on plastic incompressibility within time adaptive finite elements combined with projection techniques abstract this article treats the interpretation of quasi static finite elements applied to constitutive equations of evolutionary type as a solution scheme to solve globally differential algebraic equations this concept is applied to finite strain viscoplasticity based on a model with non linear kinematic hardening under the assumption of plastic incompressibility the model is based on multiple multiplicative decomposition both for the deformation gradient into an elastic and an inelastic part as well as for the inelastic part into a kinematic hardening energy storage and a dissipative part both intermediate configurations are described by inelastic right cauchy green tensors satisfying inelastic incompressibility in the theoretical context the attention in view of the numerical treatment within finite elements is focused on diagonally implicit runge kutta methods which destroy the assumption of plastic incompressibility during the time integration due to an additive structure of the integration step in combination with a multilevel newton algorithm these algorithms embed the classical strain driven radial return method to this end a concept of geometric numerical integration is applied where the plastic incompressibility condition is taken into account as an additional side condition since the literature states large integration errors if the side condition is not taken into account a particular focus lies on the application of a time adaptive procedure accordingly the article investigates i the algorithmic treatment of kinematic hardening within time adaptive finite elements ii the influence of the perzyna type viscoplasticity approach in view of an order reduction phenomenon and iii the influence of taking into account the exact fulfillment of plastic incompressibility using a projection method having the advantage of simple implementation

stress computation and consistent tangent operator using non linear kinematic hardening models one possibility of formulating the tinite element method is founded on the principle of virtual displacement in which we want to include a rate independent elastoplastic constitutive model based on the assumption of a yield surface the constitutive equations result from the assumptions of small deformations hooke s law for the elastic domain the normality rule for the evolution of plastic strains the von mises yield condition and a special kind of kinematic hardening due to armstrong and frederick 1 in which linear kinematic hardening is generalized with a saturation term we show that it is not generally recommendable to propose large load steps to this end we investigate the influences of the non linear kinematic hardening model on the stress computation and the resulting consistent elastoplastic tangent operator the main topics of this paper are 1 development of a problem optimized backward euler method with regard to the kinematic hardening model 2 study of the influence of the saturation term on the numerical accuracy through isoerror maps and 3 computation of the consistent elastoplastic tangent operator

dehn surgery on arborescent links this paper studies dehn surgery on a large class of links called arborescent links it will be shown that if an arborescent link l is sufficiently complicated in the sense that it is composed of at least 4 rational tangles t pl qi with all qj 2 and none of its length 2 tangles are of the form t 1 2ql 1 2q2 then all complete surgeries on l produce haken manifolds the proof needs some result on surgery on knots in tangle spaces let t r 2s p 2q b ti u t2 li k be a tangle with k a closed circle and let m b int n ti u t2 we will show that if s 1 and p 1 mod 2q then om remains incompressible after all nontrivial surgeries oln k two bridge links are a subclass of arborescent links for such a link l p q most dehn surgeries on it are non haken however it will be shown that all complete surgeries yield manifolds containing essential laminations unless p q has a partial fraction decomposition of the form 1 r 1 s in which case it does admit non laminar surgeries

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

consistent tangent operator for plasticity models based on the plastic strain rate potential a stress updating integration algorithm is derived for use with plastic strain rate potentials and with the backward implicit euler method an explicit expression is also deduced for the consistent tangent modulus this analysis extends an earlier treatment developed for elastic perfectly plastic materials in that it applies to materials which harden isotropically the method is intended for use in finite element calculations that employ plasticity models based on the plastic strain rate potential it is particularly suitable for cases where the form of the plastic dual potential has been obtained from texture measurements or from crystallographic models that describe texture evolution during metal forming

a quantum computing primer for operator theorists this is an exposition of some of the aspects of quantum computation and quantum information that have connections with operator theory after a brief introduction we discuss quantum algorithms we outline basic properties of quantum channels or equivalently completely positive trace preserving maps the main theorems for quantum error detection and correction are presented and we conclude with a description of a particular passive method of quantum error correction

remarks on rate constitutive equations for finite deformation problems computational implications it is explicitly shown that if the spatial elasticity tensor of an elastic material is taken as isotropic for all possible configurations then its coefficients cannot be constants they must depend nontrivially on the jacobian determinant of the deformation gradient moreover the assumption typically made for computational purposes that its coefficients remain constant for all possible configurations is incompatible with elasticity it is further shown that an assumption widely used in the computational literature in the context of finite deformation plasticity namely relating an objective stress rate to the rate of deformation tensor through a fourth rank constant isotropic tensor is also incompatible with elasticity thus furnishing an example of an hypoelastic material which is not elastic

an efficient stress algorithm with applications in viscoplasticity and plasticity this paper deals with two main topics the first one concerns the equivalence of stress algorithms based on a backward euler step applied on viscoplastic models of chaboche type and their elastoplastic counterpart generally the stress algorithm yields a system of non linear algebraic equations and the corresponding consistent tangent operator occurring in the principle of virtual displacements leads to a system of linear equations this procedure can be obtained utilizing only numerical methods the second topic concerns a special constitutive relation based on a kinematic hardening model using a sum of armstrong frederick terms which is equivalent to a multi surface plasticity model applying this model a so called problem adapted stress algorithm is derived where only one non linear equation must be solved this result is independent of the number of terms in the hardening model furthermore only the viscoplastic algorithm must be implemented since it includes the elastoplastic constitutive model as a special case 1997 by john wiley sons ltd

finite strain viscoplasticity with nonlinear kinematic hardening phenomenological modeling and time integration abstract this article deals with a viscoplastic material model of overstress type the model is based on a multiplicative decomposition of the deformation gradient into elastic and inelastic part an additional multiplicative decomposition of inelastic part is used to describe a nonlinear kinematic hardening of armstrong frederick type two implicit time stepping methods are adopted for numerical integration of evolution equations such that the plastic incompressibility constraint is exactly satisfied the first method is based on the tensor exponential the second method is a modified euler backward method special numerical tests show that both approaches yield similar results even for finite inelastic increments the basic features of the material response predicted by the material model are illustrated with a series of numerical simulations

an updated lagrangian finite element sensitivity analysis of large deformations using quadrilateral elements a continuum parameter and shape sensitivity analysis is presented for metal forming processes using the finite element method the sensitivity problem is posed in a novel updated lagrangian framework as suitable for very large deformations when remeshing operations are performed during the analysis in addition to exploring the issue of transfer of variables between meshes for finite deformation analysis the complex problem of transfer of design sensitivities derivatives between meshes for large deformation inelastic analyses is also discussed a method is proposed that is shown to give accurate estimates of design sensitivities when remeshing operations are performed during the analysis sensitivity analysis for the consistent finite element treatment of near incompressibility within the context of the assumed strain methods is also proposed in particular the performance of four noded quadrilateral elements for the sensitivity analysis of large deformations is studied the results of the continuum sensitivity analysis are validated by a comparison with those obtained by a finite difference approximation i e using the solution of a perturbed deformation problem the effectiveness of the method is demonstrated by applications in the design optimization of metal forming processes copyright 2001 john wiley sons ltd

an eulerian finite element formulation for modelling stationary finite strain elastic deformation processes a new finite element formulation aimed at the modelling of stationary finite strain elastic deformation processes is presented the new formulation is based on an eulerian description of motion and on the transport of the deformation gradient tensor copyright 2004 john wiley sons ltd

an analysis of a new class of integration algorithms for elastoplastic constitutive relations an accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors is carried out in this paper for simplicity attention is confined to infinitesimal deformations the integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations general rate independent and rate dependent behaviour with plastic hardening or softening associated or non associated flow rules and nonlinear elastic response can be efficiently treated within the present framework isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding

on the implementation of inelastic constitutive equations with special reference to large deformation problems abstract methods for finite element analysis of inelastic problems are reviewed problems with currently popular methods based on rate principles of virtual work are pointed out a formulation is presented based on the exact incremental virtual work equation the procedure for integration of the constitutive rate equations to obtain incremental constitutive equations is based on the assumption of a constant strain rate or straight strain path during the increment full newton raphson iteration is used to solve the resulting set of nonlinear equations the treatment of the constitutive equations in this newton raphson scheme leads to a linearized form which is substantially different from the classical rate equations the procedure is implemented in a finite element program and its effectiveness is shown in a number of examples

numerical simulation of martensitic phase transitions in shape memory alloys using an improved integration algorithm the numerical simulation of structures made of shape memory materials is of increasing interest in different fields among others the computation of pipe connectors or medical devices like endoscopic instruments and stents is a challenge in such practical applications the pseudoelastic effect as well as the one way and two way shape memory effects are utilized these material properties are caused by martensitic phase transitions between austenite and martensite in the present contribution a recently proposed constitutive theory is numerically treated in the context of the finite element method this constitutive theory is formulated in the framework of continuum thermomechanics for geometrically linear problems and is able to represent the occurring martensitic phase transitions in shape memory alloys for the numerical integration of the evolution equations the backward euler method is applied in spite of the complexity of the constitutive theory it is shown that an improved integration procedure can be formulated which merely involves the solution of three non linear equations for three scalar valued unknown variables numerical examples show the capability of the proposed model and the improved integration algorithm copyright 2006 john wiley sons ltd

an implicit integration algorithm with a projection method for viscoplastic constitutive equations robinson s viscoplastic model a representative of the so called overstress models is integrated by use of the generalized midpoint rule the solution of the non linear system of algebraic equations arising from time discretization of the constitutive equations is determined using a projection method in combination with newton s method consistent tangent moduli are calculated and the quadratic convergence of the global newton equilibrium iteration is shown the time increment size is controlled by the convergence behaviour of the equilibrium iteration and the accuracy of the numerical integration various numerical examples are considered to demonstrate the efficiency of the methods

minimal and maximal operator spaces and operator systems in entanglement theory abstract we examine k minimal and k maximal operator spaces and operator systems and investigate their relationships with the separability problem in quantum information theory we show that the matrix norms that define the k minimal operator spaces are equal to a family of norms that have been studied independently as a tool for detecting k positive linear maps and bound entanglement similarly we investigate the k super minimal and k super maximal operator systems that were recently introduced and show that their cones of positive elements are exactly the cones of k block positive operators and unnormalized states with schmidt number no greater than k respectively we characterize a class of norms on the k super minimal operator systems and show that the completely bounded versions of these norms provide a criterion for testing the schmidt number of a quantum state that generalizes the recently developed separability criterion based on trace contractive maps

efficient implicit integration for finite strain viscoplasticity with a nested multiplicative split abstract an efficient and reliable stress computation algorithm is presented which is based on implicit integration of the local evolution equations of multiplicative finite strain plasticity viscoplasticity the algorithm is illustrated by an example involving a combined nonlinear isotropic kinematic hardening numerous backstress tensors are employed for a better description of the material behavior the considered material model exhibits the so called weak invariance under arbitrary isochoric changes of the reference configuration and the presented algorithm retains this useful property even more the weak invariance serves as a guide in constructing this algorithm the constraint of inelastic incompressibility is exactly preserved as well the proposed method is first order accurate concerning the accuracy of the stress computation the new algorithm is comparable to the euler backward method with a subsequent correction of incompressibility ebmsc and the classical exponential method em regarding the computational efficiency the new algorithm is superior to the ebmsc and em some accuracy tests are presented using parameters of the aluminum alloy 5754 o and the 42crmo4 steel fem solutions of two boundary value problems using msc marc are presented to show the correctness of the numerical implementation

unlinking via simultaneous crossing changes given two distinct crossings of a knot or link projection we consider the question under what conditions can we obtain the unlink by changing both crossings simultaneously more generally for which simultaneous twistings at the crossings is the genus reduced though several examples show that the answer must be complicated they also suggest the correct necessary conditions on the twisting numbers let l be an oriented link in s3with a generic projection onto the plane r let a be a short arc in r2 transverse to both strands of l at a crossing so that the strands pass through a in opposite directions then the inverse image of a contains a disk punctured twice with opposite orientation by l define a crossing disk d for a link l in s3 to be a disk which intersects l in precisely two points of opposite orientation it is easy to see that any crossing disk arises in the manner described twisting the link q times as it passes through d is equivalent to doing llq surgery on dd in s3 and adds 29 crossings to this projection of l we say that this new link l q is obtained by adding q twists at d call dd a crossing circle for l a crossing disk d and its boundary do are essential if dd bounds no disk disjoint from l this is equivalent to the requirement that l cannot be isotoped off d in s3 od here we examine how a link can be turned into the unlink via simultaneous twists on disjoint crossing disks in particular we prove an analogue for pairs of crossing disks of the following theorem a much more general version of which is proven in st 1 41 see also gal

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

a paradigm for higher order polygonal elements in finite elasticity using a gradient correction scheme abstract recent studies have demonstrated that polygonal elements possess great potential in the study of nonlinear elastic materials under finite deformations on the one hand these elements are well suited to model complex microstructures e g particulate microstructures and microstructures involving different length scales and incorporating periodic boundary conditions on the other hand polygonal elements are found to be more tolerant to large localized deformations than the standard finite elements and to produce more accurate results in bending and shear with mixed formulations lower order mixed polygonal elements are also shown to be numerically stable on voronoi type meshes without any additional stabilization treatment however polygonal elements generally suffer from persistent consistency errors under mesh refinement with the commonly used numerical integration schemes as a result non convergent finite element results typically occur which severely limit their applications in this work a general gradient correction scheme is adopted that restores the polynomial consistency by adding a minimal perturbation to the gradient of the displacement field with the correction scheme the recovery of optimal convergence for solutions of displacement based and mixed formulations with both linear and quadratic displacement interpolants is confirmed by numerical studies of several boundary value problems in finite elasticity in addition for mixed polygonal elements the various choices of the pressure field approximations are discussed and their performance on stability and accuracy are numerically investigated we present applications of those elements in physically based examples including a study of filled elastomers with interphasial effect and a qualitative comparison with cavitation experiments for fiber reinforced elastomers

thermomechanical response of solids at high strains natural approach abstract the paper develops in pursuance of 4 the theoretical framework appertaining to coupled thermomechanical deformations of solids subject to large as well as inelastic deformations the essential feature of the analysis is a consistent natural formulation which encompasses also all thermodynamic aspects on the other hand it must be admitted that current concepts on mechanical constitutive assumptions 5 6 are not sufficiently sophisticated to permit a precise generalisation for the purpose of incorporating thermomechanical effects and delivering a fully compatible theory of the coupled problem uniqueness and bifurcation of the solutions as well as stable postcritical deformation paths are also considered in this account furthermore algorithms for the solution of the nonlinear algebraic equations representing the discretised problem and in particular quasi newton techniques are discussed the paper concludes with a number of applications of technical relevance

on the numerical treatment of finite deformations in elastoviscoplasticity abstract this paper deals with the generalization of a geometric linear viscoplastic model to finite strains and its numerical application we owe the original formulation of the applied model to perzyna and chaboche it includes nonlinear isotropic and kinematic hardening as well as a nonlinear rate dependence the constitutive equations are integrated numerically in the context of a finite element formulation from theoretical considerations it is known that in the case of vanishing viscosity or slow processes rate independent plasticity arises as an asymptotic limit accordingly the numerical formulation includes this property in fact the stress algorithm corresponding to viscoplasticity is reduced to the asymptotic limit in a most simple way namely by setting the viscosity parameter equal to zero furthermore it is shown that the numerical integration of the constitutive model involves the solution of only one nonlinear equation for one scalar unknown this even applies to a sum of armstrong frederick terms the algorithm incorporates the inelastic incompressibility on the level of the gau points numerical computations of examples taken from metal forming technology show the physical significance of the model and the reliability of the numerical algorithm these calculations have been carried out by means of the finite element program psu

some computational aspects of large deformation rate dependent plasticity problems abstract the governing equations for a finite element formulation of boundary value problems for large deformation metal forming processes are derived using a principle of virtual work formulated in a lagrangian reference system the updated lagrangian method is used to simplify the equations the resulting nonlinear equilibrium equations are solved using newton s method a constitutive model for large deformation rate dependent plasticity is developed the model incorporates a one parameter implicit integration operator for stability and accuracy the stressrate strain rate relation is written in terms of the jaumann rate of stress numerous example problems are solved to demonstrate the effectiveness of the numerical algorithms

a formulation of the mitc4 shell element for finite strain elasto plastic analysis abstract a finite strain elasto plastic formulation is developed for the mitc4 shell element the developed formulation is based on lee s multiplicative decomposition of the deformation gradient and on the hyperelastic expression of von mises flow rule expressed in terms of hencky s strain tensor the formulation incorporates thickness stretching degrees of freedom that are condensed at the element level by imposing the classical in layer plane stress condition a symmetric and consistent tangent stiffness matrix is also developed

cones of positive maps and their duality relations the structure of cones of positive and k positive maps acting on a finite dimensional hilbert space is investigated special emphasis is given to their duality relations to the sets of superpositive and k superpositive maps we characterize k positive and k superpositive maps with regard to their properties under taking compositions a number of results obtained for maps are also rephrased for the corresponding cones of block positive k block positive separable and k entangled operators due to the jamiolkowski choi isomorphism generalizations to a situation where no such simple isomorphism is available are also made employing the idea of mapping cones as a side result to our discussion we show that extreme entanglement witnesses which are optimal should be of special interest in entanglement studies

robustness of isogeometric structural discretizations under severe mesh distortion abstract this paper investigates higher order and higher continuity functions in isogeometric structural analysis under distortion of the control and physical meshes first the concepts behind isogeometric analysis are briefly reviewed the effect of perturbing control points upon the geometrical mapping is observed in the one dimensional setting the concept is extended to multiple dimensions with a series of cases where the interior of a cube is distorted in different ways and patch tests are performed to assess accuracy a circular fillet patch is introduced through the appropriate degeneration of a control mesh in order to address the problem of modeling small features in finite element models the fillet patch is tested with two problems of linear elasticity and is shown to be accurate the investigation is further extended to the setting of large deformation nearly incompressible nonlinear elasticity with two examples which make use of the recently proposed f projection method

implementation of cyclic plasticity models based on a general form of kinematic hardening this paper deals with implementation of cyclic plastic constitutive models in which a general form of strain hardening and dynamic recovery is employed to represent the multilinear as well as non linear evolution of back stress first in order to incorporate such a general form of kinematic hardening in finite element methods successive substitution and its convergence are discussed for implicitly integrating stress moreover a new expression of consistent tangent modulus is derived by introducing a set of fourth rank constitutive parameters into discretized kinematic hardening then the constitutive parameters introduced are specified in three cases of the general form of kinematic hardening the three cases have distinct capabilities of simulating ratcheting and cyclic stress relaxation numerical examples are given to verify the convergence in successive substitution and the new expression of consistent tangent stiffness error maps for implicitly integrating stress under non proportional as well as proportional loading are also given to show that the multilinear case of the general form provides high accuracy even if strain increment is very large copyright 2002 john wiley sons ltd

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

on the theoretical and numerical modelling of armstrong frederick kinematic hardening in the finite strain regime abstract on the theoretical level the present paper presents a detailed comparison of recent finite strain models for armstrong frederick kinematic hardening thereby two strategies are discussed 1 chaboche type concepts considering the back stress as internal variable 2 continuum mechanical extensions of the classical rheological model using only strain like internal variables it is shown in the paper that models of the second kind can be recast in the format of anisotropic inelasticity with structure tensors second the work focuses on the algorithmic treatment of the kinematic hardening concepts presented before this problem has been tackled up to now only in the context of linearized models in contrast to isotropic finite elastoplasticity the integration cannot be carried out with respect to principal axes therefore a new integration algorithm is developed which is suitable for the anisotropic case but still retains plastic incompressibility in the case of small elastic deformation the algorithm reduces to a system of only one non linear equation and twelve linear equations in general the computational effort of the new scheme does not exceed the one of the backward euler scheme which has the disadvantage that plastic incompressibility is not fulfilled automatically several numerical examples show that the representatives of both approaches 1 and 2 yield similar results if physically reasonable material parameters are chosen

cones with a mapping cone symmetry in the finite dimensional case abstract in the finite dimensional case we present a new approach to the theory of cones with a mapping cone symmetry first introduced by stormer our method is based on a definition of an inner product in the space of linear maps between two algebras of operators and the fact that the jamiolkowski choi isomorphism is an isometry we consider a slightly modified class of cones although not substantially different from the original mapping cones by stormer using the new approach several known results are proved faster and often in more generality than before for example the dual of a mapping cone turns out to be a mapping cone as well without any additional assumptions the main result of the paper is a characterization of cones with a mapping cone symmetry saying that a given map is an element of such cone if and only if the composition of the map with the conjugate of an arbitrary element in the dual cone is completely positive a similar result was known in the case where the map goes from an algebra of operators into itself and the cone is a symmetric mapping cone our result is proved without the additional assumptions of symmetry and equality between the domain and the target space we show how it gives a number of older results as a corollary including an exemplary application

accuracy and stability of integration algorithms for elastoplastic constitutive relations an analysis of accuracy and stability of algorithms for the integration of elastoplastic constitutive relations is carried out in this paper reference is made to a very general internal variable formulation of plasticity and to two families of algorithms that generalize the well known trapezoidal and midpoint rules to fit the present context other integration schemes such as the radial return mean normal and closest point procedures are particular cases of this general formulation the meaning of first and second order accuracy in the presence of the plastic consistency condition is examined in detail and the criteria derived are used to identify two second order accurate members of the proposed algorithms a general methodology is also derived whereby the numerical stability properties of integration schemes can be systematically assessed with the aid of this methodology the generalized midpoint rule is seen to have far better stability properties than the generalized trapezoidal rule finally numerical examples are presented that illustrate the performance of the algorithms

on nonisothermal elastoplastic analysis of shell components employing realistic hardening responses abstract in the present paper efficient numerical algorithms for elastoplastic analysis of shell like structural components will be proposed employing nonisothermal realistic highly nonlinear hardening responses the closest point projection integration algorithm is presented using a reissner mindlin type kinematic shell model completely formulated in tensor notation further a consistent elastoplastic tangent modulus is derived which ensures high convergence rates in the global iteration approach the integration algorithm has been implemented into a layered assumed strain isoparametric finite element which also enables geometrical nonlinearities including finite rotations the nonisothermal elastoplastic response of a circular cylindrical shell and a box column under axial compression is analysed under the assumption of an adiabatic process the increase in temperature is computed during elastoplastic deformation robustness and numerical stability of the proposed algorithms are demonstrated

extension of positive maps into b h soient 7b h et 7b k des espaces de hilbert complexes et soit a un sous espace lineaire auto adjoint norme clos d operateurs bornes b 7b k sur 7b k contenant l operateur identite si on note par b a 7b h les applications positives dans l ensemble b a 7b h des applications lineaires bornees de a dans b 7b h on etudie le probleme d extension pour des applications dans b a 7b h aux applications dans b b 7b k 7b h

equivalent plastic strain gradient enhancement of single crystal plasticity theory and numerics we propose a visco plastic strain gradient plasticity theory for single crystals the gradient enhancement is based on an equivalent plastic strain measure two physically equivalent variational settings for the problem are discussed a direct formulation and an alternative version with an additional micromorphic like field variable which is coupled to the equivalent plastic strain by a lagrange multiplier the alternative formulation implies a significant reduction of nodal degrees of freedom the local algorithm and element stiffness matrices of the finite element discretization are discussed numerical examples illustrate the advantages of the alternative formulation in three dimensional simulations of oligo crystals by means of the suggested formulation complex boundary value problems of the proposed plastic strain gradient theory can be solved numerically very efficiently

integration methods for complex plastic constitutive equations abstract this paper shows new results concerning the finite element computations with complex plastic and viscoplastic constitutive equations the integration procedure then needs special numerical treatments when a large number of internal variables are present or for stiff non linearities implicit and explicit integration methods are compared the general solution proposed can be applied either in plasticity or in viscoplasticity for isotropic or anisotropic materials several options are proposed in the numerical scheme and for the completion step for the semi implicit scheme numerical tests are performed in order to compare the relative performances of the various approaches

geometric integrators for multiplicative viscoplasticity analysis of error accumulation abstract the inelastic incompressibility is a typical feature of metal plasticity viscoplasticity over the last decade there has been a great amount of research related to construction of numerical integration algorithms which exactly preserve this property in this paper we examine both numerically and mathematically the excellent accuracy and convergence characteristics of such integrators in order to simplify the considerations we consider strain driven processes without hardening effects in terms of a classical model of multiplicative viscoplasticity we illustrate the notion of exponential stability of the exact solution we show that this property enables the construction of effective and stable numerical algorithms if the incompressibility is exactly satisfied on the other hand if the incompressibility constraint is violated spurious degrees of freedom are introduced in general this results in the loss of the exponential stability and a dramatic deterioration of convergence of numerical methods

spectral conditions for positive maps we provide partial classification of positive linear maps in matrix algebras which is based on a family of spectral conditions this construction generalizes the celebrated choi example of a map which is positive but not completely positive it is shown how the spectral conditions enable one to construct linear maps on tensor products of matrix algebras which are positive but only on a convex subset of separable elements such maps provide basic tools to study quantum entanglement in multipartite systems

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

enhanced linear triangle for plasticity problems in j 2 solids due to their economy and capability to reproduce high gradient zones low order elements are of great interest in the calculations involving localized failure however the performance of the simplest element the three nodes triangle under incompressible and bending dominated situations is very poor and the computed results unreliable this paper presents an inexpensive three fields u p formulation solving these issues as shown in the examples of application

separable states and positive maps abstract using the natural duality between linear functionals on tensor products of c algebras with the trace class operators on a hilbert space h and linear maps of the c algebra into b h we study the relationship between separability entanglement and the peres condition of states and positivity properties of the linear maps

generation of mapping cones from small sets we answer in the affirmative a recently posed question that asked if there exists an untypical convex mapping cone i e one that does not arise from the transpose map and the cones of k positive and k superpositive maps we explicitly construct such a cone based on atomic positive maps our general technique is to consider the smallest convex mapping cone generated by a single map and we derive several results on such mapping cones we use this technique to also present several other examples of untypical mapping cones including a family of cones generated by spin factors we also provide a full characterization of mapping cones generated by single elements in the qubit case in terms of their typicality

objectivity of incremental constitutive relations over finite time steps in computational finite deformation analyses abstract computational techniques which preserve the objectivity of incremental constitutive relations for finite elastic or inelastic materials for finite time steps during which the material elements may undergo finite rotations are presented these techniques are useful in finite deformation finite rotations and finite strain computational analysis of two as well as three dimensional solids and structures

the structural physical approximations and optimal entanglement witnesses we introduce the notions of positive and copositive types for entanglement witnesses depending on the distance to the positive part and copositive part an entanglement witness w is of positive type if and only if its partial transpose w is of copositive type we show that if the structural physical approximation spa of w is separable then w should be of copositive type and the spa of w is never separable unless w is of both positive and copositive types this shows that the spa conjecture is meaningful only for those of copositive type we provide examples to show that the spa conjecture fails even for the case of copositive types

hourglass control in linear and nonlinear problems abstract mesh stabilization techniques for controlling the hourglass modes in under integrated hexahedral and quadrilateral elements are described it is shown that the orthogonal hourglass techniques previously developed can be obtained from simple requirements that insure the consistency of the finite element equations in the sense that the gradients of linear fields are evaluated correctly it is also shown that this leads to an hourglass control that satisfies the patch test the nature of the parameters which relate the generalized stresses and strains for controlling hourglass modes is examined by means of a mixed variational principle and some guidelines for their selection are discussed finally effective means of implementing these hourglass procedure in computer codes are described applications to both the laplace equation and the equations of solid mechanics in 2 and 3 dimensions are considered

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

cones and norms in the tensor product of matrix spaces abstract this paper is of expository nature in the tensor product of two matrix spaces m m and m n we consider three natural cones the first is the cone p 0 of positive semi definite matrices the second is the cone p generated by tensor products of positive semi definite matrices in the factor spaces and the third cone p is defined as the dual cone of p correspondingly in the tensor space identified with m mn besides the spectral and the trace norms we consider several tensor norms generated by sepectral and or trace norms in the factor spaces we will study relations among those norms as well as relations among the three kinds of order intervals in the tensor product

the incremental flow formulation for the numerical analysis of 3 dimensional viscous deformation processes continuum formulation and computational aspects abstract the incremental flow formulation recently presented j bonet the incremental flow formulation for the numerical analysis of plane stress and thin sheet forming processes comput methods appl mech engrg in press is applied herein for the analysis of three dimensional viscous deformation processes using this technique the equilibrium equations become functions of the nodal positions instead of nodal velocities as in the case of the standard flow formulation consequently geometrical constraints such as the incompressibility of the flow can be enforced in an exact manner the discretization techniques essential for a successful implementation of this method are also discussed in particular the element proposed is the 8 noded hexahedron with a mean quadrature integration technique finally some applications relating to the superplastic forming of thick sheet are used to illustrate the effectiveness of the methods presented

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

on the computational significance of the strain space formulation of plasticity theory the strain space and traditional stress space formulations of plasticity theory are compared we show how plasticity theory has been implemented numerically to solve static and dynamic problems and conclude that the numerical loading criteria that have been used for two decades are identical to the strain space loading criteria proposed by naghdi and co workers

an excursion into large rotations the present discourse develops an enlarged exploration of the matrix formulation of finite rotations in space initiated in 1 it is shown how a consistent but subtle matrix calculus inevitably leads to a number of elegant expressions for the transformation or rotation matrix t appertaining to a rotation about an arbitrary axis also analysed is the case of multiple rotations about fixed or follower axes particular attention is paid to an explicit derivation of a single compound rotation vector equivalent to two consecutive arbitrary rotations this theme is discussed in some detail for a number of cases semitangential rotations for which commutativity holds first proposed in 2 3 are also considered furthermore an elementary geometrical analysis of large rotations is also given finally we deduce in an appendix using a judicious reformulation of quarternions the compound pseudovector representing the combined effect of n rotations in the author s opinion the present approach appears preferable to a pure vectorial scheme and even more so to an indicial formulation and is computationally more convenient

a perturbed lagrangian formulation for the finite element solution of contact problems making use of a perturbed lagrangian formulation a finite element procedure for contact problems is developed for the general case in which node to node contact no longer holds the proposed procedure leads naturally to a discretization of the contact interface into contact segments within the context of a bilinear interpolation for the displacement field a mixed finite element approximation is introduced by assuming discont naous contact pressure constant on the contact segment because of this piece wise constant approximation the gap function enters into the formulation in an average sense instead of through a point wise definition numerical examples are presented that illustrate the performance of the proposed procedure current finite element formulations for contact problems based on either the classical lagrange parameter procedure l 3 12 203 or the penalty function method 4 6 11 are characterized by a point wise enforcement of the contact constraint condition in the sense that penetration of the bodies is established on a nodal basis moreover in this methods the recovery of the contact pressure over the element from the contact nodal forces generally requires an additional procedure within the framework of classical lagrange multiplier methods the contact condition is exactly satisfied by transforming the constrained problem into an unconstrained one with the introduction of additional variables lagrange multipliers these extra variables add computational effort to the solution process which often requires special procedures to handle the presence of zero diagonal terms penalty methods on the other hand enable one to transform the constrained problem into an unconstrained one without introducing additional variables the constraint condition is now satisfied only approximately for finite values of the penalty parameter the main difhculty associated with these methods however lies in the poor conditioning of the problem as the penalty is increased to more accurately enforce the constraint condition this is a well understood phenomenon particularly in the context of the incompressible and nearly incompressible problem in solid and fluid mechanics e g see l 22 25 for a review recently augmented lagrangian procedures have been proposed as a promising way to partially overcome these difficulties and regularize the penalty formulation e g see the survey in 7 8 within the framework of zinearited e u c it is possible to restrict the finite element formulation of contact problems by assuming that node to node contact occurs this is in fact the case often considered in the literature l 2 4 6 12 20 211 in the general context of fully

inverse motion based form finding for quasi incompressible finite electroelasticity this work deals with inverse motion based form finding for electroelasticity the inverse motion problem is formulated for the electroelastic case and the resulting equations are implemented within a finite element framework a four field variational approach is adopted taking into consideration the typically incompressible behavior of the elastomer materials commonly used in electromechanical applications by means of numerical simulations the inverse motion based form finding makes it possible to design the referential configuration so that a given set of loads and boundary conditions results in a prespecified deformed configuration the computational finite element framework established in this work allows for such numerical simulations and testing and thereby the possibility to improve the design and accuracy in electroelastic applications such as grippers sensors and seals less

there is no direct generalization of positive partial transpose criterion to the three by three case we show that there cannot exist a straightforward generalization of the famous positive partial transpose criterion to three by three systems we call straightforward generalizations that use a finite set of positive maps and arbitrary local rotations of the tested two partite state in particular we show that a family of extreme positive maps discussed in a paper by ha and kye open syst inf dyn 18 323 337 2011 cannot be replaced by a finite set of witnesses in the task of entanglement detection in three by three systems in a more mathematically elegant parlance our result says that the convex cone of positive maps of the set of three dimensional matrices into itself is not finitely generated as a mapping cone

formulation and numerical solution of non smooth elasto visco plasticity models abstract in this work we describe in detail a model for small strain elasto visco plasticity with convex non smooth yield functions and associative nonlinear kinetic laws restricted to linear hardening using concepts of non smooth convex geometry numerical methods are developed to integrate the evolution equations of the model these algorithms are analyzed and shown to inherit a discrete dissipation inequality irrespective of the smoothness of the yield function the results are applied to models based on tresca s and drucker prager s yield criteria which include all possible types of non smoothness numerical examples are shown to illustrate the performance of the methods

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

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

numerical integration of rate constitutive equations in finite deformation analysis abstract in analysis of finite deformation problems the use of constitutive equations in rate form is often required in a spatial setting these equations may express a relationship between some objective rate of spatial stress tensor and the rate of deformation constitutive equations of this type characterize a variety of material models including hyperelasticity hypoelasticity and elastoplasticity employing geometrical concepts a family of unconditionally stable and incrementally objective algorithms is proposed for the integration of such rate constitutive equations these algorithms which are appropriate for finite deformation analysis are applicable to any choice of stress rate and in most cases employ quantities that arise naturally in the context of finite element analysis examples illustrate the objectivity and accuracy of the algorithms

penalty finite element methods for the analysis of stokesian flows a study of a class of finite element methods for the analysis of stokes problem based on the use of exterior penalty formulations is described the effects of selective reduced integration i e the use of quadrature rules for integrating the penalty terms which are of lower order than that required to integrate polynomial approximations of these terms exactly are investigated error estimates are derived and the numerical stability of these methods as depicted by a special babuska brezzi condition is explored in some detail the results of several numerical experiments with these methods are also given

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

dehn surgery on knots in 3 manifolds it has been known for over 30 years that every closed connected orientable 3manifold is obtained by surgery on a link in s3 8 however a classification of such 3 manifolds in terms of this surgery construction has remained elusive this is due primarily to the lack of uniqueness of the surgery description in 5 kirby gave us a calculus of surgery diagrams however the lack of a canonical surgical method of getting from one 3 manifold to another has hampered further progress in this paper we show that if one restricts attention to the case where a surgery curve is homotopically trivial in a 3 manifold then one has the following uniqueness theorem

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

on the modelling of non linear kinematic hardening at finite strains with application to springback comparison of time integration algorithms the paper discusses the derivation and the numerical implementation of a finite strain material model for non linear kinematic and isotropic hardening the kinematic hardening component represents a continuum extension of the classical rheological model of armstrong frederick kinematic hardening in addition a comparison between several numerical algorithms for the integration of the evolution equations is conducted in particular a new form of the exponential map that preserves the plastic volume and the symmetry of the internal variables as well as two modifications of the backward euler scheme are discussed finally the applicability of the model for springback prediction is demonstrated by performing simulations of the draw bending process and a comparison with experiments the results show an excellent agreement between simulation and experiment copyright 2007 john wiley sons ltd

a return mapping algorithm for cyclic viscoplastic constitutive models abstract this paper presents a return mapping algorithm for cyclic viscoplastic constitutive models that include material memory effects the constitutive model is based on multi component forms of kinematic and isotropic hardening variables in conjunction with von mises yield criterion armstrong frederick a f type rules are used to describe the nonlinear evolution of each of the multi component kinematic hardening variables a saturation type exponential rule is used to describe the nonlinear evolution of each of the isotropic hardening variables the concept of memory surface is used to describe the strain range dependent material memory effects that are induced by the prior strain histories in this paper the above class of cyclic viscoplastic constitutive models is formulated within a consistent thermodynamic framework that encompasses the standard generalized materials framework furthermore a complete algorithmic treatment of the above rate dependent constitutive model is also presented for any desired stress or strain constrained configuration subspace a generalized midpoint algorithm is used to integrate the rate constitutive equations the consistent tangent operator is obtained by linearizing the return mapping algorithm and is found to be unsymmetric due to the presence of nonlinear evolution rules for the kinematic hardening variables several numerical examples representing the cyclic hardening and softening behavior transient and stabilized hysteresis behavior and the non fading memory effects of the material are presented these examples demonstrate the accuracy and robustness of the present algorithmic framework for modeling the cyclic viscoplastic behavior of the material

second order accurate integration algorithms for von mises plasticity with a nonlinear kinematic hardening mechanism abstract two second order numerical schemes for von mises plasticity with a combination of linear isotropic and nonlinear kinematic hardening are presented the first scheme is the generalized midpoint integration procedure originally introduced by ortiz and popov in 1985 detailed and applied here to the case of armstrong frederick nonlinear kinematic hardening the second algorithm is based on the constitutive model exponential based reformulation and on the integration procedure previously introduced by the authors in the context of linearly hardening materials there are two main targets to the work firstly we wish to extensively test the generalized midpoint procedure since in the scientific literature no thorough numerical testing campaign has been carried out on this second order algorithm secondly we wish to extend the exponential based integration technique also to nonlinear hardening materials a wide numerical investigation is carried out in order to compare the performance of the two methods

constitutive equations for micropolar hyper elastic materials in this paper the concept of hyper elasticity in the micropolar continuum theory is investigated the restrictions on the fourth order elasticity tensors are investigated using the representation theorems a general form of constitutive equations for micropolar hyper elastic isotropic materials is presented as some special cases generalizations of the neo hookean and mooney rivlin type materials to the micropolar continuum theory are presented the generalized constitutive equations reduce to those of the microplar linear elasticity theory when the deformations are infinitesimal also updated lagrangian finite element formulations for the micropolar hyper elastic materials are presented considering two planar examples it is shown that an increase in the micropolar parameter results in the reduction of the deformation of the bodies also it is shown that for a specimen with very small dimensions e g in the micron level the micropolar effects are more sensible furthermore it is shown that the influence of the micropolar parameters is dependent not only on the size of the body but also to its geometry and loading conditions for the problems in which the deformation is very close to a homogeneous state the micropolar effects are negligible