y long in 1999 pacific j math 187 113 149 in particular the splitting numbers maslov type mean index and the homotopy component of symplectic matrix we establish various inequalities of the maslov type index theory for iterations of symplectic paths starting from the identity as an application these results are used to study rabinowitz conjecture on the prescribed minimal period solution problem of nonlinear hamiltonian systems

the minimal period problem of periodic solutions for autonomous superquadratic second order hamiltonian systems abstract in this paper we study the existence of periodic solutions with prescribed minimal period for superquadratic autonomous second order hamiltonian systems defined on r n with no convexity assumptions we use the direct variational approach for this problem on a w 1 2 space of even functions and prove new iteration inequalities on morse indices using these tools and the saddle point theorem we obtain results under precisely rabinowitz superquadratic condition on potential functions we show that for every t 0 the above mentioned system possesses a t periodic even solution with minimal period not smaller than t n 2

analysis of mixed finite elements methods for the stokes problem a unified approach we develop a method for the analysis of mixed finite element methods for the stokes problem in the velocity pressure formulation a technical macroelement condition which is sufficient for the classical babuska brezzi inequality to be valid is introduced using this condition we are able to verify the stability and optimal order of convergence of several known mixed finite element methods

error analysis of some finite element methods for the stokes problem we prove the optimal order of convergence for some two dimensional finite element methods for the stokes equations first we consider methods of the taylor hood type the triangular p3 p2 element and the qk qk 1 i k 2 family of quadrilateral elements then we introduce two new low order methods with piecewise constant approximations for the pressure the analysis is performed using our macroelement technique which is reviewed in a slightly altered form

closed characteristics on partially symmetric compact convex hypersurfaces in r2n abstract in this paper we study the multiplicity of closed characteristics on partially symmetric convex compact hypersurfaces in r 2n the main ingredient of the proof is a new p index function and its iteration theory for symplectic matrix paths and some symplectic orthogonal matrix p this theory yields estimates on this multiplicity via index estimates for a new type of iterations of any symplectic matrix path 0 sp 2n defined by t p t p for any t 0

convergence in the incompressible limit of finite element approximations based on the hu washizu formulation the classical hu washizu mixed formulation for plane problems in elasticity is examined afresh with the emphasis on behavior in the incompressible limit the classical continuous problem is embedded in a family of hu washizu problems parametrized by a scalar for which alpha lambda big mu corresponds to the classical formulation with and being the lame parameters uniform well posedness in the incompressible limit of the continuous problem is established for 1 finite element approximations are based on the choice of piecewise bilinear approximations for the displacements on quadrilateral meshes conditions for uniform convergence are made explicit these conditions are shown to be met by particular choices of bases for stresses and strains and include bases that are well known as well as newly constructed bases though a discrete version of the spherical part of the stress exhibits checkerboard modes it is shown that a independent a priori error estimate for the displacement can be established furthermore a independent estimate is established for the post processed stress the theoretical results are explored further through selected numerical examples

iteration inequalities of the maslov p index theory with applications abstract in this paper the p splitting numbers and p mean index for a symplectic path starting from the identity with p s p 2 n are defined first and then by using the maslov p index theory for a symplectic path various inequalities of the maslov p index theory for iterations of symplectic paths starting from the identity are established as an application these results are used to study the minimal period problem of p symmetric periodic solution of nonlinear autonomous hamiltonian systems

f bar based linear triangles and tetrahedra for finite strain analysis of nearly incompressible solids part i formulation and benchmarking this paper proposes a new technique which allows the use of simplex finite elements linear triangles in 2d and linear tetrahedra in 3d in the large strain analysis of nearly incompressible solids the new technique extends the f bar method proposed by de souza neto et al int j solids and struct 1996 33 3277 3296 and is conceptually very simple it relies on the enforcement of near incompressibility over a patch of simplex elements rather than the point wise enforcement of conventional displacement based finite elements within the framework of the f bar method this is achieved by assuming for each element of a mesh a modified f bar deformation gradient whose volumetric component is defined as the volume change ratio of a pre defined patch of elements the resulting constraint relaxation effectively overcomes volumetric locking and allows the successful use of simplex elements under finite strain near incompressibility as the original f bar procedure the present methodology preserves the displacement based structure of the finite element equations as well as the strain driven format of standard algorithms for numerical integration of path dependent constitutive equations and can be used regardless of the constitutive model adopted the new elements are implemented within an implicit quasi static environment in this context a closed form expression for the exact tangent stiffness of the new elements is derived this allows the use of the full newton raphson scheme for equilibrium iterations the performance of the proposed elements is assessed by means of a comprehensive set of benchmarking two and three dimensional numerical examples

multiple periodic points of the poincare map of lagrangian systems on tori in this paper suppose l t x p 1 over 2 a x p cdot p v t x a is positive definite and symmetric and both a and v are c 3 and 1 periodic in all of their variables we prove that the poincare map i e the time 1 solution map of the lagrangian system

on the linearization of regge calculus we study the linearization of three dimensional regge calculus around euclidean metric we provide an explicit formula for the corresponding quadratic form and relate it to the curl t curl operator which appears in the quadratic part of the einstein hilbert action and also in the linear elasticity complex we insert regge metrics in a discrete version of this complex equipped with densely defined and commuting interpolators we show that the eigenpairs of the curl t curl operator approximated using the quadratic part of the regge action on regge metrics converge to their continuous counterparts interpreting the computation as a non conforming finite element method

a new obstruction to embedding lagrangian tori n let 2n be endowed with the canonical symplectic form a i 1 dxi dy i and consider a lagrangian embedding of a compact manifold j l r 2 a a well known result due to g r o m o v g states that the cohomology class of a in h z e 2 l is non zero we identify l with its image in r2 an equivalent assertion is that the liouville form 2 y 7 1 xldy i pulls back to a closed form j 2 on l whose cohomology class does not vanish g r o m o v s proof uses subtle properties of holomorphic maps into c he shows that there is always a holomorphic disk a in c with boundary in l on such a disk a is positive hence sa a soa 2 0 in this paper we shall only consider the case l t and give an elementary proof of gromov s result elementary should be understood in the sense of number theory that is without using holomorphic functions in fact our result is somewhat more precise and can be stated as follows

closed characteristics on compact convex hypersurfaces in r 2n for any given compact c 2 hypersurface in r 2n bounding a strictly convex set with nonempty interior in this paper an invariant n is defined and satisfies n n 2 1 where a denotes the greatest integer which is not greater than a r the following results are proved in this paper there always exist at least n geometrically distinct closed characteristics on if all the geometrically distinct closed characteristics on are nondegenerate then n n if the total number of geometrically distinct closed characteristics on is finite there exists at least an elliptic one among them and there exist at least n 1 of them possessing irrational mean indices if this total number is at most 2 n 2 there exist at least two elliptic ones among them

compatibility condition and existence results in discrete finite incompressible elasticity abstract a theory on the existence of solutions of the discretized equilibrium equations in incompressible finite elasticity is given a compatibility condition between the space of displacements and the space of pressures is introduced and is studied in a particular case of finite element spaces using q 1 and q 0 isoparametric elements an original assembling of these elements is presented which leads to discrete spaces satisfying the compatibility condition

periodic solutions with prescribed minimal period for convex autonomous hamiltonian systems clarke has shown that the problem of findingt periodic solutions for a convex hamiltonian system is equivalent to the problem of finding critical points to a certain functional dual to the classical action functional in this paper we relate the morse index of the critical point to the minimal period of the correspondingt periodic solution in particular we show that if the critical point is obtained by the ambrosetti rabinowitz mountain pass theorem the corresponding solution has minimal periodt that is it cannot bet k periodic withk integer k 2 as a consequence we prove that if the hamiltonian is flat near an equilibrium and superquadratic near infinity then for anyt 0 the corresponding hamiltonian system has a periodic solution with minimal periodt

formulation of implicit finite element methods for multiplicative finite deformation plasticity some constitutive and computational aspects of finite deformation plasticity are discussed attention is restricted to multiplicative theories of plasticity in which the deformation gradients are assumed to be decomposable into elastic and plastic terms it is shown by way of consistent linearization of momentum balance that geometric terms arise which are associated with the motion of the intermediate configuration and which in general render the tangent operator non symmetric even for associated plastic flow both explicit i e no equilibrium iteration and implicit finite element formulations are considered an assumed strain formulation is used to accommodate the near incompressibility associated with fully developed isochoric plastic flow as an example of explicit integration the rate tangent modulus method is reviewed in some detail an implicit scheme is derived for which the consistent tangents resulting in quadratic convergence of the equilibrium iterations can be written out in closed form for arbitrary material models all the geometrical terms associated with the motion of the intermediate configuration and the treatment of incompressibility are given explicitly examples of application to void growth and coalescence and to crack tip blunting are developed which illustrate the performance of the implicit method

the mortar finite element method with lagrange multipliers the present paper deals with a variant of a non conforming domain decomposition technique the mortar finite element method in the opposition to the original method this variant is never conforming because of the relaxation of the matching constraints at the vertices and the edges in 3d of subdomains it is shown that written under primal hybrid formulation the approximation problem issued from a discretization of a second order elliptic equation in 2d is nonetheless well posed and provides a discrete solution that satisfies optimal error estimates with respect to natural norms finally the parallelization advantages consequence of this variant are also addressed

remarks on 4cst elements for incompressible materials abstract three node triangular elements obtained from the intersecting diagonals of quadrilaterals are thoroughly investigated for the penalty method formulation of incompressible problems such as stokes flow navier stokes flow and small deformation rubber elasticity equivalence of the present formulation to the one using 4 node quadrilateral isoparametric elements with selective reduced integration is presented convergence instability phenomenon smoothing of the pressure distribution are studied together with decompositions into triangular elements

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

uniform convergence and a posteriori error estimators for the enhanced strain finite element method enhanced strain elements frequently employed in practice are known to improve the approximation of standard non enhanced displacement based elements in finite element computations the first contribution in this work towards a complete theoretical explanation for this observation is a proof of robust convergence of enhanced element schemes it is shown that such schemes are locking free in the incompressible limit in the sense that the error bound in the a priori estimate is independent of the relevant lame constant the second contribution is a residual based a posteriori error estimate the l 2 norm of the stress error is estimated by a reliable and efficient estimator that can be computed from the residuals

diamond elements a finite element discrete mechanics approximation scheme with guaranteed optimal convergence in incompressible elasticity we present a finite element discretization scheme for the compressible and incompressible elasticity problems that possess the following properties i the discretization scheme is defined on a triangulation of the domain ii the discretization scheme is defined and is identical in all spatial dimensions iii the displacement field converges optimally with mesh refinement and iv the inf sup condition is automatically satisfied the discretization scheme is motivated both by considerations of topology and analysis and it consists of the combination of a certain mesh pattern and a choice of interpolation that guarantees optimal convergence of displacements and pressures rigorous proofs of the satisfaction of the inf sup condition are presented for the problem of linearized incompressible elasticity we additionally show that the discretization schemes can be given a compelling interpretation in terms of discrete differential operators in particular we develop a discrete analogue of the classical tensor differential complex in terms of which the discrete and continuous boundary value problems are formally identical we also present numerical tests that demonstrate the dimension independent scope of the scheme and its good performance in problems of finite elasticity

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

minimal period estimates of periodic solutions for superquadratic hamiltonian systems in this paper we study the minimal period problem for the first order hamiltonian systems which may not be strictly convex by using variational methods and the iteration formula of the maslov type index theory we obtain estimates of the minimal period of the corresponding nonconstant periodic solutions

stability of finite elements under divergence constraints a finite dimensional stability test for checking velocity pressure finite element trial spaces is presented applications are made to a new class of element pairs proposed in this paper as well as to existing spaces

on the average indices of closed geodesics on definit la notion d indices moyens de geodesiques fermees on demontre une relation entre ces indices pour une variete compacte simplement connexe dotee d une metrique admissible

nontrivial solutions of operator equations and morse indices of critical points of min max type on montre que si les hypotheses du theoreme de point selle sont satisfaites si dim y 2 et si f 1 c contient seulement des points critiques non degeneres alors f 1 c contient au moins un point critique u 0 tel que 2 indice de morse u 0 dim y

stabilized four node tetrahedron with nonlocal pressure for modeling hyperelastic materials summary non linear hyperelastic response of reinforced elastomers is modeled using a novel three dimensional mixed finite element method with a nonlocal pressure field the element is unconditionally convergent and free of spurious pressure modes nonlocal pressure is obtained by an implicit gradient technique and obeys the helmholtz equation physical motivation for this nonlocality is shown an implicit finite element scheme with consistent linearization is presented finally several hyperelastic examples are solved to demonstrate the computational algorithm including the inf sup and verifications tests copyright q 2008 john wiley sons ltd

hyperbolic closed characteristics on compact convex smooth hypersurfaces inr2n in this paper we prove that on every compactc2hypersurface inr2nbounding a convex set with non empty interior either there exists a sequence of variationally visible hyperbolic closed characteristcs with their minimal periods tending to infinity or there exists at least one variationally visible nonhyperbolic closed characteristic

subharmonic pl solutions of first order hamiltonian systems abstract in this paper for any symplectic matrix p the existence of subharmonic p l solutions of the first order non autonomous superquadratic hamiltonian systems is considered under the convex condition the existence of infinitely many geometrically distinct p l solutions is proved

fast 2d inversion of large borehole em induction data sets with an efficient frechet derivative approximation in addition to reliability and stability the efficiency and expediencyofinversionmethodshavelongbeenastrongconcernfor their routine applications by well log interpreters we have developedandsuccessfullyvalidatedanewinversionmethodtoestimate2dparametricspatialdistributionsofelectricalresistivity from array induction measurements acquired in a vertical well the central component of the method is an efficient approximation to frechet derivatives where both the incident and adjoint fields are precomputed and kept unchanged during inversion to further enhance the overall efficiency of the inversion we combined the new approximation with both the improved numerical mode matching method and domain decomposition examples of application with synthetic data sets show that the new method iscomputerefficientandcapableofretrievingoriginalmodelresistivities even in the presence of noise performing equally well in both high and low contrasts of formation resistivity in thin resistive beds the new inversion method estimates more accurate resistivities than standard commercial deconvolution software we also considered examples of application with field data sets that confirm the new method can successfully process a large data set that includes 200 beds in approximately 40 minutes of cpu time on a desktop computer in addition to 2d parametric spatial distributions of electrical resistivity the new inversion methodprovidesaqualitativeindicatoroftheuncertaintyofestimated parameters based on the estimator s covariance matrix the uncertainty estimator provides a qualitative measure of the nonuniqueness of estimated resistivity parameters when the data misfitlieswithinthemeasurementerrornoise

on the c1 continuous discretization of non linear gradient elasticity a comparison of nem and fem based on bernstein bezier patches in gradient elasticity the appearance of strain gradients in the free energy density leads to the need of c 1 continuous discretization m ethods in the present work the performances of c 1 finite elements and the c 1 natural element method nem are compared the triangular argyris and hsieh clough tocher finite elements are reparametrized in terms of the bernstein polynomials the quadrilateral bogner fox schmidt element is used in an isoparametric framework for which a preprocessing algorithm is presented additionally the c 1 nem is applied to non linear gradient elasticity several numerical examples are analyzed to compare the convergence behavior of the different methods it will be illustrated that the isoparametric elements and the nem show a significantly better performance than the triangular elements

mixed finite elements for elasticity there have been many efforts dating back four decades to develop stable mixed finite elements for the stress displacement formulation of the plane elasticity system this requires the development of a compatible pair of finite element spaces one to discretize the space of symmetric tensors in which the stress field is sought and one to discretize the space of vector fields in which the displacement is sought although there are number of well known mixed finite element pairs known for the analogous problem involving vector fields and scalar fields the symmetry of the stress field is a substantial additional difficulty and the elements presented here are the first ones using polynomial shape functions which are known to be stable we present a family of such pairs of finite element spaces one for each polynomial degree beginning with degree two for the stress and degree one for the displacement and show stability and optimal order approximation we also analyze some obstructions to the construction of such finite element spaces which account for the paucity of elements available

stable and semistable low order finite elements for viscous flows it is shown that i the bilinear constant and linear constant box elements are not uniformly stable and ii certain element pairs derived from those above by restricting the pressure spaces are stable the notion of div semistability is developed to study the behavior of the bilinear constant and linear constant box elements in detail

automatically inf sup compliant diamond mixed finite elements for kirchhoff plates we develop a mixed finite element approximation scheme for kirchhoff plate theory based on the reformulation of kirchhoff plate theory of ortiz and morris 1 in this reformulation the moment equilibrium problem for the rotations is in direct analogy to the problem of incompressible two dimensional elasticity this analogy in turn opens the way for the application of diamond approximation schemes hauret et al 2 to kirchhoff plate theory we show that a special class of meshes derived from an arbitrary triangulation of the domain the diamond meshes results in the automatic satisfaction of the corresponding inf sup condition for kirchhoff plate theory the attendant optimal convergence properties of the diamond approximation scheme are demonstrated by means of the several standard benchmark tests we also provide a reinterpretation of the diamond approximation scheme for kirchhoff plate theory within the framework of discrete mechanics in this interpretation the discrete moment equilibrium problem is formally identical to the classical continuous problem and the two differ only in the choice of differential structures it also follows that the satisfaction of the inf sup condition is a property of the cohomology of a certain discrete transverse differential complex this close connection between the classical inf sup condition and cohomology evinces the important role that the topology of the discretization plays in determining convergence in mixed problems