a three invariant hardening plasticity for numerical simulation of powder forming processes via the arbitrary lagrangian eulerian fe model in this paper a three invariant cap plasticity model with an isotropic hardening rule is presented for numerical simulation of powder compaction processes a general form is developed for single cap plasticity which can be compared with some common double surface plasticity models proposed for powders in literature the constitutive elasto plastic matrix and its components are derived based on the definition of yield surface hardening parameter and non linear elastic behaviour as function of relative density of powder different aspects of the new single plasticity are illustrated by generating the classical plasticity models as special cases of the proposed model the procedure for determination of powder parameters is described by fitting the model to reproduce data from triaxial compression and confining pressure experiments the three invariant cap plasticity is performed within the framework of an arbitrary lagrangian eulerian formulation in order to predict the non uniform relative density distribution during large deformation of powder die pressing in ale formulation the reference configuration is used for describing the motion instead of material configuration in lagrangian and spatial configuration in eulerian formulation this formulation introduces some convective terms in the finite element equations and consists of two phases each time step is analysed according to lagrangian phase until required convergence is attained then the eulerian phase is applied to keep mesh configuration regular because of relative displacement between mesh and material all dependent variables such as stress and strain are converted through the eulerian phase finally the numerical schemes are examined for efficiency and accuracy in the modelling of a rotational flanged component an automotive component a conical shaped charge liner and a connecting rod copyright 2005 john wiley sons ltd

variational r adaption in elastodynamics we develop a variational r adaptive finite element framework for solid dynamic applications and explore its conceptual links with the theory of dynamic configurational forces the central idea underlying the proposed approach is to allow hamilton s principle of stationary action to determine jointly the evolution of the displacement field and the discretization of the reference configuration of the body this is accomplished by rendering the action stationary with respect to the material and spatial nodal coordinates simultaneously however we find that a naive consistent galerkin discretization of the action leads to intrinsically unstable solutions remarkably we also find that this unstable behavior is eliminated when a mixed multifield version of hamilton s principle is adopted additional features of the proposed numerical implementation include the use of uncoupled space and time discretizations the use of independent space interpolations for velocities and deformations the application of these interpolations over a continuously varying adaptive mesh and the application of mixed variational integrators with independent time interpolations for velocities and nodal parameters the accuracy robustness and versatility of the approach are assessed and demonstrated by way of convergence tests and selected examples

global well posedness for a boussinesq navier stokes system with critical dissipation abstract in this paper we study a fractional diffusion boussinesq model which couples a navier stokes type equation with fractional diffusion for the velocity and a transport equation for the temperature we establish global well posedness results with rough initial data

a finite element framework for continua with boundary energies part ii the three dimensional case this paper in line with part i 53 is concerned with the finite element implementation of boundary potential energies and the study of their impact on the deformations of solids thereby the main thrust is the fully three dimensional formulation and implementation incorporating anisotropic effects boundary effects can play a dominant role in the material behavior the most prominent example being surface tension however the common modelling in continuum mechanics takes exclusively the bulk into account nevertheless neglecting possible contributions from the boundary within this contribution the boundary potentials are allowed in general to depend not only on the boundary deformation but also on the boundary deformation gradient and the spatial boundary normal for the formulation of the finite element method the concept of convected curvilinear coordinates attached to the boundary is employed and the corresponding derivations completely based on a tensorial representation are carried out afterwards the discretization of the generalized weak formulation including boundary potentials is performed and eventually numerical examples are presented to demonstrate the boundary effects due to different proposed material models in contrast to the previous literature on this topic the current manuscript covers jointly the following issues related to boundary energies 1 the formulation and implementation represents a fully three dimensional framework at large deformations 2 the formulation of the problem and the proposed material models are based on finite strains however it is shown that the linearization would lead to the small strain models proposed previously in the literature and 3 the current manuscript covers the issue of anisotropy effects on the boundary energies which to the best of our knowledge has not been exemplified earlier

on the asymptotic integrability of a higher order evolution equation describing internal waves in a deep fluid a higher order nonlocal evolution equation describing internal waves in a deep fluid is shown to be asymptotically integrable only if the coefficients of the higher order terms satisfy certain constraints in this case the nonlocal equation can be transformed to the integrable benjamin ono equation the asymptotic integrability of the reductions of the higher order evolution equation to a complex burgers equation to an envelope wave equation and to a finite dimensional dynamical system is also considered

an error estimate free and remapping free variational mesh refinement and coarsening method for dissipative solids at finite strains a variational h adaptive finite element formulation is proposed the distinguishing feature of this method is that mesh refinement and coarsening are governed by the same minimization principle characterizing the underlying physical problem hence no error estimates are invoked at any stage of the adaption procedure as a consequence linearity of the problem and a corresponding hilbert space functional framework are not required and the proposed formulation can be applied to highly non linear phenomena the basic strategy is to refine respectively unrefine the spatial discretization locally if such refinement respectively unrefinement results in a sufficiently large reduction respectively sufficiently small increase in the energy this strategy leads to an adaption algorithm having o n complexity local refinement is effected by edge bisection and local unrefinement by the deletion of terminal vertices dissipation is accounted for within a time discretized variational framework resulting in an incremental potential energy in addition the entire hierarchy of successive refinements is stored and the internal state of parent elements is updated so that no mesh transfer operator is required upon unrefinement the versatility and robustness of the resulting variational adaptive finite element formulation is illustrated by means of selected numerical examples

on deformational and configurational mechanics of micromorphic hyperelasticity theory and computation abstract a micromorphic continuum formulation is presented in the context of both the spatial and the material motion problem for both approaches the kinematics as well as the balance relations together with the various representations of the occurring stress fields are derived the relations between the spatial motion problem and the material motion problem quantities are examined in detail upon a hyperelastic constitutive assumption a finite element approximation is derived and the material force method which is especially suited for defect mechanics problems is successfully applied to the present micromorphic continuum theory

dark soliton generation for the intermediate nonlinear schrodinger equation the generation of dark solitons due to a small change of the initial data is studied within the framework of the intermediate nonlinear schrodinger inls equation in particular we analyze the spectral problem associated with the inls equation when the potential consists of a small perturbation imposed on a constant background we derive a criterion for the perturbation to generate a pair of new discrete eigenvalues as well as their explicit expressions in terms of the perturbation in addition we demonstrate that the eigenvalues appear without a threshold on the magnitude of the perturbation we also consider both the shallow and deep water limits of various results obtained for the inls spectral problem in the former case the limiting procedure can be performed smoothly whereas in the latter case the spectral equation exhibits a new feature of bound states showing that the eigenvalue is exponentially small compared with the magnitude of the perturbation

on a solution strategy for energy based mesh optimization in finite hyperelastostatics the objective of this work is the development of a numerical solution strategy for energy based mesh optimization in finite hyperelastostatics in finite element computations that rely on the principle of minimum potential energy the variational principle itself provides the basis for r adaptive methods the numerical solution can be improved by further minimizing the discrete potential energy with respect to the material node point positions in this paper we regard the mesh optimization as a nonlinear minimization problem with equality and inequality constraints the equality constraints correspond to the spatial equilibrium condition whereas the inequality constraints are given by the natural restriction that material elements with a negative volume jacobian are inadmissible based on this interpretation we develop a stable numerical solution strategy in which two approaches of nonlinear programming are combined applying a barrier method the minimization problem is transformed into a sequence of problems without inequality constraints each problem of the sequence is solved by means of a newton scheme that operates on the constrained surface given by the spatial equilibrium condition

nonlinear evolution equations associated with a riemann hilbert scattering problem in an earlier paper nonlinear evolution equations associated with a riemann hilbert scattering problem which reduces in an appropriate limit to the zakharov shabat akns scattering problem were considered here we discuss certain necessary constraints associated with the scattering problem and their impact upon the associated evolution equations moreover the direct linearization of the nonlinear evolution equations and an algorithm to construct ann soliton solution are given

application of material forces to hyperelastostatic fracture mechanics i continuum mechanical setting the concern of this work is a consequent exploitation of the notion of material forces for the application within hyperelastostatic fracture mechanics contrary to physical forces material forces act on the material manifold thus essentially representing the tendency of defects like cracks or inclusions to move relative to the ambient material based on the formulation of the appropriate quasi static balance laws in the material space we aim at a fresh look onto classical aspects of hyperelastostatic fracture mechanics operating throughout within the geometrically nonlinear setting we emphasize on the one hand the duality of the direct and the inverse motion description and on the other hand we re establish the classical path integrals from elementary equilibrium considerations in the material space

on the initial value problem for the modified benjamin ono equation the initial value problem for the modified benjamin ono equation is solved by exploiting the fokas ablowitz inverse scattering transform for a certain complex extension of the benjamin ono equation the asymptotics of the jost functions for small positive values of the spectral parameter are sharpened and lead to a previously overlooked nongeneric case

a formulation of finite elastoplasticity based on dual co and contra variant eigenvector triads normalized with respect to a plastic metric the article presents a new formulation of isotropic elastoplasticity at large strains in both the lagrangian and the eulerian geometric setting and addresses aspects of its numerical implementation the key ingredients on the theoretical side are the introduction of a plastic metric for the description of the local history dependent inelastic material response the definition of a convex elastic domain in the space of the local stress like variable conjugate to the plastic metric denoted as the plastic force and a fully equivalent lagrangian and eulerian representation of all constitutive functions in spectral form for general non cartesian coordinate charts in terms of dual co and contra variant eigenvector triads which are normalized with respect to the plastic metric on the numerical side we propose a stress update algorithm for general non associative isotropic elasto visco plastic response with an arbitrary number of scalar internal variables the algorithm is based on an exponential map integrator and is recast into a general return mapping scheme methodically organized with tensorial pre and postprocessing and a constitutive box in the eigenvalue space furthermore we propose a new perturbation stabilization technique which dramatically enhances the convergence of the general return algorithm the theoretical and numerical developments are applied to a constitutive model problem with large elastic and large plastic strains the von mises tresca type associative plastic flow in ogden type large strain elastic materials

a quasi static discontinuous galerkin configurational force crack propagation method for brittle materials summary this paper presents a framework for r adaptive quasi static configurational force cf brittle crack propagation cast within a discontinuous galerkin dg symmetric interior penalty sipg finite element scheme cracks are propagated in discrete steps with a staggered algorithm along element interfaces which align themselves with the predicted crack propagation direction the key novelty of the work is the exploitation of the dg face stiffness terms existing along element interfaces to propagate a crack in a mesh independent r adaptive quasi static fashion driven by the cf at the crack tip this adds no new degrees of freedom to the data structure additionally as dg methods have element specific degrees of freedom a geometry driven p adaptive algorithm is also easily included allowing for more accurate solutions of the cf on a moving crack front further for non determinant systems we introduce an average boundary condition that restrains rigid body motion leading to a determinant system to the authors knowledge this is first time such a boundary condition has been described the proposed formulation is validated against single and multiple crack problems with single and mixed mode cracks demonstrating the predictive capabilities of the method this article is protected by copyright all rights reserved

an integrated approach to shape optimization and mesh adaptivity based on material residual forces abstract this contribution is concerned with the coupling of finite element based shape optimization to methods of mesh adaptivity therein the nodal points of a finite element mesh serve as design variables in an optimization problem that aims to minimize a cost functional with respect to different constraints in order to avoid the occurrence of oscillating boundaries in the optimal design trials we generate the respective design updates through solving a series of fictitious boundary value problems on an updated lagrangian configuration the design update process is accompanied by adaptive mesh refinement to obtain more accurate results for the structural analysis and the design sensitivity analysis for the mesh adaptation process we consider r adaptive node relocation h adaptive mesh refinement and a combination of both approaches in each case the derivations rest upon the notion of material residual forces induced by finite element discretization and the coupling of shape optimization and mesh adaptivity is of intermittent type i e mesh adaptivity is invoked once a certain number of design updates has been generated we examine the benefits of the proposed method on the basis of some numerical examples in comparison to the same shape optimization method not involving adaptive mesh refinement where we evaluate the corresponding numerical costs the gain in accuracy and the effects on the optimal shapes being obtained

numerical modelling of large deformation in metal powder forming abstract in this paper the transient dynamic analysis of metal powder during the cold compaction process is simulated by the finite element method based on a total and updated lagrangian formulation since the compaction process involves a very large reduction in volume the behaviour of the powders is assumed to be that of a rate independent elasto plastic material the process is therefore described by a large displacement finite element formulation for the spatial discretization a generalized newmark scheme is used for the time domain discretization and then the final nonlinear equations are solved by a newton raphson procedure a combination of a mohr coulomb and elliptical cap yield model is utilised as a constitutive model to describe the nonlinear behaviour of powder materials an incremental elasto plastic material model is used to simulate the compaction process and a plasticity theory for friction is employed in the treatment of the powder tooling interface the interfacial behaviour between the die and powder is modelled by using an interface element mesh finally the powder behaviour during the compaction of a plane bush a cutting tool and a rotational flanged component is analysed numerically the predictive compaction forces at different displacements the variation with time of the displacement relative density and stress contours are obtained it is shown that the proposed large displacement elasto plastic finite element approach is capable of simulating the metal powder during compaction

arbitrary lagrangian eulerian finite element analysis of free surface flow an arbitrary lagrangian eulerian ale description of newtonian fluid flow is presented it allows the simulation of free surfaces with the finite element method fem we develop a robust node repositioning algorithm which consists of two parts an energy minimization principle controls the positions of the internal nodes a good approximation of the boundaries is ensured by explicitly enforcing the free surface conditions numerical examples are done employing the mini element

on the profiles of locally self similar solutions for the 2d inviscid boussinesq equations abstract in this paper we investigate the locally self similar solutions of the 2d inviscid boussinesq equations and mainly focus on the possible velocity and temperature blowup profiles we derive the formula of the pressure profiles in terms of the velocity and temperature profiles in the case that the possible nontrivial profiles have non decaying spatial asymptotics then using the local energy inequality of the profiles and iterative method we prove some nonexistence results and obtain the energy behavior concerning these possible profiles

eulerian formulation using stabilized finite element method for large deformation solid dynamics this paper describes an eulerian formulation for large deformation solid dynamics in the present eulerian approach an advective equation is solved using the stream upwind petrov galerkin finite element method the eulerian finite element method is applied to path dependent solid analyses such as impact bar and ductile necking problems these computational results using the eulerian finite element method are compared with the results obtained from using the lagrangian finite element method and an eulerian formulation based on a finite difference method copyright 2007 john wiley sons ltd

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

a total ale fe formulation for axisymmetric and torsional problems including viscoplasticity thermodynamic coupling and dynamics this paper first extends a recent assumed enhanced deformation gradient finite ring segment element int j numer methods eng 2001 50 899 918 to arbitary lagrange euler ale computations by setting up the assumed tensor on the computational configuration and second shows an elegant way of incorporating dynamics into real ale computations no splitting into purely lagrange steps and then remeshing steps by introducing material mesh velocities and accelerations and spatial mesh velocities and accelerations copyright 2006 john wiley sons ltd

well posedness for the nonlocal nonlinear schrodinger equation abstract we establish local well posedness for small initial data in the usual sobolev spaces h s r s 1 and global well posedness in h 1 r for the cauchy problem associated to the nonlocal nonlinear schrodinger equation t u i x 2 u u x u 2 i u t h x u 2 i u 2 u where u u x t x t r t h is a singular integral operator 0 0 and 0 are real constants our method of proof is based on the smoothing effects produced by the linear schrodinger equation

a spectral transform for the intermediate nonlinear schrodinger equation a new spectral transform system is introduced to solve the initial value problem for the intermediate nonlinear schrodinger inls equation describing envelope waves in a deep stratified fluid the spectral system is a combination of the zakharov shabat linear system and a local riemann hilbert problem in a strip of the complex plane the inverse scattering transform technique is developed and the backlund darboux transformation soliton solutions and an infinite number of conservation laws are constructed it is shown that all these properties of the inls equation are closely related to those of the intermediate long wave equation

local well posedness for the nonlocal derivative nonlinear schrodinger equation in besov spaces abstract in this paper we study the cauchy problem associated with the one dimensional integro differential nonlocal derivative nonlinear schrodinger equation in the besov space b 2 1 2 1 r the local well posedness for small initial data in b 2 1 2 1 r is established our method of proof combines the contraction principle applied to the associated integral equation together with interpolations of some smoothing effects kato s smoothing effects strichartz estimate and estimates for the maximal function for phase localized functions associated to the linear dispersive part of the equation and a fractional vector valued leibniz s rule derived by molinet and ribaud in 2004

direct and inverse scattering problems of the nonlinear intermediate long wave equation the inverse scattering transformation method associated with a nonlinear singular integrodifferential equation is discussed the equation describes long internal gravity waves in a stratified fluid of finite depth and reduces to the korteweg de vries equation as shallow water limit and the benjamin ono equation as deep water limit both limits of the method and novel aspects of the theory are also discussed

on the numerical implementation of variational arbitrary lagrangian eulerian vale formulations this paper is concerned with the implementation of variational arbitrary lagrangian eulerian formulations also known as variational r adaption methods these methods seek to minimize the energy function with respect to the finite element mesh over the reference configuration of the body we propose a solution strategy based on a viscous regularization of the configurational forces this procedure eliminates the ill posedness of the problem without changing its solutions i e the minimizers of the regularized problems are also minimizers of the original functional we also develop strategies for optimizing the triangulation or mesh connectivity and for allowing nodes to migrate in and out of the boundary of the domain selected numerical examples demonstrate the robustness of the solution procedures and their ability to produce highly anisotropic mesh refinement in regions of high energy density

an ale formulation based on spatial and material settings of continuum mechanics part 1 generic hyperelastic formulation abstract the present contribution deals with the derivation of a generic hyperelastic arbitrary lagrangian eulerian formulation on the basis of a consistent variational framework the governing equations follow straightforwardly from the dirichlet principle for conservative mechanical systems thereby the key idea is the reformulation of the total variation of the potential energy at fixed referential coordinates in terms of its variation at fixed material and at fixed spatial coordinates the corresponding euler lagrange equations define the spatial and the material motion version of the balance of linear momentum i e the balance of spatial and material forces in a consistent dual format in the discretised setting the governing equations are solved simultaneously rendering the spatial and the material configuration which minimise the overall potential energy of the system the remeshing strategy of the ale formulation is thus no longer user defined but objective in the sense of energy minimisation if the governing equations are derived from a potential i e either from an incremental potential or from a total potential as in the present case they are inherently symmetric both in the continuous case and in the discrete case this symmetry property is particularly appealing since it ensures symmetric system matrices upon discretisation

a framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition part ii computational aspects computational aspects of the formulation of elastoplasticity proposed in part i of this work employing a multiplicative decomposition and based on the principle of maximum plastic dissipation are examined in detail in particular the implementation of the proposed hyperelastic j2 flow theory is shown to reduce to a trivial modification of the classical radial return algorithm which is amenable to exact linearization this results in a closed form expression for the consistent elastoplastic tangent moduli the algorithmic treatment of the general case is considered subsequently it is emphasized that objective rates and incrementally objective algorithms play no role in the present approach a number of numerical experiments are presented that illustrate the excellent performance of the proposed formulation

global regularity for the two dimensional anisotropic boussinesq equations with vertical dissipation this paper establishes the global in time existence of classical solutions to the two dimensional anisotropic boussinesq equations with vertical dissipation when only vertical dissipation is present there is no direct control on the horizontal derivatives and the global regularity problem is very challenging to solve this problem we bound the derivatives in terms of the l infty norm of the vertical velocity v and prove that v l r with 2 leqq r infty does not grow faster than sqrt r log r at any time as r increases a delicate interpolation inequality connecting v l infty and v l r then yields the desired global regularity

on the limit from the intermediate long wave equation to the benjamin ono equation the intermediate long wave equation is a physically important singular integrodifferential equation containing a parameter referred to here as for it reduces to the benjamin ono equation it has been recently shown that the inverse scattering transform schemes of the above equations have certain significant differences here it is shown that for the inverse scattering transform scheme of the intermediate long wave equation reduces to that of the benjamin ono equation

finite strain fracture of plates and shells with configurational forces and edge rotations we propose a simple and efficient algorithm for fem based computational fracture of plates and shells cf 1 with both brittle and ductile materials based on edge rotation and load control rotation axes are the crack front nodes and each crack front edge in surface discretizations affects the position of only one or two nodes modified positions of the entities maximize the mesh quality complying with the predicted crack path which depends on the specific propagation theory in use compared with xfem or with classical tip remeshing the proposed solution has algorithmic and generality advantages the propagation algorithm is simpler than the aforementioned alternatives and the approach is independent of the underlying element used for discretization for history dependent materials there are still some transfer of relevant quantities between elements however diffusion of results is more limited than with tip or full remeshing to illustrate the advantages of our approach three prototype models are used tip energy dissipation lefm cohesive zone approaches and ductile fracture both the sutton crack path criterion and the path estimated by the eshelby tensor are employed traditional fracture benchmarks including one with plastic hinges and newly proposed verification tests are solved these were found to be very good in terms of crack path and load deflection accuracy

on formation of a locally self similar collapse in the incompressible euler equations the paper addresses the question of the existence of a locally self similar blow up for the incompressible euler equations several exclusion results are proved based on the l p condition for velocity or vorticity and for a range of scaling exponents in particular in n dimensions if in self similar variables u in l p and u sim frac 1 t alpha 1 alpha then the blow up does not occur provided alpha n 2 or 1 alpha leq n p this includes the l 3 case natural for the navier stokes equations for alpha n 2 we exclude profiles with asymptotic power bounds of the form y n 1 delta lesssim u y lesssim y 1 delta solutions homogeneous near infinity are eliminated as well except when homogeneity is scaling invariant

an ale formulation based on spatial and material settings of continuum mechanics part 2 classification and applications abstract in the second paper of this two part contribution a specialisation towards neo hookean material will be made of the generic hyperelastic arbitrary lagrangian eulerian ale formulation derived in part 1 first for the sake of comparison and classification several existing ale solution schemes are discussed including total and updated approaches as well as monolithic and staggered algorithms then implementational details are provided for the newly proposed ale strategy the versality and the limitations of the present formulation are shown by means of a set of one dimensional and multi dimensional numerical examples in particular it is shown that with the proposed ale formulation potential energies can be obtained that are minimum for the considered topology

variational h adaption in finite deformation elasticity and plasticity we ropose a variational h adaption strategy in which the evolution of the mesh is driven directly by the governing minimum principle this minimum principle is the principle of minimum potential energy in the case of elastostatics and a minimum principle for the incremental static problem of elasto viscoplasticity in particular the mesh is refined locally when the resulting energy or incremental pseudo energy released exceeds a certain threshold value in order to avoid global recomputes we estimate the local energy released by mesh refinement by means of a lower bound obtained by relaxing a local patch of elements this bound can be computed locally which reduces the complexity of the refinement algorithm to o n we also demonstrate how variational h refinement can be combined with variational r refinement to obtain a variational hr refinement algorithm because of the strict variational nature of the h refinement algorithm the resulting meshes are anisotropic and outperform other refinement strategies based on aspect ratio or other purely geometrical measures of mesh quality the versatility and rate of convergence of the resulting approach are illustrated by means of selected numerical examples copyright 2007 john wiley sons ltd

a cauchy stress based solution for a necking elastic constitutive model under large deformation a finite element based method for solution of large deformation hyperelastic constitutive models is developed which solves the cauchy stress balance equation using a single rotation of stress from principal directions to a fixed co ordinate system features of the method include stress computation by central differencing of the hyperelastic energy function mixed integration order incompressibility enforcement and an iterative solution method that employs notional small strain stiffness the method is applied to an interesting and difficult elastic model that replicates polymer necking the method is shown to give good agreement with published results from a well established finite element package and with published experimental results it is shown that details of the manner in which incompressibility is enforced affects whether key experimental phenomena are clearly resolved copyright 2005 john wiley sons ltd

arbitrary lagrangian eulerian ale formulation for hyperelastoplasticity summary the arbitrary lagrangian eulerian ale description in nonlinear solid mechanics is nowadays standard for hypoelastic plastic models an extension to hyperelastic plastic models is presented here a fractional step method a common choice in ale analysis is employed for time marching every time step is split into a lagrangian phase which accounts for material effects and a convection phase where the relative motion between the material and the finite element mesh is considered in contrast to previous ale formulations of hyperelasticity or hyperelastoplasticity the deformed configuration at the beginning ofthe time step not the initial undef ormed configuration is chosen as the reference configuration as a consequence convecting variables is required in the description ofthe elastic response this is not the case in previous f were only the plastic response contains convection terms in exchange for the extra convective terms however the proposed ale approach has a major advantage only the quality ofthe mesh in the spatial domain must be ensured by the ale remeshing strategy in previous formulations it is also necessary to keep the distortion ofthe mesh in the material domain under control thus the f potential ofthe ale description as an adaptive technique can be exploited here these aspects are illustrated in detail by means ofthree numerical examples a necking test a coining test and a powder compaction test copyright c 2000 john wiley sons ltd

stability of nonlinear periodic internal waves in a deep stratified fluid stability of the nonlinear periodic solutions of the benjamin ono equation with respect to one dimensional perturbations and taking into account transverse modulations is analytically studied the full set of eigenfrequencies and of small perturbations is found in the one dimensional case the dispersion equation for long wave oblique perturbations is obtained these perturbations are shown to be unstable under either sign of the dispersion of the linear dispersion relation the instability limits and the maximum growth rates are determined in the extreme cases of strongly and weakly nonlinear waves

nonexistence of self similar singularities for the 3d incompressible euler equations we prove that there exists no self similar finite time blowing up solution to the 3d incompressible euler equations if the vorticity decays sufficiently fast near infinity in mathbb r 3 by a similar method we also show nonexistence of self similar blowing up solutions to the divergence free transport equation in mathbb r n this result has direct applications to the density dependent euler equations the boussinesq system and the quasi geostrophic equations for which we also show nonexistence of self similar blowing up solutions

on the self similar solutions of the 3d euler and the related equations we generalize and localize the previous results by the author on the study of self similar singularities for the 3d euler equations more specifically we extend the restriction theorem for the representation for the vorticity of the euler equations in a bounded domain and localize the results on asymptotically self similar singularities we also present progress towards relaxation of the decay condition near infinity for the vorticity of the blow up profile to exclude self similar blow ups the case of the generalized navier stokes equations having the laplacian with fractional powers is also studied we apply the similar arguments to the other incompressible flows e g the surface quasi geostrophic equations and the 2d boussinesq system both in the inviscid and supercritical viscous cases

on the optimum support size in meshfree methods a variational adaptivity approach with maximum entropy approximants we present a method for the automatic adaption of the support size of meshfree basis functions in the context of the numerical approximation of boundary value problems stemming from a minimum principle the method is based on a variational approach and the central idea is that the variational principle selects both the discretized physical fields and the discretization parameters here those defining the support size of each basis function we consider local maximum entropy approximation schemes which exhibit smooth basis functions with respect to both space and the discretization parameters the node location and the locality parameters we illustrate by the poisson linear and non linear elasticity problems the effectivity of the method which produces very accurate solutions with very coarse discretizations and finds unexpected patterns of the support size of the shape functions copyright 2009 john wiley sons ltd

a finite element framework for continua with boundary energies part iii the thermomechanical case abstract this paper in line with the previous works javili and steinmann 28 29 is concerned with the numerical implementation of boundary potential energies and the study of their impact on the deformations of solids thereby the main thrust in this contribution is the extension to thermomechanical effects although boundary effects can play a dominant role in material behavior the common modelling in continuum mechanics takes exclusively the bulk into account nevertheless neglecting possible contributions from the boundary in the approach of this contribution the boundary is equipped with its own thermodynamic life i e we assume separate boundary energy entropy and the like furthermore the generalized local balance laws are given according to javili and steinmann 30 afterwards the derivations of a generalized weak formulation including boundary potentials completely based on a tensorial representation are carried out which is employed for the discretization and finite element implementation eventually numerical examples are presented to demonstrate the boundary effects due to the proposed thermohyperelastic material model

an u ale formulation of 3 d unsteady viscoelastic flow the arbitrary lagrange euler ale formulation is applied to the analysis of unsteady viscoelastic flow of an upper convected maxwell ucm medium it is shown how the requirement of incremental objectivity affects the stress updating scheme the current implementation of the ale formulation uses the time discontinuous galerkin least squares td gls method to handle the advective parts of the equations further the ale formulation is compared with an updated ale formulation that is shown to give comparable results but is much more cost effective the technique presented is particularly effective for free surface flows three applications are given

generalized intermediate long wave hierarchy in zero curvature representation with noncommutative spectral parameter the simplest generalization of the intermediate long wave hierarchy ilw is considered to show how to extend the zakharov shabat dressing method to nonlocal i e integro partial differential equations the purpose is to give a procedure of constructing the zero curvature representation of this class of equations this result obtains by combining the drinfeld sokolov formalism together with the introduction of an operator valued spectral parameter namely a spectral parameter that does not commute with the space variable x this extension provides a connection between the ilwk hierarchy and the saveliev vershik continuum graded lie algebras in the case of ilw2 the fairlie zachos sinh algebra was found

a class of integro differential equations constrained from the kp hierarchy in this paper we give a class of integro differential evolution equations which generalizes the ilwk hierarchy we show the generalized lax pairs the bilinear representations and the rational and n soliton solutions for these integro differential equations we also give the hamiltonian formalism for the simplest set of equations among these integro differential equations which is the coupling of the ilw equation and the time dependent schrodinger equations

constraints of the kadomtsev petviashvili hierarchy for the kadomtsev petviashvili kp hierarchy constructed in terms of the famous sato theory a k constraint is proposed that leads the hierarchy to the nonlinear system involving a finite number of dynamical coordinates the eigenvalue problem of the k constrained system is naturally obtained from the linear system of the kp hierarchy which takes the form of kth order polynomial coupled with a first order one thus we are able to derive the correspondent lax pair recursion operator bi hamiltonian structures and conserved quantities the constraints for the bkp hierarchy are also sketched

global well posedness of the 2d boussinesq equations with fractional laplacian dissipation abstract as a continuation of the previous work 48 in this paper we focus on the cauchy problem of the two dimensional 2d incompressible boussinesq equations with fractional laplacian dissipation we give an elementary proof of the global regularity of the smooth solutions of the 2d boussinesq equations with a new range of fractional powers of the laplacian the argument is based on the nonlinear lower bounds for the fractional laplacian established in 13 consequently this result significantly improves the recent works 13 45 48

on the locally self similar solution of the surface quasi geostrophic equation with decaying or non decaying profiles motivated by the numerical simulation and the study on several 1d models we consider the locally self similar singular solutions for the surface quasi geostrophic equation with decaying or non decaying blowup profiles based on a suitable local lp inequality in terms of the profile and the bootstrapping method we show some exclusion results and derive the asymptotic behavior of the possible blowup profiles

tetrahedral composite finite elements we develop and analyse a composite ct3d tetrahedral element consisting of an ensemble of 12 four node linear tetrahedral elements coupled to a linear assumed deformation defined over the entire domain of the composite element the element is designed to have well defined lumped masses and contact tractions in dynamic contact problems while at the same time minimizing the number of volume constraints per element the relation between displacements and deformations is enforced weakly by recourse to the hu washizu principle the element arrays are formulated in accordance with the assumed strain prescription the formulation of the element accounts for fully non linear kinematics integrals over the domain of the element are computed by a five point quadrature rule the element passes the patch test in arbitrarily distorted configurations our numerical tests demonstrate that ct element has been found to possess a convergence rate comparable to those of linear simplicial elements and that these convergence rates are maintained as the near incompressible limit is approached we have also verified that the element satisfies the babuska brezzi condition for a regular mesh configuration these tests suggest that the ct3d element can indeed be used reliably in calculations involving near incompressible behaviour which arises e g in the presence of unconfined plastic flow

global regularity for the 2d boussinesq equations with partial viscosity terms abstract in this paper we prove the global in time regularity for the 2d boussinesq system with either the zero diffusivity or the zero viscosity we also prove that as diffusivity viscosity tends to zero the solutions of the fully viscous equations converge strongly to those of zero diffusion viscosity equations our result for the zero diffusion system in particular solves the problem no 3 posed by moffatt in r l ricca ed kluwer academic publishers dordrecht the netherlands 2001 pp 3 10

arbitrary lagrangian eulerian finite element analysis of strain localization in transient problems non local models guaranty that finite element computations on strain softening materials remain sound up to failure from a theoretical and computational viewpoint the non locality prevents strain localization with zero global dissipation of energy and consequently finite element calculations converge upon mesh refinements to non zero width localization zones one of the major drawbacks of these models is that the element size needed in order to capture the localization zone must be smaller than the internal length hence the total number of degrees of freedom becomes rapidly prohibitive for most engineering applications and there is an obvious need for mesh adaptivity this paper deals with the application of the arbitrary lagrangian eulerian ale formulation well known in hydrodynamics and fluid structure interaction problems to transient strain localization in a non local damageable material it is shown that the ale formulation which is employed in large boundary motion problems can also be well suited for non linear transient analysis of softening materials where localization bands appear the remeshing strategy is based on the equidistribution of an indicator that quantifies the interelement jump of a selected state variable two well known one dimensional examples illustrate the capabilities of this technique the first one deals with localization due to a propagating wave in a bar and the second one studies the wave propagation in a hollow sphere

goal oriented r adaptivity based on variational arguments in the physical and material spaces abstract the error in a local quantity of interest depends on the error in the corresponding dual solution or generalized green s function this fact is used in dual weighted based goal oriented error estimation techniques and h or p adaptive algorithms this contribution is concerned with a novel approach for goal oriented r adaptivity based on energy minimization principles for the primal and the dual problems the minimization of the energy of the primal problem as well as the minimization of the energy of the dual problem with respect to a design function lead to the primal and dual material residuals respectively these residuals are error indicators for the discretization error on the current mesh we propose a goal oriented mesh optimization algorithm which ends in an optimized mesh with respect to a chosen quantity of interest by means of selected computational examples we demonstrate the capability of the proposed framework

material forces in open system mechanics the basic concern of the present work is the exploitation of the notion of material forces in the theoretical and computational analysis of open systems with particular application to biomechanical problems based on a completely dual framework for the spatial and the material motion problem we introduce the balance equations for open system thermodynamics in combination with the appropriate constitutive equations they constitute the basis of the finite element formulation derived thereafter for the spatial motion problem the solution of the governing equations basically the balance of mass and momentum renders the discrete nodal values of the density and the deformation as primary unknowns for the material motion problem the computational analysis of the balance of momentum yields the discrete material node point forces which can be interpreted as driving forces for the local rearrangement of material inhomogeneities once the spatial motion problem has been solved the material force method is nothing but a mere post processing step from an algorithmic point of view as a convincing benefit of the proposed strategy the computation of the material forces is extremely cheap and requires no additional finite element data structure in the context of biomechanics material forces give further insight into complex biomechanically induced processes such as functional adaption morphogenesis healing or growth for example material forces on the boundary can be considered as a measure of shape sensitivity and thus indicate morphological changes while material forces in the interior indicate the tendency to create new mass locally or to equilibrate local density inhomogeneities

an arbitrary lagrangian eulerian finite element approach for fluid structure interaction phenomena the present contribution is concerned with the design of a family of consistent fluid structure interaction algorithms based on a unique temporal and spatial discretization of the governing equations the characterization of the moving fluid structure interface is realized by means of the arbitrary lagrangian eulerian technique the spatial discretization is performed with the finite element method whereby either a first order upwind scheme or the classical second order upwind petrov galerkin technique are used to discretize the linearized fluid equations while the standard bubnov galerkin method is applied to the structural equations in order to streamline coupling the structure is discretized in a velocity based fashion the temporal discretization of both the fluid and the structural equations is embedded in the generalized framework by making use of classical newmark approximations in time to quantify the sources of error of the proposed algorithms systematic studies in terms of the one dimensional piston model problem are presented copyright 2003 john wiley sons ltd

multi scale expansions in the theory of systems integrable by the inverse scattering transform abstract it is shown that using multi scale expansions conventionally employed in the theory of nonlinear waves one can transform systems integrable by the ist method into other systems of this type

generalized internal long waves equations construction hamiltonian structure and conservation laws a general class of the ilw type equations is constructed we introduce a hamiltonian structure and construct an infinite number of conservation laws

a new unconditionally stable fractional step method for non linear coupled thermomechanical problems a new class of time stepping algorithms for strongly coupled thermomechanical problems is presented which retains the computational convenience of traditional staggered algorithms without upsetting the unconditional stability property characteristic of fully implicit monolithic schemes 11 the proposed schemes are fractional step methods associated with a two phase operator split of the full non linear system of thermoelasticity into an adiabatic elastodynamics phase followed by a heat conduction phase at fixed configuration this operator split is shown to inherit the contractivity property of the full problem of evolution thus leading to unconditionally b stable product formula algorithms in sharp contrast with this stability result traditional staggered algorithms based on an isothermal mechanical phase followed by a heat conduction phase with an effective heat source are shown to lead at best to conditionally stable schemes it is further shown that the actual implementation of these two classes of schemes is essentially identical the numerical simulations presented include both dynamic and quasi static problems and are shown to closely replicate the stability estimates and non linear stability results derived for these two classes of staggered schemes

global well posedness for a class of 2d boussinesq systems with fractional dissipation abstract the incompressible boussinesq equations not only have many applications in modeling fluids and geophysical fluids but also are mathematically important the well posedness and related problem on the boussinesq equations have recently attracted considerable interest this paper examines the global regularity issue on the 2d boussinesq equations with fractional laplacian dissipation and thermal diffusion attention is focused on the case when the thermal diffusion dominates we establish the global well posedness for the 2d boussinesq equations with a new range of fractional powers of the laplacian

nonlocal integrable partners to generalized mkdv and two dimensional toda lattice equation in the formalism of a dressing method with quantized spectral parameter two new hierarchies milw2 and a two dimensional nonlocal toda lattice are constructed the characteristic property of the first one is the connection with the ilw2 hierarchy by means ofgl 2 miura transformation on the other hand milw2 equations turn out to be symmetry equations for a two dimensional nonlocal toda lattice a new version of the dressing technique with quantized spectral parameter is proposed

a new computational model for tresca plasticity at finite strains with an optimal parametrization in the principal space abstract a new computational model for the rate independent elasto plastic solids characterized by yield surfaces containing singularities and general nonlinear isotropic hardening is presented within the context of fully implicit return mapping algorithms a numerical scheme for integration of the constitutive equations is formulated in the space of principal stresses as a direct consequence of the principal stress approach the representation of a yield surface is cast in terms of optimal parameterization which for the tresca yield criterion takes a simple linear form the associated return mapping equations then reduce to a remarkably simple format in addition due to assumed isotropy of the models the associated algorithmic incremental constitutive functionals can be identified as particular members of a class of isotropic tensor functions of one tensor in which the function eigenvalues are expressed in terms of the eigenvalues of the argument this observation leads to a simple closed form derivation of the consistent tangent moduli associated with the described integration algorithms the extension of the present model to finite strains is carried out following standard multiplicative plasticity described in terms of logarithmic stretches and exponential approximation to the flow rule the efficiency and robustness of the computational model are illustrated on a range of numerical examples

an arbitrary lagrangian eulerian finite element method for finite strain plasticity this paper presents a new arbitrary lagrangian eulerian ale finite element formulation for finite strain plasticity in non linear solid mechanics we consider the models of finite strain plasticity defined by the multiplicative decomposition of the deformation gradient in an elastic and a plastic part f fefp with the stresses given by a hyperelastic relation in contrast with more classical ale approaches based on plastic models of the hypoelastic type the ale formulation presented herein considers the direct interpolation of the motion of the material with respect to the reference mesh together with the motion of the spatial mesh with respect to this same reference mesh this aspect is shown to be crucial for a simple treatment of the advection of the plastic internal variables and dynamic variables in fact this advection is carried out exactly through a particle tracking in the reference mesh a calculation that can be accomplished very efficiently with the use of the connectivity graph of the fixed reference mesh a staggered scheme defined by three steps the smoothing the advection and the lagrangian steps leads to an efficient method for the solution of the resulting equations we present several representative numerical simulations that illustrate the performance of the newly proposed methods both quasi static and dynamic conditions are considered in these model examples copyright 2003 john wiley sons ltd