a locking free fem for cavitation computation in nearly incompressible nonlinear elasticity abstract a reduced selective integration finite element method coupled with a gradient flow method is introduced for the cavitation computation in nearly incompressible nonlinear elasticity numerical experiments show that for the iso parametric biquadratic finite element approximation of the displacement field the method is locking free and efficient for the nearly incompressible cavitation computation and has the same optimal convergence rates as in the compressible case for the elastic energy as well as the deformation and stress field if and only if the reduced integration is applied to the bulk energy term using no more than 2 gaussian quadrature nodes in each dimension

generalized mixed quasivariational inclusions and generalized mixed resolvent equations for fuzzy mappings in this paper we introduce the concept of generalized mixed quasivariational inclusions and generalized mixed resolvent equations for fuzzy mappings by using the resolvent operator technique for maximal monotone mapping we obtain that the generalized mixed quasivariational inclusions for fuzzy mappings are equivalent to the fuzzy fixed point problems and the generalized mixed resolvent equations for fuzzy mappings respectively we suggest a number of iterative algorithms establish the existence results of solutions for the generalized mixed quasivariational inclusions for fuzzy mappings and prove the convergence of the algorithms the results presented in this paper are improvements of previously known results

finite element analysis of anisotropic non linear incompressible elastic solids by a mixed model a mixed finite element method is presented for geometrically and materially non linear analysis of anisotropic incompressible hyperelastic materials an incremental iteractive total lagrangian formulation is adopted the nodal displacements and the hydrostatic pressure are independently interpolated leading to a mixed system of equations with characteristic zero diagonal terms computations are carried out using a three dimensional linear displacement constant pressure element a mixed penalty approximation is then employed to eliminate the pressure variables at the element level the anisotropic material handling capability of the formulation is tested through a number of transversely isotropic problems and the results compared to analytical solutions to demonstrate the applicability of this formulation to model complex anisotropic problems the inflation of a cut toroidal tube with helical fibre orientation is analysed

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

a hybrid finite element formulation of the linear biphasic equations for hydrated soft tissue a hybrid finite element method has been developed for application to the linear biphasic model of soft tissues the biphasic model assumes that hydrated soft tissue is a mixture of two incompressible immiscible phases one solid and one fluid and employs mixture theory to derive governing equations for its mechanical behaviour these equations are time dependent involving both fluid and solid velocities and solid displacement and will be solved by spatial finite element and temporal finite difference approximation the first step in the derivation of this hybrid method is application of a finite difference rule to the solid phase thus obtaining equations with only velocities at discrete times as primary variables a weighted residual statement of the temporally discretized governing equations employing c continuous interpolations of the solid and fluid phase velocities and discontinuous interpolations of the pore pressure and elastic stress is then derived the stress and pressure functions are chosen so that the total momentum equation of the mixture is satisfied they are jointly referred to as an equilibrated stress and pressure field the corresponding weighting functions are chosen to satisfy a relationship analogous to this equilibrium relation the resulting matrix equations are symmetric as an illustration of the hybrid biphasic formulation six noded triangular elements with complete linear several incomplete quadratic and complete quadratic stress and pressure fields in element local co ordinates are developed for two dimensional analysis and tested against analytical solutions and a mixed penalty finite element formulation of the same equations the hybrid method is found to be robust and produce excellent results preferred elements are identified on the basis of these results

optimal structural design considering flexibility a topology optimization method based on the homogenization method the homogenization design method has been successfully applied to a variety of optimization problems such as the stiffness maximization problem and the eigen frequency maximization problem in this study a methodology to obtain the optimal structure design considering flexibility is developed as a new extension of the homogenization design method first flexibility is formulated using the mutual energy concept second a new multi objective function is proposed to obtain optimal solutions incorporating flexibility and stiffness next the topology optimization procedure is constructed using the homogenization method and sequential linear programming slp finally some examples are presented to confirm that the methodology presented here can provide flexible structures satisfying the problem specifications

completely generalized strongly quasivariational inequalities for fuzzy mappings abstract in this paper we prove an existence theorem of solutions and develop the algorithms of approximating solutions for a completely generalized strongly variational inequality problem for fuzzy mappings and a completely generalized strongly complementarity problem for fuzzy mappings by using the projection method

a mathematical framework for finite strain elastoplastic consolidation part 1 balance laws variational formulation and linearization a mathematical formulation for finite strain elasto plastic consolidation of fully saturated soil media is presented strong and weak forms of the boundary value problem are derived using both the material and spatial descriptions the algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the kirchhoff pore water pressure balance laws are written for the soil water mixture following the motion of the soil matrix alone it is shown that the motion of the fluid phase only affects the jacobian of the solid phase motion and therefore can be characterized completely by the motion of the soil matrix furthermore it is shown from energy balance consideration that the effective or intergranular stress is the appropriate measure of stress for describing the constitutive response of the soil skeleton since it absorbs all the strain energy generated in the saturated soil water mixture finally it is shown that the mathematical model is amenable to consistent linearization and that explicit expressions for the consistent tangent operators can be derived for use in numerical solutions such as those based on the finite element method

sharp distortion theorems for quasiconformal mappings continuing their earlier work on distortion theory the authors prove some dimension free distortion theorems for k quasiconformal mappings in r for example one of the present results is the following sharp variant of the schwarz lemma if f is a k quasiconformal self mapping of the unit ball bn n 2 with f 0 0 then 41 k2ixik i if x i 411 k2ixil k for all x in b

finite element hourglassing control a new hourglassing control technique for quadrilateral and hexahedral elements used in dynamic finite element codes is presented based on expansion of the strees in a taylor series and retention of additional terms beyond the usual constant stress term this technique has the advantage that actual rather than artificial material properties are used simplifications that render this technique competitive with artificial viscosity and stiffness procedures in terms of additional storage and computation requirements are described

nonconvex fuzzy mappings and the fuzzy pre variational inequality in this paper we introduce the concepts of fuzzy pseudoconvex fuzzy invex fuzzy pseudoinvex and fuzzy preinvex mapping from r n to the set of fuzzy numbers and put forward the concepts of fuzzy extended directional differential subgradient and subdifferential some properties are obtained for fuzzy pseudoconvex fuzzy invex fuzzy pseudoinvex and fuzzy preinvex mapping relations are discussed between the fuzzy pre variational inequality and the fuzzy vector optimization problem

a locking free solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of lagrangian elements abstract this paper presents a new finite element solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of the classical bilinear or trilinear lagrangian elements it solves the primal variable displacement in the strain div formulation and can handle both displacement and traction boundary conditions it is a locking free solver based on conforming finite elements the solver has second order accuracy in displacement and first order accuracy in stress and dilation divergence of displacement as validated by theoretical analysis and illustrated by numerical experiments on benchmarks deal ii implementation is also discussed

locking spurious mechanisms and pressure divergence in penalty finite element methods for stokes flow problems abstract solution locking spurious mechanisms and pressure divergence exhibited in the stokes flow calculations by the penalty finite element methods are analyzed employing a fourier analysis technique comparison of the approximate discrete operator components with the corresponding continuum ones enables one to explicitly identify the conditions for avoiding locking spurious mechanisms and pressure divergence in terms of discrete operator components which are applicable to either the finite difference or finite element discretizations a synthesis approach is explored to eliminate the solution locking spurious mechanisms and pressure divergence in uniformly reduced integrated four noded elements extensions of the present analysis and synthesis approach to navier stokes equations appear to be straightforward if one deals with a set of consistently linearized operators

an integration scheme for prandtl reuss elastoplastic constitutive equations we investigate the generalized midpoint rule for the time integration of elastoplastic constitutive equations for pressure independent yield criteria the incremental equations are divided into one scalar hydrostatic pressure dilation rate equation and a stress deviator strain rate deviator tensorial equation this formulation is applied to two classical problems bulging of a tube under internal pressure and tension test on a notched specimen

treatment of internal constraints by mixed finite element methods unification of concepts a general method to generate assumed stress and strain fields within the context of mixed finite element methods is presented the assumed fields are constructed in such a way that internal constraints are satisfied a priori consequently the locking behaviour commonly observed in finite element solutions of problems with internal constraints is avoided to this end the assumed stress and strain fields are constructed to satisfy a priori the homogeneous part of the equilibrium equations thus avoiding fraeijs de veubeke s limitation principle results obtained using the proposed methodology on a nearly incompressible plane strain problem and thin plate application using a shear deformable theory are indicated

large deformation triangular and tetrahedral element formulations for unstructured meshes abstract the increasing use of automatic mesh generators and remeshers has spurred the need for accurate and efficient triangular and tetrahedral elements in unstructured meshes in large deformation analysis of solids accuracy and efficiency require the treatment of volumetric locking and element distortions respectively in this paper a mixed formulations is proposed to treat these issues and applied to triangular and tetrahedral elements the formulations enforces in the weak sense the expression for the volumetric strain in terms of the deformation gradient the mixed formulation is combined with an irreducible formulation to provide a balance between the treatment of volumetric locking and the maintenance of an adequate critical timestep three techniques are proposed to determine such a balance at the local element level example computations in two and three dimensions of an iron cylinder impacting a rigid surface are used to demonstrate the formulations and to compare them to the irreducible displacement based formulation

analysis of transient response of saturated porous elastic soil under cyclic loading using element free galerkin method a two dimensional numerical procedure is presented to analyse the transient response of saturated porous elastic soil layer under cyclic loading the procedure is based on the element free galerkin method and incorporated into the periodic conditions temporal and spatial periodicity its shape function is constructed by moving least square approximants essential boundary conditions are implemented through lagrange multipliers and the periodic conditions are implemented through a revised variational formulation time domain is discretized through the crank nicolson scheme analytical solutions are developed to assess the effectiveness and accuracy of the current procedure in one and two dimensions for only temporal periodic problems a one dimensional transient problem of finite thickness soil layer is analysed for sinusoidal surface loading for both temporal and spatial periodic problems a typical two dimensional wave induced transient problem with the seabed of finite thickness is analysed finally a moving boundary problem is analysed it is found that the current procedure is simple efficient and accurate in predicting the response of soil layer under cyclic loading 2002 elsevier science ltd all rights reserved

implicit explicit schemes for nonlinear consolidation abstract a general analytical procedure capable of performing linear and nonlinear consolidation analysis of saturated porous media is proposed a brief review of the coupled field equations is included and the constitutive assumptions are stated explicitly time integration of the resulting nonlinear semidiscrete finite element equations is performed by using an implicit explicit predictor multicorrector scheme developed by hughes and co workers it is shown that the algorithm can be simply and concisely implemented the technique allows for a convenient selection of implicit and explicit elements and for a convenient implicit explicit split of the various operators appearing in the equations the procedure proves to be extremely effective in dealing with consolidation problems numerical results which demonstrate the versatility and accuracy of the proposed procedures are presented

distortion of quasiconformal maps in terms of the quasihyperbolic metric abstract we extend a theorem of gehring and osgood from 1979 relating to the distortion of the quasihyperbolic metric by a quasiconformal mapping between euclidean domains to the setting of metric measure spaces of q bounded geometry when the underlying target space is bounded we require that the boundary of the image has at least two points we show that even in the manifold setting this additional assumption is necessary

finite element formulations for hyperelastic transversely isotropic biphasic soft tissues abstract this paper presents a finite element model for the three dimensional 3 d nonlinear analysis of soft hydrated tissues such as articular cartilage in diarthrodial joints under physiologically relevant loading conditions a biphasic continuum description is used to represent the soft tissue as a two phase mixture of incompressible inviscid fluid and a hyperelastic transversely isotropic solid alternate mixed penalty and velocity pressure finite element formulations are used to solve the nonlinear biphasic governing equations including the effects of a strain dependent permeability and a hyperelastic solid phase under finite deformation the resulting first order nonlinear system of equations are discretized in time using an implicit finite difference scheme and solved using the newton raphson method a significant contribution of this work is the implementation and testing of a biphasic description with a transversely isotropic hyperelastic solid phase this description considers a helmholtz free energy function of five invariants of the cauchy green deformation tensor and the preferred direction of the material allowing for asymmetric behavior in tension and compression an exponential form is suggested and a set of material parameters is identified to represent the response of soft tissues in ranges of deformation and stress observed experimentally after demonstrating the behavior of this constitutive model in simple tension and compression a sample problem of unconfined compression is used to further validate the finite element implementation

generalized convex fuzzy mappings and fuzzy variational like inequality in this paper we introduce the concepts of some generalized convex fuzzy mappings from r n to the set of fuzzy numbers under the condition of upper or lower semicontinuity a new criterion be obtained for the existence of a fuzzy preinvex mapping a fuzzy preinvex mapping can be achieved when the invex subset of r n satisfies certain conditions the relations between generalized convex fuzzy mappings are discussed and some properties are obtained that relate the concepts of fuzzy pseudoinvex and fuzzy prequasiinvex mapping fuzzy invex and fuzzy preinvex mapping fuzzy preinvex and fuzzy prequasiinvex mapping we also discuss the relationship between the fuzzy variational like inequality the fuzzy weak variational like inequality and fuzzy optimization problems and an application example of a fuzzy variational like inequality the fuzzy variational like inequality representation of a fuzzy transportation equilibrium problem

elastoplastic consolidation at finite strain part 2 finite element implementation and numerical examples a mathematical model for finite strain elastoplastic consolidation of fully saturated soil media is implemented into a finite element program the algorithmic treatment of finite strain elastoplasticity for the solid phase is based on multiplicative decomposition and is coupled with the algorithm for fluid flow via the kirchhoff pore water pressure a two field mixed finite element formulation is employed in which the nodal solid displacements and the nodal pore water pressures are coupled via the linear momentum and mass balance equations the constitutive model for the solid phase is represented by modified cam clay theory formulated in the kirchhoff principal stress space and return mapping is carried out in the strain space defined by the invariants of the elastic logarithmic principal stretches the constitutive model for fluid flow is represented by a generalized darcy s law formulated with respect to the current configuration the finite element model is fully amenable to exact linearization numerical examples with and without finite deformation effects are presented to demonstrate the impact of geometric nonlinearity on the predicted responses the paper concludes with an assessment of the performance of the finite element consolidation model with respect to accuracy and numerical stability

finite element analysis of linear and non linear planar deformations of elastic initially curved beams reference epfl article 102719view record in web of science record created on 2007 04 23 modified on 2016 08 08

nonlinear transient phenomena in saturated porous media abstract in this report the transient static and dynamic response of saturated porous medium is analyzed the saturated porous medium viewed as a two phase system whose state is described by the stresses displacements velocities and accelerations within each phase the coupled field and constitutive equations based on mixture s theories are presented and solved numerically by the use of the finite element method time integration is achieved by using an implicit explicit predictor multicorrector scheme developed by hughes and co workers the procedure allows for a convenient selection of implicit and explicit elements and for an implicit explicit split of the various operators appearing in the differential equations accuracy and versatility of the proposed procedure are demonstrated by applying it to obtain solution to various dynamic and pseudo static one and two dimensional initial value problems

on a systematic development of trilinear three dimensional solid elements based on simo s enhanced strain formulation a systematic development of eight node trilinear three dimensional solid elements based on simo s theoretical framework for the enhanced assumed strain formulation is presented for linear elasticity the starting point is a regular brick followed by parallelepipeds and then arbitrarily distorted elements the advantages and deficits of various enhanced strain formulations are extensively discussed using the regular brick for arbitrarily distorted elements a simple modification of the element stiffness matrix is proposed to achieve a more reliable and very efficient element on some numerical examples the advantages and limits of the family of enhanced strain elements and the improved elements are discussed

dynamics of porous media at finite strain we present a finite element model for the analysis of a mechanical phenomenon involving dynamic expulsion of fluids from a fully saturated porous solid matrix in the regime of large deformation momentum and mass conservation laws are written in lagrangian form by a pull back from the current configuration to the reference configuration following the solid matrix motion a complete formulation based on the motion of the solid and fluid phases is first presented then approximations are made with respect to the material time derivative of the relative flow velocity vector to arrive at a so called v p formulation which is subsequently implemented in a finite element model we show how the resulting finite element matrix equations can be consistently linearized using a compressible neo hookean hyperelastic material with a kelvin solid viscous enhancement for the solid matrix as a test function for the nonlinear constitutive model numerical examples are presented demonstrating the significance of large deformation effects on the transient dynamic responses of porous structures as well as the strong convergence profile exhibited by the iterative algorithm

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

the b bar method and the limitation principles abstract the generalized elastic material provides a reference model to cast in a unitary framework many structural models which are based on nonlinear monotone multivalued relations such as viscoelasticity plasticity and unilateral models the modified forms of the hu washizu and hellinger reissner principles and the displacement based variational formulation are recovered for the generalized elastic material starting from a functional in the complete set of state variables the related limitation principles are derived and their specialization to elasticity and elastoplasticity with mixed hardening are provided it is shown that the interpolating fields for the pressure and the volumetric strain usually adopted in the b bar method lead to a limitation principle accordingly the same elastic and elastoplastic solutions can be obtained by means of an approximate mixed displacement pressure variational principle a second application is concerned with the conditions ensuring the coincidence of the solutions between an approximate two field mixed formulation and the displacement based method numerical examples are provided to show the coincidence of the solutions obtained from different mixed finite element formulations in elasticity or elastoplasticity under the validity of the limitation principles

improved convected particle domain interpolation method for coupled dynamic analysis of fully saturated porous media involving large deformation abstract based on the u p form governing equations and the convected particle domain interpolation technique the improved convected particle domain interpolation based material point method ccpdi is developed in this paper for the coupled dynamic and contact analysis of fully saturated porous media involving large deformation the numerical artifact noises due to material points crossing computational grid boundaries that usually occur in large deformation are eliminated by using the smoother interpolation functions presented in the convected particle domain interpolation technique the discrete equations are derived in the framework of the generalized interpolation material point method the boundary load tracking algorithm and a modified contact algorithm are proposed based on the definition of particle domains to apply accurately the surface loads on the motive boundaries and to capture correctly the contact time behaviors in large deformation problems respectively simulations of several representative one and two dimensional problems are presented to demonstrate the accuracy and effectiveness of the proposed methods compared to those obtained by using the coupling material point method and or finite element method the simulation results illustrate that the proposed ccpdi method can be successfully used in simulating the large deformation coupled dynamic responses of the solid skeleton and fluid phase in fully saturated porous media and the large deformation impact between solid and saturated porous bodies

accuracy of some finite element models for arch problems abstract this paper presents a theoretical accuracy study of some finite element models for thin arches as is well known the selection of finite elements for curved members is quite a delicate problem we obtain order estimates of errors of finite element solutions by means of the perturbation theory of mixed models and the technique of asymptotic expansion in particular we theoretically show that certain finite element models may suffer from the so called locking phenomenon numerical results are also given to be compared with the theoretical error estimates

quasiconformal maps in metric spaces with controlled geometry this paper develops the foundations of the theory of quasiconformal maps in metric spaces that satisfy certain bounds on their mass and geometry the principal message is that such a theory is both relevant and viable the first main issue is the problem of definition which we next describe quasiconformal maps are commonly understood as homeomorphisms that distort the shape of infinitesimal balls by a uniformly bounded amount this requirement makes sense in every metric space given a homeomorphism f from a metric space x to a metric space y then for x x and r 0 set

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

quasiconformal deformations and volume growth we determine when a metric measure space admits a uniformizing density which has ahlfors regular volume growth a characterization of uniformizing conformal densities in terms of doubling and a lifting procedure are the key ingredients in our presentation we also furnish an application characterizing metric doubling measures

b and f projection methods for nearly incompressible linear and non linear elasticity and plasticity using higher order nurbs elements abstract this paper presents projection methods to treat the incompressibility constraint in small and large deformation elasticity and plasticity within the framework of isogeometric analysis after reviewing some fundamentals of isogeometric analysis we investigate the use of higher order non uniform rational b splines nurbs within the b projection method the higher continuity property of such functions is explored in nearly incompressible applications and shown to produce accurate and robust results a new non linear f projection method based on a modified minimum potential energy principle and inspired by the b method is proposed for the large deformation case it leads to a symmetric formulation for which the consistent linearized operator for fully non linear elasticity is derived and used in a newton raphson iterative procedure the performance of the methods is assessed on several numerical examples and results obtained are shown to compare favorably with other published techniques

mixed finite element with drilling rotations for plane problems in finite elasticity abstract in this work we apply the mixed finite element method to construct a two dimensional membrane element with drilling rotations for geometrically nonlinear elasticity only the 4 node element interpolation is discussed but the formulation is plausible for higher order elements as well numerical examples for both linear and nonlinear analyses demonstrate that the element yields rather stiff but indeed convergent results