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

subdivision surfaces a new paradigm for thin shell finite element analysis we develop a new paradigm for thin shell finite element analysis based on the use of subdivision surfaces for i describing the geometry of the shell in its undeformed configuration and ii generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the kirchhoff love theory of thin shells the particular subdivision strategy adopted here is loop s scheme with extensions such as required to account for creases and displacement boundary conditions the displacement fields obtained by subdivision are h2 and consequently have a finite kirchhoff love energy the resulting finite elements contain three nodes and element integrals are computed by a one point quadrature the displacement field of the shell is interpolated from nodal displacements only in particular no nodal rotations are used in the interpolation the interpolation scheme induced by subdivision is non local i e the displacement field over one element depend on the nodal displacements of the element nodes and all nodes of immediately neighbouring elements however the use of subdivision surfaces ensures that all the local displacement fields thus constructed combine conformingly to define one single limit surface numerical tests including the belytschko et al 10 obstacle course of benchmark problems demonstrate the high accuracy and optimal convergence of the method

strain driven homogenization of inelastic microstructures and composites based on an incremental variational formulation the paper investigates computational procedures for the treatment of a homogenized macro continuum with locally attached micro structures of inelastic constituents undergoing small strains the point of departure is a general internal variable formulation that determines the inelastic response of the constituents of a typical micro structure as a generalized standard medium in terms of an energy storage and a dissipation function consistent with this type of inelasticity we develop a new incremental variational formulation of the local constitutive response where a quasi hyperelastic micro stress potential is obtained from a local minimization problem with respect to the internal variables it is shown that this local minimization problem determines the internal state of the material for finite increments of time we specify the local variational formulation for a setting of smooth single surface inelasticity and discuss its numerical solution based on a time discretization of the internal variables the existence of the quasi hyperelastic stress potential allows the extension of homogenization approaches of elasticity to the incremental setting of inelasticity focusing on macro strain driven micro structures we develop a new incremental variational formulation of the global homogenization problem where a quasi hyperelastic macro stress potential is obtained from a global minimization problem with respect to the fine scale displacement fluctuation field it is shown that this global minimization problem determines the state of the micro structure for finite increments of time we consider three different settings of the global variational problem for prescribed linear displacements periodic fluctuations and constant stresses on the boundary of the micro structure and discuss their numerical solutions based on a spatial discretization of the fine scale displacement fluctuation field the performance of the proposed methods is demonstrated for the model problem of von mises type elasto visco plasticity of the constituents and applied to a comparative study of micro to macro transitions of inelastic composites copyright 2002 john wiley sons ltd

error estimation and adaptive meshing in strongly nonlinear dynamic problems we present work aimed at developing a general framework for mesh adaption in strongly nonlinear possibly dynamic problems we begin by showing that the solutions of the incremental boundary value problem for a wide class of materials including nonlinear elastic materials compressible newtonian fluids and viscoplastic solids obey a minimum principle provided that the constitutive updates are formulated appropriately this minimum principle can be taken as a basis for asymptotic error estimation in particular we chose to monitor the error of a lower order projection of the finite element solution the optimal mesh size distribution then follows from a posteriori error indicators which are purely local i e can be computed element by element we demonstrate the robustness and versatility of the computational framework with the aid of convergence studies and selected examples of application

a reduction theorem for highest weight modules over toroidal lie algebras let open image in new window be a toroidal lie algebra corresponding to a semisimple lie algebra open image in new window we describe all borel subalgebras of open image in new window which contain the cartan subalgebra open image in new window where open image in new window is a fixed cartan subalgebra of open image in new window we show that each such borel subalgebra open image in new window determines a parabolic decomposition open image in new window where open image in new window is a proper toroidal subalgebra of open image in new window and open image in new window our first main result is that for any weight which does not vanish on open image in new window an arbitrary subquotient of the verma module open image in new window is induced from its open image in new window submodule of open image in new window invariant vectors this reduces the study of subquotients of open image in new window to the study of subquotients of verma modules over open image in new window we then introduce categories open image in new window and open image in new window and their respective blocks open image in new window and open image in new window corresponding to a central charge which is nonzero on open image in new window our second main result is that the functors of induction and open image in new window invariants are mutually inverse equivalences of the category open image in new window and the full subcategory of open image in new window whose objects are generated by their open image in new window invariants

langlands duality for representations and quantum groups at a root of unity we give a representation theoretic interpretation of the langlands character duality of fh and show that the langlands branching multiplicities for symmetrizable kac moody lie algebras are equal to certain tensor product multiplicities for finite type quantum groups the connection with tensor products can be explained in terms of tilting modules

ale method for solidification modelling abstract in this paper an arbitrary lagrangian eulerian ale formulation has been developed for the simulation of casting processes the method is applied both to mould filling simulation where it can provide accurate free surface description and to the study of thermo mechanical phenomena occurring in the subsequent cooling down of cast parts prediction of solute transport and of distortions and stresses in the first three sections all governing equations constitutive equations momentum energy solute transport are given then the ale formulation is presented mesh updating with evolving free surfaces using conservative normal vectors to enforce mass conservation treatment of advection terms using an original nodal upwind method definition of lagrangian and eulerian lagrangian regions finally examples of applications are given

finite element model of ionic nanowires with size dependent mechanical properties determined by ab initio calculations a finite element procedure for modeling crystalline nanostructures such as nanowires is proposed the size effects exhibited by nano objects are captured by taking into account a surface energy following the classical gurtin murdoch surface elasticity theory an appropriate variational form and a finite element approach are provided to model and solve relevant problems numerically we describe a simplified technique based on projection operators for constructing the surface elements the methodology is completed with a computational procedure based on ab initio calculations to extract elastic coefficients of general anisotropic surfaces the fem continuum model is validated by comparisons with complete ab initio models of nanowires with different diameters where size dependent mechanical properties are observed the fem continuum model can then be used to model similar nanostructures in ranges of sizes or geometries where analytical or atomistic model are limited the validated model is applied to the analysis of size effects in the bending of an aln nanowire

quasiconvexity and relaxation of nonconvex problems in the calculus of variations keywords quasiconvexity relaxation reference caa article 1982 002doi 10 1016 0022 1236 82 90046 5view record in web of science record created on 2008 11 25 modified on 2017 05 12

the t analogs of q characters at roots of unity for quantum affine algebras and beyond abstract the q characters were introduced by frenkel and reshetikhin the q characters of representations of quantum affine algebras and deformations of w algebras in recent developments in quantum affine algebras and related topics in contemp math vol 248 amer math soc providence ri 1999 pp 163 205 to study finite dimensional representations of the untwisted quantum affine algebra u q g for q generic the e characters at roots of unity were constructed by frenkel and mukhin the q characters at roots of unity adv math 171 1 2002 139 167 to study finite dimensional representations of various specializations of u q g at q s 1 in the finite simply laced case nakajima t analogue of the q characters of finite dimensional representations of quantum affine algebras in physics and combinatorics proc nagoya 2000 internat workshop world scientific singapore 2001 pp 181 212 quiver varieties and t analogs of q characters of quantum affine algebras ann of math in press preprint arxiv math qa 0105173 defined deformations of q characters called q t characters for q generic and also at roots of unity the definition is combinatorial but the proof of the existence uses the geometric theory of quiver varieties which holds only in the simply laced case in algebraic approach to q t characters adv math in press preprint arxiv math qa 0212257 we proposed an algebraic general non necessarily simply laced new approach to q t characters for q generic in this paper we propose two developments of this approach we treat the root of unity case and the case of a larger class of generalized cartan matrices including finite and affine cases except a 1 1 a 2 2 in particular we generalize the construction of analogs of kazhdan lusztig polynomials at roots of unity of h nakajima quiver varieties and t analogs of q characters of quantum affine algebras ann of math in press preprint arxiv math qa 0105173 to those cases we also study properties of various objects used in this article deformed screening operators at roots of unity t deformed polynomial algebras bicharacters arising from symmetrizable cartan matrices deformation of the frenkel mukhin s algorithm

evaluation representations of quantum affine algebras at roots of unity the purpose of this paper is to compute the drinfel d polynomials for two types of evaluation representations of quantum affine algebras at roots of unity and construct those representations as the submodules of evaluation schnizer modules moreover we obtain the necessary and sufficient condition for that the two types of evaluation representations are isomorphic to each other

multiresolution molecular mechanics atomistic continuum coupling methods combine accurate atomistic methods and efficient continuum methods to simulate the behavior of highly ordered crystalline systems coupled methods utilize the advantages of both approaches to simulate systems at a lower computational cost while retaining the accuracy associated with atomistic methods many concurrent atomistic continuum coupling methods have been proposed in the past however their true computational efficiency has not been demonstrated the present work presents an efficient implementation of a concurrent coupling method called the multiresolution molecular mechanics mmm for serial parallel and adaptive analysis first we present the features of the software implemented along with the associated technologies the scalability of the software implementation is demonstrated and the competing effects of multiscale modeling and parallelization are discussed then the algorithms contributing to the efficiency of the software are presented these include algorithms for eliminating latent ghost atoms from calculations and measurement based dynamic balancing of parallel workload the efficiency improvements made by these algorithms are demonstrated by benchmark tests the efficiency of the software is found to be on par with lammps a state of the art molecular dynamics md simulation code when performing full atomistic simulations speed up of the mmm method is shown to be directly proportional to the reduction of the number of the atoms visited in force computation finally an adaptive mmm analysis on a nanoindentation problem containing over a million atoms is performed yielding an improvement of 6 3 8 5 times in efficiency over the full atomistic md method for the first time the efficiency of a concurrent atomistic continuum coupling method is comprehensively investigated and demonstrated

multiresolution molecular mechanics surface effects in nanoscale materials abstract surface effects have been observed to contribute significantly to the mechanical response of nanoscale structures the newly proposed energy based coarse grained atomistic method multiresolution molecular mechanics mmm yang to 2015 57 is applied to capture surface effect for nanosized structures by designing a surface summation rule sr s within the framework of mmm combined with previously proposed bulk summation rule sr b the mmm summation rule sr mmm is completed sr s and sr b are consistently formed within sr mmm for general finite element shape functions analogous to quadrature rules in finite element method fem the key idea to the good performance of sr mmm lies in that the order or distribution of energy for coarse grained atomistic model is mathematically derived such that the number position and weight of quadrature type sampling atoms can be determined mathematically the derived energy distribution of surface area is different from that of bulk region physically the difference is due to the fact that surface atoms lack neighboring bonding as such sr s and sr b are employed for surface and bulk domains respectively two and three dimensional numerical examples using the respective 4 node bilinear quadrilateral 8 node quadratic quadrilateral and 8 node hexahedral meshes are employed to verify and validate the proposed approach it is shown that mmm with sr mmm accurately captures corner edge and surface effects with less 0 3 degrees of freedom of the original atomistic system compared against full atomistic simulation the effectiveness of sr mmm with respect to high order element is also demonstrated by employing the 8 node quadratic quadrilateral to solve a beam bending problem considering surface effect in addition the introduced sampling error with sr mmm that is analogous to numerical integration error with quadrature rule in fem is very small

verma type modules of level zero for affine lie algebras we study the structure of verma type modules of level zero induced from non standard borel subalgebras of an affine kac moody algebra for such modules in general position we describe the unique irreducible quotients construct a bgg type resolution and prove the bgg duality in certain categories all results are extended to generalized verma type modules of zero level

an arbitrary lagrangian eulerian σ ales model with non hydrostatic pressure for shallow water flows abstract an arbitrary lagrangian eulerian model in the coordinate system ales is developed for shallow water flows based on the unsteady reynolds averaged navier stokes equations unlike the conventional coordinate system non hydrostatic pressure is incorporated and the effect of a moving free surface included giving a general scheme the standard k turbulence model is used to calculate the eddy viscosity wave flows over bars are appropriate test cases for which experimental data are available and comparisons are favourable the model is also applied to the important practical problem of wave and wave current flows over a trench for which experimental data are available only for the steady current alone case the inclusion of vertical grid velocity has negligible effect on computational efficiency the solution of poisson s equation for non hydrostatic pressure at each time step is solved efficiently by the conjugate gradient method but represents the main component of computer time the model may readily be extended to three dimensions

plane bias extension test for a continuum with two inextensible families of fibers a variational treatment with lagrange multipliers and a perturbation solution in the present paper a system constituted by two families of nearly inextensible fibers is studied the interest towards this kind of structures which can be suitably modeled by 2d continua with inextensible curves comes form both theoretical and applicative motivations indeed the advantageous weight strength ratio and the particularly safe behavior in fractures make them attractive in many engineering fields while the mechanical properties displayed by them are theoretically interesting and still not well understood in full generality we focused on dead loading traction boundary value problems assuming particular forms for the deformation energy associated to every node of the structure the main result of the paper consists in the determination of the nonlinear integral equations describing fibers directions for a specific class of deformation energies a perturbative analysis of a particular solution is also performed and some physical justification for one of the considered forms for the energy density are provided in the appendix

irreducible representations for toroidal lie algebras abstract in this work a large number of irreducible representations with finite dimensional weight spaces are constructed for some toroidal lie algebras to accomplish this we develop a general theory of z n graded lie algebras with polynomial multiplication we construct modules by the standard inducing procedure and study their irreducible quotients using the vertex operator technics

finite dimensional representations of quantum affine algebras at roots of unity we describe explicitly the canonical map x spec ue b spec ze where u b is a quantum loop algebra at an odd root of unity e here ze is the center of ue g and spec r stands for the set of all finite dimensional irreducible representations of an algebra r we show that spec z is a poisson proalgebraic group which is essentially the group of points of g over the regular adeles concentrated at 0 and oo our main result is that the image under x of spec u b is the subgroup of principal adeles department of mathematics harvard university cambridge massachusetts 02138 e mail address beckfmath harvard edu department of mathematics massachusetts institute of technology cambridge massachusetts 02139 e mail address kacimath mit edu this content downloaded from 207 46 13 124 on wed 22 jun 2016 06 11 29 utc all use subject to http about jstor org terms

a fictitious energy approach for shape optimization this paper deals with shape optimization of continuous structures as in early works on shape optimization coordinates of boundary nodes of the fe domain are directly chosen as design variables convergence problems and problems with jagged shapes are eliminated by a new regularization technique an artificial inequality constraint added to the optimization problem limits a fictitious total strain energy that measures the shape change of the design with respect to a reference design the energy constraint defines a feasible design space whose size can be varied by one parameter the upper energy limit by construction the proposed regularization is applicable to a wide range of problems although in this paper the application is restricted to linear elastostatic problems

global convergence properties of conjugate gradient methods for optimization this paper explores the convergence of nonlinear conjugate gradient methods without restarts and with practical line searches the analysis covers two classes of methods that are globally convergent on smooth nonconvex functions some properties of the fletcher reeves method play an important role in the first family whereas the second family shares an important property with the polak ribiere method numerical experiments are presented

borel subalgebras and categories of highest weight modules for toroidal lie algebras abstract in this article we begin an investigation of the conjugacy classes of borel subalgebras together with verma modules induced from standard borel subalgebras of a toroidal lie algebra t in two variables we define for each highest weight a category o of representations of t that contain these verma modules and show that when a certain central element acts nontrivially this category is equivalent to the category o m for an extension of a suitable affine kac moody algebra m t from this equivalence we obtain a bgg type resolution and bgg duality theorem in the setting of o

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 continuum model for the mechanical behavior of nanowires including surface and surface induced initial stresses the continuum modeling of the mechanical behavior of nanowires has recently attracted much attention due to its simplicity and efficiency however there are still some critical issues to be solved in this paper we demonstrate the importance of accounting for the effects of initial stresses in the nanowires that are caused by deformation due to surface stresses we note that such initial stresses have previously been neglected in most existing continuum models by considering the local geometrical nonlinearity of strains during the incremental flexural motion a new formulation of the euler bernoulli beam model for nanowires is developed through the incremental deformation theory in which effects of the surface stress the surface induced initial stress and surface elasticity are naturally incorporated it is found through comparisons to existing experimental and computational results for both fcc metal and ceramic nanowires that the surface induced initial stresses which are neglected in the young laplace model can significantly influence the overall mechanical properties of nanowires we additionally demonstrate and quantify the errors induced by using the young laplace model due to its approximation of surface stresses acting on only the top and bottom surfaces of nanowires

on the limited memory bfgs method for large scale optimization we study the numerical performance of a limited memory quasi newton method for large scale optimization which we call the l bfgs method we compare its performance with that of the method developed by buckley and lenir 1985 which combines cycles of bfgs steps and conjugate direction steps our numerical tests indicate that the l bfgs method is faster than the method of buckley and lenir and is better able to use additional storage to accelerate convergence we show that the l bfgs method can be greatly accelerated by means of a simple scaling we then compare the l bfgs method with the partitioned quasi newton method of griewank and toint 1982a the results show that for some problems the partitioned quasi newton method is clearly superior to the l bfgs method however we find that for other problems the l bfgs method is very competitive due to its low iteration cost we also study the convergence properties of the l bfgs method and prove global convergence on uniformly convex problems

the convergence properties of some new conjugate gradient methods abstract in this paper a new conjugate gradient formula k is given to compute the search directions for unconstrained optimization problems general convergence results for the proposed formula with some line searches such as the exact line search the wolfe powell line search and the grippo lucidi line search are discussed under the above line searches and some assumptions the global convergence properties of the given methods are discussed the given formula k 0 and has the similar form with k prp preliminary numerical results show that the proposed methods are efficient

a framework for creating low order shell elements free of membrane locking summary this paper proposes a first step towards a framework to develop shell elements applicable to any deformation regime here we apply it to the large and moderate deformations of respectively plates and shells showing with standard benchmarks that the resulting low order discretization is competitive against the best elements for either membrane dominated or bending dominated scenarios additionally we propose a new test for measuring membrane locking which highlights the mesh independence properties of our element our strategy is based on building a discrete model that mimics the smooth behavior by construction rather than discretizing a smooth energy the proposed framework consists of two steps i defining a discrete kinematics by means of constraints and ii formulating an energy that vanishes on such a constraint manifold we achieve i by considering each triangle as a tensegrity structure constructed to be unstretchable but bendable isometrically in a discrete sense we then present a choice for ii based on assuming a linear strain field on each triangle using tools from differential geometry for coupling the discrete membrane energy with our locking free kinematic description we argue that such a locking free element is only a member of a new family that can be created using our framework i and ii copyright 2016 john wiley sons ltd

geometry of the analytic loop group abstract we introduce and study a notion of analytic loop group with a riemann hilbert factorization relevant for the representation theory of quantum affine algebras at roots of unity u g with non trivial central charge we introduce a poisson structure and study properties of its poisson dual group we prove that the hopf poisson structure is isomorphic to the semi classical limit of the center of u g it is a geometric realization of the center then the symplectic leaves and corresponding equivalence classes of central characters of u g are parameterized by certain g bundles on an elliptic curve

error estimates and convergence rates for various incompressible elements this note reports numerical experiments on the efficiency of simple error estimates derived earlier1 applied to incompressible mixed or related penalty type formulations the rate of convergence and performance of various mixed elements is compared numerical results from a driven cavity and an incompressible elastic problem demonstrate that the t6b1 3d and t6 3c elements give a faster rate of convergence than the t6 1d element however in the case of a plane extrusion analysis stronger singularity the rate of convergence for the t6b1 3d element drops and is inferior to that of the t6 1d while the t6 3c element still proves superior to the other two elements

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

theory and finite element formulation of rubberlike membrane shells using principal stretches a theory of rubberlike membrane shells undergoing large elastic deformations is derived the stresses are deduced from ogden s material law which is formulated in terms of the principal values of the right stretch tensor incompressibility is fulfilled exactly using the plane stress constraint furthermore a finite element formulation of the membrane theory is given the use of the tangential stiffness matrix derived analytically provides a quadratically convergent solution process several numerical examples show the robustness of the developed finite element

arbitrary lagrangian eulerian finite element analysis of free surface flow using a velocity vorticity formulation this paper describes the application of velocity vorticity formulation of the navier stokes equations for two dimensional free surface flow using an arbitrary lagrangian eulerian method the velocity poisson equations and the vorticity transport equations are solved using a finite element method to obtain the velocity and the vorticity fields in the interior region of the computational domain the boundary fitted coordinates system is adopted to solve the boundary equations for kinematic and dynamic conditions at the free surface using a finite difference method the numerical model for the velocity vorticity formulation is validated for a square cavity flow at re 400 and 1000 the solitary wave reflected from a vertical wall is chosen as a test case for comparison and validation of the free surface flow model then the proposed numerical model is used to obtain flow results for the following free surface flow cases i interaction between two opposite solitary waves ii seiche phenomenon in a rectangular reservoir and iii solitary wave through a submerged rectangular structure in a viscous fluid the efficiency of the present numerical model for numerical treatment of free surface flows is discussed furthermore the advantage of this formulation with respect to primitive variables formulation is addressed from the computational point of view

a fictitious domain approach for a mixed finite element method solving the two phase stokes problem with surface tension forces abstract in this article we study a mixed finite element formulation for solving the stokes problem with general surface forces that induce a jump of the normal trace of the stress tensor on an interface that splits the domain into two subdomains equality of velocities is assumed at the interface the interface conditions are taken into account with multipliers a suitable lagrangian functional is introduced for deriving a weak formulation of the problem a specificity of this work is the consideration of the interface with a fictitious domain approach the latter is inspired by the xfem approach in the sense that cut off functions are used but it is simpler to implement since no enrichment by singular functions is provided in that context getting convergence for the dual variables defined on the interface is non trivial for that purpose an augmented lagrangian technique stabilizes the convergence of the multipliers which is important because their value would determine the dynamics of the interface in an unsteady framework theoretical analysis is provided where we show that a discrete inf sup condition independent of the mesh size is satisfied for the stabilized formulation this guarantees optimal convergence rates that we observe with numerical tests the capacity of the method is demonstrated with robustness tests and with an unsteady model tested for deformations of the interface that correspond to ellipsoidal shapes in dimension 2

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

anisotropic membrane wrinkling theory and analysis abstract a complete theory of wrinkling of anisotropic elastic membranes is presented based on the notion of relaxed energy function the theory is obtained as a particular case of a general theory of saturated elasticity it is shown that when any given hyperelastic constitutive law is supplemented with a saturation condition the right cauchy green strain tensor abides by an additive decomposition law governed by a normality rule for the case of wrinkling these results are implemented into a numerical procedure and examples are presented

a computational framework for free surface fluid flows accounting for surface tension abstract this work is concerned with the simulation of incompressible newtonian fluid flow problems with free surfaces in the presence of surface tension the computational framework presented is based on the stabilised velocity pressure finite element method the movement and deformation of the computational domain are accounted for by employing the arbitrary lagrangian eulerian ale description of the fluid kinematics the numerical model is extended to incorporate surface tension effects a novel partitioned solution procedure is developed based on the newton raphson methodology which incorporates full linearisation of the overall incremental problem several numerical examples are provided to demonstrate the efficiency of the methodology

non convex potentials and microstructures in finite strain plasticity a mathematical model for a finite strain elastoplastic evolution problem is proposed in which one time step of an implicit time discretization leads to generally non convex minimization problems the elimination of all internal variables enables a mathematical and numerical analysis of a reduced problem within the general framework of calculus of variations and nonlinear partial differential equations the results for a single slip system and von mises plasticity illustrate that finite strain elastoplasticity generates reduced problems with non quasiconvex energy densities and so allows for non attainment of energy minimizers and microstructures

a novel variational algorithmic formulation for wrinkling at finite strains based on energy minimization application to mesh adaption this paper is concerned with an efficient novel algorithmic formulation for wrinkling at finite strains in contrast to previously published numerical implementations the advocated method is fully variational more precisely the parameters describing wrinkles or slacks together with the unknown deformation mapping are computed jointly by minimizing the potential energy of the considered mechanical system furthermore the wrinkling criteria are naturally included within the presented variational framework the proposed method allows to employ three dimensional constitutive models without any additional modification i e a projection in plane stress space is not required analogously to the wrinkling parameters the non vanishing out of plane component of the strain tensor results conveniently from relaxing the respective helmholtz energy of the membrane the proposed framework is very general and does not rely on any assumption regarding the symmetry of the material i e arbitrary anisotropic hyperelastic models can be consistently taken into account the advantages associated with such a variational method are manifold for instance it opens up the possibility of applying standard optimization algorithms to the numerical implementation this is especially important for highly non linear or singular problems such as wrinkling on the other hand minimization principles provide a suitable basis for a posteriori error estimation and thus for adaptive finite element formulations as a prototype a variational error indicator leading to an efficient h adaption for wrinkling is briefly discussed the performance of the wrinkling approach is demonstrated by selected finite element analyses

a variational formulation for finite deformation wrinkling analysis of inelastic membranes this paper is concerned with a novel fully variational formulation for finite deformation analysis of inelastic membranes with wrinkling in contrast to conventional approaches every aspect of the physical problem derives from minimization of suitable energy functionals a variational formulation of finite strain plasticity theory which leads to a minimization problem for the constitutive updates serves as the starting point for the derivations in order to take into account the kinematics induced by wrinkles and slacks a relaxed version of the finite strain functional is postulated in effect the local incremental stress strain relations are established via differentiation of the relaxed energy functional with respect to the strains hence the presented formulation is fully analogous to that of hyperelasticity with the sole exception that the aforementioned functional depends on history variables and accordingly it is path dependent the advantages associated with the developed variational method are manifold from a practical point of view the possibility of applying standard optimization algorithms to solve the minimization problem describing inelastic membranes is remunerative from a mathematical point of view on the other hand the energy of the system induces some sort of natural metric representing an essential requirement for error estimation and thus for adaptive finite element methods the presented derivation of the model allows to consider possible material symmetries in the elastic as well as plastic response of the material as a prototype a von mises type model is implemented the efficiency and performance of the resulting algorithm are demonstrated by means of numerical examples

a computational formulation for constrained solid and liquid membranes considering isogeometric finite elements abstract a geometrically exact membrane formulation is presented that is based on curvilinear coordinates and isogeometric finite elements and is suitable for both solid and liquid membranes the curvilinear coordinate system is used to describe both the theory and the finite element equations of the membrane in the latter case this avoids the use of local cartesian coordinates at the element level consequently no transformation of derivatives is required the formulation considers a split of the in plane and out of plane membrane contributions which allows the construction of a stable formulation for liquid membranes with constant surface tension the proposed membrane formulation is general and accounts for dead and live loading as well as enclosed volume area and contact constraints the new formulation is illustrated by several challenging examples considering linear and quadratic lagrange elements as well as isogeometric elements based on quadratic nurbs and cubic t splines it is seen that the isogeometric elements are much more accurate than standard lagrange elements the gain is especially large for the liquid membrane formulation since it depends explicitly on the surface curvature

a continuum method for modeling surface tension abstract a new method for modeling surface tension effects on fluid motion has been developed interfaces between fluids of different properties or colors are represented as transition regions of finite thickness across which the color variable varies continuously at each point in the transition region a force density is defined which is proportional to the curvature of the surface of constant color at that point it is normalized so that the conventional description of surface tension on an interface is recovered when the ratio of local transition region thickness to local radius of curvature approaches zero the continuum method eliminates the need for interface reconstruction simplifies the calculation of surface tension enables accurate modeling of two and three dimensional fluid flows driven by surface forces and does not impose any modeling restrictions on the number complexity or dynamic evolution of fluid interfaces having surface tension computational results for two dimensional flows are given to illustrate the properties of the method

convexity conditions for strain dependent energy functions for membranes the forms that the convexity polyconvexity and rank one convexity inequalities take when the strain energy is required to be a function of the strain g are studied it is shown in particular that w g must be an increasing function of g in the sense that w g w g if g g is non negative definite relatively simple sufficient conditions in terms of g alone are given necessary and sufficient conditions in terms of g alone are found to be rather complex

a new class of unitarizable highest weight representations of infinite dimensional lie algebras ii on donne les details rigoureux pour le probleme de classification on redemontre l unitarite de la representation exceptionnelle on considere les produits tensoriels et les problemes d integrabilite

on the discrete variant of the traction method in parameter free shape optimization abstract one of the major challenges in the parameter free approach to computational shape optimization is the avoidance of oscillating i e non smooth boundaries in the optimal design trials in order to achieve this we investigate a method for regularization that corresponds to the discrete variant of the so called traction method in this approach the design updates are generated in terms of a displacement field which is obtained as the solution to an auxiliary boundary value problem that is defined on the actual design domain the main idea herein is to apply fictitious nodal forces corresponding to the discrete sensitivity of the objective function we propose an algorithm in which constraint functions will be taken into account by using an augmented lagrangian formulation and a step length control ensures a sufficient decrease condition in terms of the objective function within each iteration we examine the benefits of the proposed regularization method on the basis of some numerical examples in comparison to an unregularized steepest descent algorithm

finite element modelling of surface tension effects using a lagrangian eulerian kinematic description abstract an algorithm has been devised to model surface tension forces during fluid motion it makes use of an eulerian formulation applied to the governing equations and a lagrangian treatment of the free surface it is assumed that the effect of air on the free surface movement is negligible thus only the fluid domain is considered during the analysis the free surface is subjected to a surface tension force proportional to the local curvature this manifests itself as a simple and accurate method of modelling surface tension effects by virtue of the free surface being explicitly determined the method is validated by modelling the effect of surface tension on a static rod a further numerical example is used to illustrate the effect of surface tension on a non equilibrium square rod wall adhesion modelling is demonstrated by modelling the wetting of a capillary tube finally the method is used in an industrial context to model the filling of mould cavities for which surface tension forces are important

comparison of several staggered atomistic to continuum concurrent coupling strategies abstract in this contribution several staggered schemes used to couple continuum mechanics cm and molecular mechanics mm are proposed the described approaches are based on the atomistic to continuum correspondence obtained by spatial averaging in the spirit of irving and kirkwood and noll similarities between this and other concurrent coupling schemes are indicated thus providing a broad overview of different approaches in the field the schemes considered here are decomposed into the surface type displacement or traction boundary conditions and the volume type the latter restricts the continuum displacement field and possibly its gradient in some sense to the atomistic discrete displacements using lagrange multipliers a large strain cm formulation incorporating lagrange multipliers and a strategy to solve the resulting coupled linear system using an iterative solver is presented finally the described coupling methods are numerically examined using two examples uniaxial deformation and a plate with a hole relaxed under surface tension accuracy and convergence rates of each method are reported it was found that the displacement surface coupling scheme and the lagrangian volume scheme based on either discrete displacements or the h 1 norm derived from continuous displacement fields provide the best performance

tension field theory a general theory of the tension field is developed for application to the analysis of wrinkling in isotropic elastic membranes undergoing finite deformations the principal contribution is a partial differential equation describing a geometrical property of tension trajectories this is one of a system of two equations which describes the state of stress independently of the deformation this system is strongly elliptic at any stable solution whereas the deformation is described by a system of parabolic type controllable solutions i e those states that can be maintained in any isotropic elastic material by application of edge tractions and lateral pressure alone are obtained the general axisymmetric problem is solved implicitly and the theory is applied to the solution of two representative examples existing small strain theories are shown to correspond to a singular limit of the general theory at which the underlying system changes from elliptic to parabolic type

the variational formulation of viscoplastic constitutive updates we present a class of constitutive updates for general viscoplastic solids including such aspects of material behavior as finite elastic and plastic deformations non newtonian viscosity rate sensitivity and arbitrary flow and hardening rules the distinguishing characteristic of the proposed constitutive updates is that by construction the corresponding incremental stress strain relations derive from a pseudo elastic strain energy density this in turn confers the incremental boundary value problem a variational structure in particular the incremental deformation mapping follows from a minimum principle this minimum principle may conveniently be taken as a basis for error estimation and mesh adaption the accuracy and robustness of the variational constitutive updates is demonstrated with the aid of convergence tests involving the finitely deforming mises solid and ductile single crystals the ability of the updates to resolve the complex patterns of slip activity which arise in the latter application is particularly noteworthy

anti self dual yang mills connections over complex algebraic surfaces and stable vector bundles on presente une correspondance entre la geometrie algebrique et la geometrie differentielle des fibres vectoriels soit une surface algebrique projective x qui a un plongement donne x cp n et soit une metrique de kahler sur x dont la classe de cohomologie associee est duale a la classe de section d hyperplan h un fibre sur x est stable par rapport au plongement projectif si et seulement si il admet une connexion irreductible d hermite einstein par rapport a la metrique cette connexion est alors unique

the q characters at roots of unity abstract we consider various specializations of the untwisted quantum affine algebras at roots of unity we define and study the q characters of their finite dimensional representations

local modification of meshes for adaptive and or multigrid finite element methods abstract a mesh generation approach that allows the local modification of meshes of simplices is reviewed and discussed the generation and modification of sequences of nested irregular grids as needed for multigrid algorithms in the adaptive finite element setting can also be managed in 2 dimensions the meshes constructed are guaranteed to be nondegenerate and smooth empirical evidence has shown the 3d algorithm is in practice a powerful and realiable tool for mesh refinement