large strain viscoelastic constitutive models this paper discusses a new continuum formulation for viscoelastic materials at finite strains the model proposed is based on the multiplicative decomposition of the isochoric component of deformation gradient into elastic and viscous contribution and the generalized maxwell rheological model the inelastic or viscous components of the deformation gradient provide the internal variables required for the irreversible thermo mechanical model nonlinear rate type of evolution equations are then proposed for the internal variables these are based on a particular linear relaxation form of the generalized maxwell model which leads to a viscoelastic formulation that can be seen as a particular case of a large strain viscoplastic model based on maximum plastic dissipation in addition to the rate evolution equations simple incremental stress update equations are proposed these closely resemble the radial return algorithms used in von mises plasticity finally a spatial form of the viscoelastic formulation is presented for isotropic materials this formulation is based on principal directions and logarithmic stretches again incremental equations will be considered in order to permit subsequent computational implementations

a gradient enhanced large deformation continuum damage model for fibre reinforced materials a non local gradient based damage formulation within a geometrically non linear setting is presented the hyperelastic constitutive response at local material point level is governed by a strain energy which is additively composed of an isotropic matrix and of an anisotropic fibre reinforced material respectively the inelastic constitutive response is governed by a scalar 1 d type damage formulation where only the anisotropic elastic part is assumed to be affected by the damage following the concept in dimitrijevic and hackl 28 the local free energy function is enhanced by a gradient term this term essentially contains the gradient of the non local damage variable which itself is introduced as an additional independent variable in order to guarantee the equivalence between the local and non local damage variable a penalisation term is incorporated within the free energy function based on the principle of minimum total potential energy a coupled system of euler lagrange equations i e the balance of linear momentum and the balance of the non local damage field is obtained and solved in weak form the resulting coupled highly non linear system of equations is symmetric and can conveniently be solved by a standard incremental iterative newton raphson type solution scheme several three dimensional displacement and force driven boundary value problems partially motivated by biomechanical application highlight the mesh objective characteristics and constitutive properties of the model and illustratively underline the capabilities of the formulation proposed

variational and projection methods for the volume constraint in finite deformation elasto plasticity this paper focuses on the treatment of volume constraints which in the context of elasto plasticity typically arise as a result of assuming volume preserving plastic flow projection methods based on the modification of the discrete gradient operator b often proposed on an ad hoc basis are systematically obtained in the variational context furnished by a three field hu washizu principle the fully nonlinear formulation proposed here is based on a local multiplicative split of the deformation gradient into volume preserving and dilatational parts without relying on rate forms of the weak form of momentum balance this approach fits naturally in a formulation of plasticity based on the multiplicative decomposition of the deformation gradient and enables one to exactly enforce the condition of volume preserving plastic flow within the framework proposed in this paper rate forms and incrementally objective algorithms are entirely bypassed

anisotropic additive plasticity in the logarithmic strain space modular kinematic formulation and implementation based on incremental minimization principles for standard materials the paper presents a modular formulation and computational implementation of a class of anisotropic plasticity models at finite strains based on incremental minimization principles the modular kinematic setting consists of a constitutive model in the logarithmic strain space that is framed by a purely geometric pre and postprocessing on the theoretical side the point of departure is an a priori six dimensional approach to finite plasticity based on the notion of a plastic metric in a first step a geometric preprocessor defines a total and a plastic logarithmic strain measure obtained from the current and the plastic metrics respectively in a second step these strains enter in an additive format a constitutive model of anisotropic plasticity that may have a structure identical to the geometrically linear theory the model defines the stresses and consistent tangents work conjugate to the logarithmic strain measure in a third step these objects of the logarithmic space are then mapped back to nominal lagrangian or eulerian objects by a geometric postprocessor this geometric three step approach defines a broad class of anisotropic models of finite plasticity directly related to counterparts of the geometrically linear theory it is specified to a model problem of anisotropic metal plasticity on the computational side we develop an incremental variational formulation of the above outlined constitutive structure where a quasi hyperelastic stress potential is obtained from a local constitutive minimization problem with respect to the internal variables it is shown that this minimization problem is exclusively restricted to the logarithmic strain space in a structure identical to the small strain theory the minimization problem determines the internal state of the material for finite increments of time we develop a discrete formulation in terms of just one scalar parameter for the amount of incremental flow the existence of the incremental stress potential provides a natural basis for the definition of the geometric postprocessor based on function evaluations furthermore the global initial boundary value problem of the elastic plastic solid appears in the incremental setting as an energy minimization problem numerical examples show that the results obtained are surprisingly close to those obtained by a reference framework of multiplicative plasticity

a 4 node finite shell element for the implementation of general hyperelastic 3d elasticity at finite strains abstract in this paper a finite shell element for large deformations is presented based on extensible director kinematics the essential feature is an interface to arbitrary three dimensional material laws the non linear lagrangian formulation is based on the three field variational principle parametrized with the displacement vector enhanced green lagrangian strain tensor and second piola kirchhoff stress tensor the developed quadrilateral shell element is characterized by a course mesh accuracy and distortion insensitivity compared with bilinear displacement approaches furthermore plane stress response is approximately recovered in the asymptotic case of vanishing thickness a number of example problems investigating large deformation as well as finite strain applications are presented compressible and incompressible hyperelastic materials of the st venant kirchhoff neo hookean and mooney rivlin type are particularly used

a constitutive frame of elastoplasticity at large strains based on the notion of a plastic metric abstract the article presents a constitutive framework of large strain elastoplasticity in both the lagrangian and the eulerian geometric setting which takes into account anisotropic material response in summary the key ingredients of this framework are i the introduction of a plastic metric which is assumed to describe locally the history dependent inelastic material response in the sense of an internal variable formulation ii 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 iii an equivalent lagrangian and eulerian representation of all constitutive functions as isotropic tensor functions in terms of an extended set of arguments denoted as anisotropy variables iv the set up of normality rules for the evolution of the plastic metric and the anisotropy variables yielding a canonical symmetric form of the elastoplastic tangent moduli v a geometrically exact decomposition of the set of constitutive equations into possibly decoupled volumetric and isochoric contributions applications of the constitutive framework are demonstrated by means of several conceptual model problems which cover isotropic initial anisotropic and induced anisotropic elastoplastic response

the analysis of incompressible hyperelastic bodies by the finite element method abstract a method is developed for the finite element analysis of problems involving incompressible hyperelastic bodies the constitutive relation is based on a class of strain energy functions due to ogden 4 which involve sums of real powers of principal stretches incremental equilibrium equations are derived from a rate form of the principle of virtual work and an additional set of equations which express the condition of incompressibility in an average manner is appended to the equilibrium equations examples of solutions are given and compared either with closed form solutions or with numerical solutions found using conventional approaches

geometrically non linear and consistently linearized embedded strong discontinuity models for 3d problems with an application to the dissection analysis of soft biological tissues three different finite element formulations with embedded strong discontinuities are derived on the basis of the enhanced assumed strain method according to the work by jirasek and zimmermann int j numer methods engrg 50 2001 1269 they are referred to as statically optimal symmetric sos kinematically optimal symmetric kos and statically and kinematically optimal non symmetric skon formulations the effect of the discontinuities are characterized by additional degrees of freedom on the element level modifications to the standard kos and skon formulations are proposed in order to achieve consistency with the employed type of a three field hu washizu principle under mode i condition under this condition the formulation satisfies the internal compatibility at the discontinuity i e the relation between the stress in the bulk material and the traction across the discontinuity surface which is not the case for the classical kos formulation we propose a suitable explicit expression for a transversely isotropic traction law in form of a displacement energy function and assume that softening phenomena in the cohesive zone are modeled by a damage law which depends on the maximum gap displacement of the deformation path a linearization of all quantities which are related to the non linear problem leads to new closed form expressions in particular we focus attention on the linearization of the cohesive traction vector the associated element residua and stiffness matrices are provided standard static condensation of the internal degree of freedom leads to a generalized displacement model a comparative study of the modified formulations carried out by means of two numerical examples show the performance of the individual approach we employ constant strain tetrahedral elements with a single discontinuity embedded among the known stress locking phenomena associated with the sos formulation we recognized that the non symmetric skon formulation was not able to provide meaningful results for the dissection process of an arterial layer in three dimensions on distorted meshes for both numerical examples the symmetric kos formulation seems to be most suitable for representing the embedded discontinuities

computational electro elasticity and magneto elasticity for quasi incompressible media immersed in free space summary in this work a mixed variational formulation to simulate quasi incompressible electro active or magneto active polymers immersed in the surrounding free space is presented a novel domain decomposition is used to disconnect the primary coupled problem and the arbitrary free space mesh update problem exploiting this decomposition we describe a block iterative approach to solving the linearised multiphysics problem and a physically and geometrically based three parameter method to update the free space mesh several application driven example problems are implemented to demonstrate the robustness of the mixed formulation for both electro elastic and magneto elastic problems involving both finite deformations and quasi incompressible media copyright 2016 john wiley sons ltd

the orbifold chow ring of toric deligne mumford stacks the orbifold chow ring of a deligne mumford stack defined by abramovich graber and vistoli 2 is the algebraic version of the orbifold cohomology ring in troduced by w chen and ruan 7 8 by design this ring incorporates numerical invariants such as the orbifold euler characteristic and the orbifold hodge num bers of the underlying variety the product structure is induced by the degree zero part of the quantum product in particular it involves gromov witten invariants inspired by string theory and results in batyrev 3 and yasuda 28 one expects that in nice situations the orbifold chow ring coincides with the chow ring of a resolution of singularities fantechi and g ttsche 14 and uribe 25 verify this conjecture when the orbifold is symn 5 where 5 is a smooth projective surface with ks 0 and the resolution is hilbn the initial motivation for this project was to compare the orbifold chow ring of a simplicial toric variety with the chow ring of a cr pant resolution to achieve this goal we first develop the theory of toric deligne mumford stacks modeled on simplicial toric varieties a toric deligne mumford stack corresponds to a combinatorial object called a stacky fan as a first approximation this object is a simplicial fan with a distinguished lattice point on each ray in the fan more precisely a stacky fan s is a triple consisting of a finitely generated abelian group n a simplicial fan e in q z n with n rays and a map zn n where the image of the standard basis in zn generates the rays in e a rational simplicial fan e produces a canonical stacky fan s n e where n is the distinguished lattice and is the map defined by the minimal lattice points on the rays hence there is a natural toric deligne mumford stack associated to every simplicial toric variety a stacky fan encodes a group action on a quasi affine variety and the toric deligne mumford stack is the quotient if e corresponds to a smooth toric variety x e and s is the canonical stacky fan associated to e then we simply have x z we show that many of the basic concepts such as open and closed toric substacks line bundles and maps between toric deligne mumford stacks correspond to combinatorial notions we expect that many more results about toric varieties lift to the realm of stacks and hope that toric deligne mumford stacks will serve as a useful testing ground for general theories

geometrically non linear enhanced strain mixed methods and the method of incompatible modes a class of assumed strain mixed finite element methods for fully non linear problems in solid mechanics is presented which when restricted to geometrically linear problems encompasses the classical method of incompatible modes as a particular case the method relies crucially on a local multiplicative decomposition of the deformation gradient into a conforming and an enhanced part formulated in the context of a three field variational formulation the resulting class of mixed methods provides a possible extension to the non linear regime of well known incompatible mode formulations in addition this class of methods includes non linear generalizations of recently proposed enhanced strain interpolations for axisymmetric problems which cannot be interpreted as incompatible modes elements the good performance of the proposed methodology is illustrated in a number of simulations including 2 d 3 d and axisymmetric finite deformation problems in elasticity and elastoplasticity remarkably these methods appear to be specially well suited for problems involving localization of the deformation as illustrated in several numerical examples

invariant formulation of hyperelastic transverse isotropy based on polyconvex free energy functions in this paper we propose a formulation of polyconvex anisotropic hyperelasticity at finite strains the main goal is the representation of the governing constitutive equations within the framework of the invariant theory which automatically fulfill the polyconvexity condition in the sense of ball in order to guarantee the existence of minimizers based on the introduction of additional argument tensors the so called structural tensors the free energies and the anisotropic stress response functions are represented by scalar valued and tensor valued isotropic tensor functions respectively in order to obtain various free energies to model specific problems which permit the matching of data stemming from experiments we assume an additive structure a variety of isotropic and anisotropic functions for transversely isotropic material behaviour are derived where each individual term fulfills a priori the polyconvexity condition the tensor generators for the stresses and moduli are evaluated in detail and some representative numerical examples are presented furthermore we propose an extension to orthotropic symmetry

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

exact expansions of arbitrary tensor functions f a and their derivatives a general method is presented for determining the exact expansions of a tensor function f a where a is a second order tensor in n dimensional euclidean space and f a is defined by the power series it is shown that f a can be obtained by differentiating a scalar function of the eigenvalues of a using this method closed form singularity free expressions of arbitrary tensor functions and their first derivatives are deduced in two and three dimensional cases

a computational framework for a class of fully coupled models for elastoplastic damage at finite strains with reference to the linearization aspects abstract a fully coupled model for finite strain elastoplastic damage based on the multiplicative decomposition of the deformation gradient which incorporates non linear isotropic and kinematic hardening is described the numerical integration of its constitutive equations is performed by an algorithm which generalizes the standard return mapping procedures of the infinitesimal theory the exact consistent linearization of the model described is carried out in detail it provides the basis of the full newton raphson procedure for iterative solution of the associated equilibrium problem by means of finite element simulations the performance of the exact tangent modulus derived is compared with an approximate version and some practical implications are discussed

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

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

facets of the linear ordering polytope letd n be the complete digraph onn nodes and letp lo denote the convex hull of all incidence vectors of arc sets of linear orderings of the nodes ofd n i e these are exactly the acyclic tournaments ofd n we show that various classes of inequalities define facets ofp lo e g the 3 dicycle inequalities the simplek fence inequalities and various mobius ladder inequalities and we discuss the use of these inequalities in cutting plane approaches to the triangulation problem of input output matrices i e the solution of permutation resp linear ordering problems

coupled thermoviscoplasticity of glassy polymers in the logarithmic strain space based on the free volume theory the paper outlines a constitutive model for finite thermo visco plastic behavior of amorphous glassy polymers and considers details of its numerical implementation in contrast to existing kinematical approaches to finite plasticity of glassy polymers the formulation applies a plastic metric theory based on an additive split of lagrangian hencky type strains into elastic and plastic parts the analogy between the proposed formulation in the logarithmic strain space and the geometrically linear theory of plasticity makes this constitutive framework very transparent and attractive with regard to its numerical formulation the characteristic strain hardening of the model is derived from a polymer network model we consider the particularly simple eight chain model but also comment on the recently developed microsphere model the viscoplastic flow rule in the logarithmic strain space uses structures of the free volume flow theory which provides a highly predictive modeling capacity at the onset of viscoplastic flow the integration of this micromechanically motivated approach into a three dimensional computational model is a key concern of this work we outline details of the numerical implementation of this model including elements such as geometric pre and post transformations to from the logarithmic strain space a thermomechanical operator split algorithm consisting of an isothermal mechanical predictor followed by a heat conduction corrector and finally the consistent linearization of the local update algorithm for the dissipative variables as well as its relationship to the global tangent operator the performance of the proposed formulation is demonstrated by means of a spectrum of numerical examples which we compare with our experimental findings

large strain deformations of elastic shells constitutive modelling and finite element analysis this paper is concerned with the constitutive modelling of large elastic strains with applications to shells the shell theory itself is characterized by seven degrees of freedom and enjoys the following features 1 it circumvents the use of a rotation tensor preserving the euclidean structure of the configuration space and 2 it is capable to the application of a three dimensional constitutive law in addition an elastic finite strain constitutive law is developed which 1 covers the whole range of deformation experimentally given by treloar and 2 is formulated in terms of invariants avoiding the use of principal stretches the second feature means that the model is generalizable to anisotropic material behaviour and that it allows for straightforward computations of the tangent operator making the whole theory well suited for large strain computations in addition to the four node and nine node displacement based finite elements an enhanced strain finite element is examined its efficiency is compared with that of displacement based element formulations different examples of large strain shell deformations are presented it is shown that the application of the enhanced strain concept in the nonlinear constitutive range limits severely the stability of computation

adaptivity for parameter identification of incompressible hyperelastic materials using stabilized tetrahedral elements abstract this work is concerned with the identification of material parameters for isotropic incompressible hyperelastic material models besides the principal stretch based strain energy function by ogden an invariant based strain energy function by rivlin saunders is considered for which parameter sensitivities are derived the identification is formulated as a least squares minimization problem based on the finite element method to account for inhomogeneous states of stresses and strains in the experimental data which is obtained by optical measurements for the finite element method low order tetrahedral elements in a mixed displacement pressure formulation with stabilization are considered special attention is payed to an adaptive mesh refinement based on a goal oriented a posteriori error indicator to gain reliable material parameters to approximate error terms an element wise recovery technique based on enhanced gradients is introduced

random skew plane partitions and the pearcey process we study random skew 3d partitions weighted by qvol and specifically the q 1 asymptotics of local correlations near various points of the limit shape we obtain sine kernel asymptotics for correlations in the bulk of the disordered region airy kernel asymptotics near a general point of the frozen boundary and a pearcey kernel asymptotics near a cusp of the frozen boundary

an inexact algorithm for the sequential ordering problem abstract given the directed g n a and the penalty matrix c the sequential ordering problem hereafter sop consists of finding the permutation of the nodes from the set n such that it minimizes a c based function and does not violate the precedence relationships given by the set a strong sufficient conditions for the infeasibility of a sop s instance are embedded in a procedure for the sop s pre processing note that it is one of the key steps in any algorithm that attempts to solve sop by dropping the constraints related to the precedence relationships sop can be converted in the classical asymmetric traveling salesman problem hereafter astp the algorithm obtains hopefully satisfactory solutions by modifying the optimal solution to the related assignment problem hereafter ap if it is not a feasible sequential ordering hereafter fso the new solution patches the subtours if any giving preference to the patches with zero reduced cost in the linking arcs the ap based lower bound on the optimal solution to atsp is tightened by using some of the procedures given in 1 in any case a local search for improving the initial fso is performed it uses 3 and 4 changed based procedures computational results on a broad set of cases are reported

a restricted lagrangean approach to the traveling salesman problem we describe an algorithm for the asymmetric traveling salesman problem tsp using a new restricted lagrangean relaxation based on the assignment problem ap the lagrange multipliers are constrained so as to guarantee the continued optimality of the initial ap solution thus eliminating the need for repeatedly solving ap in the process of computing multipliers we give several polynomially bounded procedures for generating valid inequalities and taking them into the lagrangean function with a positive multiplier without violating the constraints so as to strengthen the current lower bound upper bounds are generated by a fast tour building heuristic when the bound strengthening techniques are exhausted without matching the upper with the lower bound we branch by using two different rules according to the situation the usual subtour breaking disjunction and a new disjunction based on conditional bounds we discuss computational experience on 120 randomly generated asymmetric tsp s with up to 325 cities the maximum time used for any single problem being 82 seconds this is a considerable improvement upon earlier methods though the algorithm discussed here is for the asymmetric tsp the approach can be adapted to the symmetric tsp by using the 2 matching problem instead of ap

the mckay correspondence as an equivalence of derived categories the classical mckay correspondence relates representations of a finite subgroup g sl 2 c to the cohomology of the well known minimal resolution of the kleinian singularity c2 g gonzalez sprinberg and verdier 10 interpreted the mckay correspondence as an isomorphism on k theory observing that the representation ring of g is equal to the g equivariant k theory of c2 more precisely they identify a basis of the k theory of the resolution consisting of the classes of certain tautological sheaves associated to the irreducible representations of g

computational micro to macro transitions for discretized micro structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy the paper investigates algorithms for the computation of homogenized stresses and overall tangent moduli of micro structures undergoing large strain deformations typically these micro structures define representative volumes of nonlinear heterogeneous materials such as inelastic composites polycrystalline aggregates or particle assemblies we consider a priori given discretized micro structures without focussing on details of specific discretization techniques for space and time the key contribution of the paper is the construction of a family of algorithms and matrix representations of overall properties of discretized micro structures which are motivated by a minimization of averaged incremental energy it is shown that the overall stresses and tangent moduli of a typical micro structure may exclusively be defined in terms of discrete forces and stiffness properties on the boundary we focus on deformation driven micro structures where the overall macroscopic deformation is controlled in this context three classical types of boundary conditions are investigated i linear deformation ii uniform tractions and iii periodic deformation and antiperiodic tractions incorporated by lagrangian multiplier methods these conditions generate three classes of constrained minimization problems with associated solution algorithms for the computation of equilibrium states and overall properties of micro structures the proposed algorithms and matrix representations of the overall properties are formally independent of the interior spatial structure and the local constitutive response of the micro structure and are therefore applicable to a broad class of model problems we demonstrate their performance for some representative model problems including finite elastic plastic deformations of composites texture developments in polycrystalline materials and equilibrium states of particle assemblies

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

a threshold accepting heuristic with intense local search for the solution of special instances of the traveling salesman problem in real life scheduling variations of the standard traveling salesman problem are very often encountered the aim of this work is to present a new heuristic method for solving three such special instances with a common approach the proposed algorithm uses a variant of the threshold accepting method enhanced with intense local search while the candidate solutions are produced through an insertion heuristic scheme the main characteristic of the algorithm is that it does not require modifications and parameter tuning in order to cope with the three different problems computational results on a variety of real life and artificial problems are presented at the end of this work and prove the efficiency and the ascendancy of the proposed method over other algorithms found in the literature

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

numerical computation of algorithmic consistent tangent moduli in large strain computational inelasticity abstract an algorithm for the numerical computation of so called algorithmic or consistent tangent moduli in finite inelasticity is presented these moduli determine the sensitivity of algorithmic expressions for stresses with respect to the change in total deformation they serve as iteration operators by application of newton type solvers for the iterative solution of non linear initial boundary value problems in finite inelasticity the underlying concept of the numerical computation is a perturbation technique based on a forward difference approximation which reduces the computation of the tangent moduli to a multiple stress computation the algorithmic procedure is material independent and surprisingly simple it is outlined for a lagrangian as well as an eulerian geometric setting and applied to model problems of finite elasticity and finite elastoplasticity

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

analysis finite element computation and error estimation in transversely isotropic nearly incompressible finite elasticity abstract in this paper we present constitutive models for nearly incompressible transversely isotropic materials in finite hyperelasticity particularly for reinforced rubber like materials which are of essential engineering interest the theory is developed using a convected curvilinear coordinate system based on a mixed two field displacement pressure energy functional furthermore an a posteriori error estimator without multiplicative constants is derived for non linear anisotropic problems which measures the discretization error in the first piola kirchhoff stresses in the l 2 norm by solving local neumann problems with equilibrated tractions illustrative numerical examples demonstrate the anisotropic material behaviour of reinforced materials and the efficiency of using adaptive finite element methods

an integral structure in quantum cohomology and mirror symmetry for toric orbifolds abstract we introduce an integral structure in orbifold quantum cohomology associated to the k group and the class in the case of compact toric orbifolds we show that this integral structure matches with the natural integral structure for the landau ginzburg model under mirror symmetry by assuming the existence of an integral structure we give a natural explanation for the specialization to a root of unity in y ruan s crepant resolution conjecture yongbin ruan the cohomology ring of crepant resolutions of orbifolds in contemp math vol 403 amer math soc providence ri 2006 pp 117 126

variational gradient plasticity at finite strains part ii local global updates and mixed finite elements for additive plasticity in the logarithmic strain space the second part of our work on variational inelasticity with long range effects outlines the formulation and finite element implementation of additive finite gradient plasticity in the logarithmic strain space it is considered to be the most simple approach to finite plasticity suitable for the purely phenomenological description of polycrystalline metals or amorphous materials if structures of the geometrically linear theories are defined in the lagrangian logarithmic strain space we start from a mixed saddle point principle for metric type additive plasticity which is specified for the important model problem of isochoric von mises plasticity with gradient extended hardening softening response the mixed variational structure includes the hardening softening variable itself as well as its dual driving force the numerical implementation exploits the underlying variational structure yielding a canonical symmetric structure of the monolithic problem it results in a novel finite element design of the coupled problem incorporating a long range hardening softening parameter and its dual driving force this allows a straightforward local definition of plastic loading unloading driven by the long range fields providing very robust finite element implementations of gradient plasticity it includes a rational method for the definition of elastic plastic boundaries epbs in gradient plasticity along with a postprocessor that defines the plastic variables in the elastic range we discuss alternative mixed finite element designs of the coupled problem including a local global solution strategy of short and long range fields all methods are derived in a rigorous format from variational principles numerical benchmarks demonstrated the excellent performance of the proposed mixed variational approach to gradient plasticity in the logarithmic strain space

the topological vertex we construct a cubic field theory which provides all genus amplitudes of the topological a model for all non compact toric calabi yau threefolds the topology of a given feynman diagram encodes the topology of a fixed calabi yau with schwinger parameters playing the role of kahler classes of the threefold we interpret this result as an operatorial computation of the amplitudes in the b model mirror which is the quantum kodaira spencer theory the only degree of freedom of this theory is an unconventional chiral scalar on a riemann surface in this setup we identify the b branes on the mirror riemann surface as fermions related to the chiral boson by bosonization

on the theory of fourth order tensors and their applications in computational mechanics many problems concerned with the mathematical treatment of fourth order tensors still remain open in the literature in the present paper they will be considered in the framework of a complete theory involving a set of notations and definitions a tensor operation algebra differentiation rules eigenvalue problems applications of fourth order tensors to isotropic tensor functions and some other relevant aspects a tensor is understood to be an invariant quantity with respect to any co ordinate system transformation which justifies the use of absolute notation preferred in this work as a most important application field of fourth order tensors elastic moduli are formulated in a material and a spatial description and given for various hyperelastic material models

an anisotropic viscoelastic fibre matrix model at finite strains continuum formulation and computational aspects this paper presents a fully three dimensional constitutive model for anisotropic vis coelasticity suitable for the macroscopic description of fibre reinforced composites that experience finite strains an essential feature of the model is that the matrix and the fibres are treated separately allowing then as many bundles of fibres as desired moreover the relaxation and or creep response is based on the multiplica tive viscoelastic split of the deformation gradient combined with the assumption of viscoelastic potentials for each compound here the composite is thought to be the superposition of an isotropic matrix material and further one dimensional continua each of them representing one family of fibres the deformation gradient and its multiplicative decomposition apply to all the continua linking them implicitly the global anisotropic response is obtained by an assembly of all the contributions con stitutive models for orthotropic and transversely isotropic materials are included as special cases it is shown how the continuum thermodynamics is crucial in setting the correct forms for the constitutive and evolution equations for the algorithmic design within the context of the finite element method the numerical eort is of the order of that devoted for isotropic computations in fact only a single scalar valued resolution procedure is added for each fibre bundle the algorithmic tangent moduli are derived for each compound and their assembly leads to consistent vis coelastic tangent modulus which is suitable for a quadratic rate of convergence when the newton raphson iterative scheme is employed the numerical eciency of the model is illustrated through a set of representative simulations

stronger multi commodity flow formulations of the capacitated sequential ordering problem the sequential ordering problem sop is the generalisation of the asymmetric travelling salesman problem in which there are precedence relations between pairs of nodes hernandez salazar introduced a multi commodity flow mcf formulation for a generalisation of the sop in which the vehicle has a limited capacity we strengthen this mcf formulation by fixing variables and adding valid equations we then use polyhedral projection together with some known results on flows cuts and metrics to derive new families of strong valid inequalities for both problems finally we give computational results which show that our findings yield good lower bounds in practice

a micropolar theory of finite deformation and finite rotation multiplicative elastoplasticity the aim of this work is to formulate a geometrically exact theory of finite deformation and finite rotation micropolar elastoplasticity to obtain a generalized nonlinear continuum framework to this end the classical deformation map is supplemented by an independent rotation field to yield an enhanced configuration space thereby the rotational part of the formulation is consequently parameterized in terms of the rotation pseudo vector via the euler rodrigues formula then micropolar hyperelasticity and multiplicative elastoplasticity are conceptionally derived as in the classical boltzmann continuum the proposed theory is consequently developed in a modern geometry oriented fashion linearization of the kinematics retrofits the well known structure of the micropolar geometrically linear theory

entropy elasticity of isotropic rubber like solids at finite strains abstract this paper presents a macroscopic continuum formulation and a numerical analysis of constitutive equations for stress entropy and heat flux describing the thermoelastic behavior of amorphous cross linked polymers above the glass transition temperature in which a specimen typically snap back with rubbery characteristics the introduced coupled thermomechanical functional extends the classical strain energy function proposed by ogden volume changes due to thermal expansion are regarded for a large temperature domain and play a remarkable role in thermoelastic materials the non linear thermoelastic problem is solved within a staggered fractional step method which is based on a two phase isentropic operator split each of the two symmetric sub problems retains the characteristic dissipative structure of the implicit monolithic scheme which consequently results to an unconditionally stable product formula algorithm the numerical analysis side shows in particular the capability of the theoretical framework reproducing the realistic physical stress deformation temperature relations of rubber distinctive attention is paid to the thermoelastic inversion phenomena a remarkable property governing the class of rubber like materials

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

using stacks to impose tangency conditions on curves we define a deligne mumford stack xp r which depends on a scheme x an effective carrier divisor d c x and a positive integer r then we show that the abramovich vistoli mod uli stack of stable maps into xq r provides compactifications of the locally closed substacks of mgtn x 3 corresponding to relative stable maps 1 introduction this paper has two main purposes the first is to introduce the rth root construction which is a way of creating stack structure along a divisor given a scheme x an effective cartier divisor d c x and a positive integer r which is invertible on x it produces a deligne mumford stack xo r when r is not invertible the construction still makes sense and produces an artin stack which has finite diagonal over x since the output is in general an artin stack we give the definition and basic properties when x is an artin stack this simplifies the exposition since we need to apply the construction multiple times this construction was known to several mathematicians before we became aware of it but very little appeared in the literature aside from a brief mention in agv 3 5 3 secondly we compare twisted stable maps into xp r with ordinary stable maps into x the theory of twisted stable maps was developed by chen and ruan cr in the symplectic category and by abramovich and vistoli av in the algebraic category the latter showed that there is a deligne mumford stack xg n x 3 parametrizing morphisms x from twisted rc marked genus g nodal curves into a deligne mumford stack x such that 3 in the case where x is a scheme this is just the space of kontsevich stable maps mg n x 3 the theory of relative stable maps was developed by several symplectic ge ometers and the algebraic definition was worked out partially by andreas gath mann ga and in general by jun li li let x be a smooth complex projective veriety d c x a smooth divisor and 3 g b x such that d 3 0 here b x denotes the group of 1 cycles modulo algebraic equivalence choose a partition d 3 q qn where each qi is a nonnegative integer then a stable map c x from a smooth curve c having marked points x xn such that f c 3 and d y qixi ls a relative stable map the space of such mor phisms was compactified by ga and li and they used this to define relative gromov witten invariants

entropic thermoelasticity at finite strains aspects of the formulation and numerical implementation abstract this paper presents a formulation of isotropic finite strain thermoelasticity and addresses some aspects of its numerical implementation on the theoretical side a eulerian setting of isotropic thermoelasticity is discussed based on the finger tensor as a strain measure novel aspects are a direct representation of the eulerian thermoelastic moduli in terms of the finger tensor and a rigorous decomposition of the thermoelastic response functions into decoupled volumetric and isochoric contributions based on a multiplicative split of the finger tensor into spherical and unimodular parts an algorithmic procedure for the computation of the stress and thermoelastic moduli based on a representation of the free energy in terms of eigenvalues of the unimodular part of the finger tensor is developed and applied to model problems of strictly entropic and modified entropic thermoelasticity furthermore two algorithms for the solution of the coupled problem are discussed based on operator splits of the global field equations of thermoelasticity the paper concludes with some representative numerical simulations of thermoelastic processes in rubber like materials

galerkin based mechanical integrators for finite elastodynamics formulated in principal stretches pitfalls and remedies in the present paper we deal with integrators relying on finite elements in time for general hyperelastic models which guarantee the conservation of the momentum maps as well as of the total energy within the calculation accuracy in the isotropic case eigenvalue based constitutive laws are on the one hand very significant to model the behaviour of various materials on the other hand it will be shown that the efficient algorithmic treatment of principal stretches based on a perturbation approach requires especially within the context of conserving schemes advanced techniques to circumvent numerical problems accordingly we propose an adequate solution strategy to avoid potential pitfalls which are related to numerical artefacts of the applied non standard quadrature rule finally the excellent numerical and mechanical performance of the resulting galerkin based time stepping schemes will be demonstrated by means of representative numerical examples

polyconvexity of generalized polynomial type hyperelastic strain energy functions for near incompressibility abstract in this article we investigate several models contained in the literature in the case of near incompressibility based on invariants in terms of polyconvexity and coerciveness inequality which are sufficient to guarantee the existence of a solution these models are due to rivlin and saunders namely the generalized polynomial type elasticity and arruda and boyce the extension to near incompressibility is usually carried out by an additive decomposition of the strain energy into a volume changing and a volume preserving part where the volume changing part depends on the determinant of the deformation gradient and the volume preserving part on the invariants of the unimodular right cauchy green tensor it will be shown that the arruda boyce model satisfies the polyconvexity condition whereas the polynomial type elasticity does not therefore we propose a new class of strain energy functions depending on invariants moreover we focus our attention on the structure of further isotropic strain energy functions

the orbifold topological vertex abstract we develop a topological vertex formalism for computing the donaldson thomas invariants of calabi yau orbifolds the basic combinatorial object is the orbifold vertex v g a generating function for the number of 3d partitions asymptotic to 2d partitions and colored by representations of a finite abelian group g acting on c 3 in the case where g z n acting on c 3 with transverse a n 1 quotient singularities we give an explicit formula for v g in terms of schur functions we discuss applications of our formalism to the donaldson thomas crepant resolution conjecture and to the orbifold donaldson thomas gromov witten correspondence we also explicitly compute the donaldson thomas partition function for some simple orbifold geometries the local football p a b 1 and the local b z 2 gerbe

quadrilateral elements for the solution of elasto plastic finite strain problems in this paper two plane strain quadrilateral elements with two and four variables are proposed these elements are applied to the analysis of finite strain elasto plastic problems the elements are based on the enhanced strain and b bar methodologies and possess a stabilizing term the pressure and dilatation fields are assumed to be constant in each element s domain and the deformation gradient is enriched with additional variables as in the enhanced strain methodology the formulation is deduced from a four field functional based on the imposition of two constraints annulment of the enhanced part of the deformation gradient and the relation between the assumed dilatation and the deformation gradient determinant the discretized form of equilibrium is presented and the analytical linearization is deduced to ensure the asymptotically quadratic rate of convergence in the newton raphson method the proposed formulation for the enhanced terms is carried out in the isoparametric domain and does not need the usually adopted procedure of evaluating the jacobian matrix in the centre of the element the elements are very effective for the particular class of problems analysed and do not present any locking or instability tendencies as illustrated by various representative examples copyright 2001 john wiley sons ltd

the quantum mckay correspondence for polyhedral singularities let g be a polyhedral group namely a finite subgroup of so 3 nakamura s g hilbert scheme provides a preferred calabi yau resolution y of the polyhedral singularity 3 g the classical mckay correspondence describes the classical geometry of y in terms of the representation theory of g in this paper we describe the quantum geometry of y in terms of r an ade root system associated to g namely we give an explicit formula for the gromov witten partition function of y as a product over the positive roots of r in terms of counts of bps states gopakumar vafa invariants our result can be stated as a correspondence each positive root of r corresponds to one half of a genus zero bps state as an application we use the crepant resolution conjecture to provide a full prediction for the orbifold gromov witten invariants of 3 g

smooth toric deligne mumford stacks we give a geometric definition of smooth toric deligne mumford stacks using the action of a torus we show that our definition is equivalent to the one of borisov chen and smith in terms of stacky fans in particular we give a geometric interpretation of the combinatorial data contained in a stacky fan we also give a bottom up classification in terms of simplicial toric varieties and fiber products of root stacks

multisurface thermoplasticity for single crystals at large strains in terms of eulerian vector updates this paper presents a formulation of large strain rate independent multisurface thermoplasticity for single crystals and addresses aspects of its numerical implementation the theoretical frame is the well established continuum slip theory based on the multiplicative decomposition of the deformation gradient into elastic and plastic parts a key feature of the present paper is the introduction and computational exploitation of a particularly simple hyperelastic stress response function based on a further multiplicative decomposition of the elastic deformation gradient into spherical and unimodular parts resulting in a very convenient representation of the schmid resolved shear stresses on the crystallographic slip systems in terms of a simple inner product of eulerian vectors this observation is intrinsically exploited on the numerical side by formulating a new fully implicit stress update algorithm and the associated consistent elastoplastic moduli in terms of these eulerian vectors the proposed return mapping algorithm treats the possibly redundant constraints of large strain multisurface plasticity for single crystals by means of an active set search furthermore it satisfies in an algorithmically exact way the plastic incompressibility condition in situations of multislip the performance of the proposed formulation is demonstrated for two representative numerical simulations of thermoplastic deformation processes in single crystals with isotropic taylor type hardening

finite element methods for constrained problems in elasticity several different variational formulations of boundary value problems with constraints are discussed with particular reference to constrained problems in elasticity special attention is given to exterior penalty methods a discussion of the conditions necessary for penalty methods to provide a basis for stable and convergent finite element methods is given in particular the use of reduced integration is discussed and criteria on the order of reduced integration rules sufficient to produce stable and convergent schemes are described applications of reduced integration penalty methods to incompressible elasticity problems and contact problems are described

computation in finite strain viscoelasticity finite elements based on the interpretation as differential algebraic equations abstract in this article the interpretation of current non linear finite element calculations applied to constitutive equations of evolutionary type as a system of differential algebraic equations is continued p ellsiepen s hartmann int j numer methods engrg 51 2001 679 this procedure is applied to a model of finite strain viscoelasticity which incorporates a particular model of non linear rate dependence three specific topics are studied firstly we investigate a possible treatment of the interpretation in view of mixed finite elements secondly the application of stiffly accurate diagonally implicit runge kutta methods which yield on element level the same structure as a backward euler based integration step is analysed it is shown that the resulting stress algorithm is reducible to the solution of only three non linear equations at each gauss point one maxwell element lastly the effect with respect to expense and achievable accuracy of a time adaptive procedure is focused which is necessary in the case of different time scales such as relaxation or creep dominated processes

a finite elastic viscoelastic elastoplastic material law with damage theoretical and numerical aspects abstract the present work is concerned with the theoretical formulation and numerical implementation of a new isotropic finite elastic viscoelastic elastoplastic material law with mullins damage for rubber like materials based on a set of dissipation inequalities published recently by the first author a phenomenological model consisting of an elastic an elastoplastic branch and n viscoelastic branches connected in parallel is exploited the total free energy and the total stress are additively decomposed into three parts corresponding to the three types of branches the damage effect is assumed to act on the three types of branches homogeneously and isotropically according to the dissipation inequalities the evolution equations of the viscoelastic and elastoplastic branches are directly formulated in terms of the corotational rates of the internal elastic logarithmic strains it is proved that in the present constitutive setting the internal elastic logarithmic strains are coaxial to the total and trial elastic logarithmic strains the present theoretical and algorithmic formulations provide an alternative geometric representation of the same constitutive model outlined in j mech phys solids 48 2000 323 the numerical simulations show that the present material law gives predictions agreeing quite well with the experimental observations and numerical simulations issued in loc cit

donaldson thomas type invariants via microlocal geometry we prove that donaldson thomas type invariants are equal to weighted euler characteristics of their moduli spaces in particular such invariants depend only on the scheme structure of the moduli space not the symmetric obstruction theory used to define them we also introduce new invariants generalizing donaldson thomas type invariants to moduli problems with open moduli space these are useful for computing donaldson thomas type invariants over stratifications

stabilization algorithm for the optimal transportation meshfree approximation scheme abstract meshfree approximation schemes possess a high potential in computer aided engineering due to their large flexibility especially the tremendous progress in processor technology within recent years relativizes the increase in computation time due to the inherent search algorithm nevertheless meshfree approximation schemes are still faced with some challenges like imposition of dirichlet boundary conditions robustness of the algorithm and accuracy the recent developed optimal transportation meshfree otm method seemed to overcome most of these problems in this paper the otm solution scheme is combined with a standard search algorithm in order to allow a simple and flexible computation however this scheme is not stable for some examples of application hence an investigation is conducted which shows that the reason for this instability is due to underintegration based on this investigation a remedy to stabilize the algorithm is suggested which is based on well known concepts to control the hourglass effects in the finite element method in contrast to the original publication the otm algorithm is derived here from the principle of virtual work local maximum entropy shape functions are used which possess a weak kronecker property this enables a direct imposition of dirichlet boundary conditions if the boundary is convex the limitations of this basis function are also addressed in this paper additionally the search algorithm presented fulfills basic topological requirements several examples are investigated demonstrating the improved behavior of the stabilized otm algorithm

on the numerical integration of three invariant elastoplastic constitutive models abstract we investigate the performance of a numerical algorithm for the integration of isotropically hardening three invariant elastoplastic constitutive models with convex yield surfaces the algorithm is based on a spectral representation of stresses and strains for infinitesimal and finite deformation plasticity and a return mapping in principal stress directions smooth three invariant representations of the mohr coulomb model such as the lade duncan and matsuoka nakai models are implemented within the framework of the proposed algorithm among the specific features incorporated into the formulation are the hardening softening responses and the tapering of the yield surfaces toward the hydrostatic axis with increasing confining pressure isoerror maps are generated to study the local accuracy of the numerical integration algorithm finally a boundary value problem involving loading of a strip foundation on a soil is analyzed with and without finite deformation effects to investigate the performance of the integration algorithm in a full scale non linear finite element simulation

compact formulations of the steiner traveling salesman problem and related problems the steiner traveling salesman problem stsp is a variant of the tsp that is particularly suitable when routing on real life road networks the standard integer programming formulations of both the tsp and stsp have an exponential number of constraints on the other hand several compact formulations of the tsp i e formulations of polynomial size are known in this paper we adapt some of them to the stsp and compare them both theoretically and computationally it turns out that just by putting the best of the formulations into the cplex branch and bound solver one can solve instances with over 200 nodes we also briefly discuss the adaptation of our formulations to some related problems

a fully implicit finite element method for bidomain models of cardiac electromechanics we propose a novel monolithic and unconditionally stable finite element algorithm for the bidomainbased approach to cardiac electromechanics we introduce the transmembrane potential the extracellular potential and the displacement field as independent variables and extend the common two field bidomain formulation of electrophysiology to a three field formulation of electromechanics the intrinsic coupling arises from both excitation induced contraction of cardiac cells and the deformation induced generation of intra cellular currents the coupled reaction diffusion equations of the electrical problem and the momentum balance of the mechanical problem are recast into their weak forms through a conventional isoparametric galerkin approach as a novel aspect we propose a monolithic approach to solve the governing equations of excitation contraction coupling in a fully coupled implicit sense we demonstrate the consistent linearization of the resulting set of non linear residual equations to assess the algorithmic performance we illustrate characteristic features by means of representative three dimensional initial boundary value problems the proposed algorithm may open new avenues to patient specific therapy design by circumventing stability and convergence issues inherent to conventional staggered solution schemes

a theoretical and computational model for isotropic elastoplastic stress analysis in shells at large strains the article presents new aspects of large strain isotropic elastoplastic analysis of shells on the shell theory side we consider several possible continuum based parametrizations of the shell deformation and investigate their applicability with respect to the implementation of general three dimensional local constitutive models as an aspect of computational shell analysis we then discuss in detail the numerical implementation of a shell based on the parametrization of the top and bottom surface in terms of a new 8 node brick type mixed finite shell element on the basis of assumed strain and enhanced strain variational approaches on the side of plasticity theory we adopt a recently proposed intermediate configuration free formulation of large strain plasticity based on the notion of a plastic metric and consider its representation with respect to the parameter manifold of the shell this frame is formulated in terms of principal strains and principal stresses with respect to dual co and contra variant eigenvector triads associated with a mixed variant elastic strain tensor the new aspect of computational plasticity is the development of a stress update algorithm for the plasticity model mentioned above which includes a general return mapping in the eigenvalue space the algorithm can be applied to general coordinate charts and is particularly convenient when formulated with respect to the space of the curvilinear coordinates of the shell parametrization we demonstrate the performance of the finite element formulation and constitutive algorithms by means of several numerical examples

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

a formula of two partition hodge integrals jmg n where tpi ci l is the first chern class of l and xj cj e is the j th chern class of the hodge bundle the study of hodge integrals is an important part of intersection theory on mg n hodge integrals also naturally arise when one computes gromov witten invariants by localization techniques for example the following generating series of hodge integrals arises when one computes local invariants of a toric fano surface in a calabi yau 3 fold by virtual localization 33

a cutting plane algorithm for the linear ordering problem the linear ordering problem is an np hard combinatorial optimization problem with a large number of applications including triangulation of input output matrices archaeological senation minimizing total weighted completion time in one machine scheduling and aggregation of individual preferences in a former paper we have investigated the facet structure of the 0 1 polytope associated with the linear ordering problem here we report on a new algorithm that is based on these theoretical results the main part of the algorithm is a cutting plane procedure using facet defining inequalities this procedure is combined with various heuristics and branch and bound techniques our computational results compare favorably with the results of existing codes in particular we could triangulate all input output matrices of size up to 60 60 available to us within acceptable time bounds

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

a displacement based finite element formulation for incompressible and nearly incompressible cardiac mechanics the lagrange multiplier lm and penalty methods are commonly used to enforce incompressibility and compressibility in models of cardiac mechanics in this paper we show how both formulations may be equivalently thought of as a weakly penalized system derived from the statically condensed perturbed lagrangian formulation which may be directly discretized maintaining the simplicity of penalty formulations with the convergence characteristics of lm techniques a modified shamanskii newton raphson scheme is introduced to enhance the nonlinear convergence of the weakly penalized system and exploiting its equivalence modifications are developed for the penalty form focusing on accuracy we proceed to study the convergence behavior of these approaches using different interpolation schemes for both a simple test problem and more complex models of cardiac mechanics our results illustrate the well known influence of locking phenomena on the penalty approach particularly for lower order schemes and its effect on accuracy for whole cycle mechanics additionally we verify that direct discretization of the weakly penalized form produces similar convergence behavior to mixed formulations while avoiding the use of an additional variable combining a simple structure which allows the solution of computationally challenging problems with good convergence characteristics the weakly penalized form provides an accurate and efficient alternative to incompressibility and compressibility in cardiac mechanics