a fuzzy user optimal route choice problems using a link based fuzzy variational inequality formulation abstract a link based fuzzy user optimal route choice problem embedding link interactions is formulated using the variational inequality approach to avoid prohibitive arithmetic computations and by taking a plausible point estimate of each link travel time interval at a certain cut level this fuzzy problem reduces to a crisp user optimal route choice model which may be readily solved by the so called diagonalization method the corresponding user optimal conditions are explicitly stated and demonstrated by means of a numerical example

a novel mixed finite element for finite anisotropic elasticity the ska element simplified kinematics for anisotropy abstract a variety of numerical approximation schemes for boundary value problems suffer from so called locking phenomena it is well known that in such cases several finite element formulations exhibit poor convergence rates in the basic variables a serious locking phenomenon can be observed in the case of anisotropic elasticity due to high stiffness in preferred directions the main goal of this paper is to overcome this locking problem in anisotropic hyperelasticity by introducing a novel mixed variational framework therefore we split the strain energy into two main parts an isotropic and an anisotropic part for the isotropic part we can apply different well established approximation schemes and for the anisotropic part we apply a constant approximation of the deformation gradient or the right cauchy green tensor this additional constraint is attached to the strain energy function by a second order tensorial lagrange multiplier governed by a simplified kinematic for the anisotropic part as a matter of fact for the tested boundary value problems the ska element based on quadratic ansatz functions for the displacements performs excellent and behaves more robust than competitive formulations

spatial representation of evolving anisotropy at large strains a phenomenological model for evolving anisotropy at large strains is presented the model is formulated using spatial quantities and the anisotropic properties of the material is modeled by including structural variables evolution of anisotropy is accounted for by introducing substructural deformation gradients which are linear maps similar to the usual deformation gradient the evolution of the substructural deformation gradients is governed by the substructural plastic velocity gradients in a manner similar to that for the continuum certain topics related to the numerical implementation are discussed and a simple integration scheme for the local constitutive equations is developed to demonstrate the capabilities of the model it is implemented into a finite element code two numerical examples are considered deformation of uniform plate with circular hole and the drawing of a cup in the two examples it is assumed that initial cubic material symmetry applies to both the elastic and plastic behavior to be specific a polyconvex helmholtz free energy function together with a yield function of quadratic type is adopted

coupled map lattices one step forward and two steps back abstract we discuss the general notion of lattice dynamical systems and some recent progress in their studies we suggest also the approach that allows to extract some information on the dynamics of finitely extended real systems from the results obtained on the infinitely extended artificial ones

a stabilisation approach for topology optimisation of hyperelastic structures with the simp method abstract this paper presents a novel computational approach for simp based topology optimisation to of hyperelastic materials at large strains during the to process for structures subjected to very large deformations and especially in the presence of intermediate density regions the standard newton solver or its arc length variant have been reported not to converge refer to references wang et al 2014 lahuerta et al 2013 and liu et al 2017 in this paper the new to stabilisation technique proposed in ortigosa et al 2019 in the context of level set to initially devised to alleviate numerical instabilities inherent to level set to is extended for the to by means of the simp method the success of the methodology rests on the combination of two distinct key ingredients first the nonlinear equilibrium equations of motion for intermediate to design stages are solved in a non exact albeit consistent incrementally linearised fashion by splitting the design load into a number of load increments second the resulting linearised tangent elasticity tensor is locally stabilised regularised in order to prevent its loss of positive definiteness and thus avoid the loss of convexity of the discrete tangent operator this solution strategy is shown to be extremely robust in the context of density based to where the constitutive law of the underlying evolving solid structure is a mixture of solid and void constituents the latter classically defined by means of a fictitious strain energy the robustness and applicability of this to methodological approach are thoroughly demonstrated through an ample spectrum of challenging numerical examples ranging from benchmark two dimensional plane stress examples to larger scale three dimensional applications crucially the performance of all the final designs has been tested at a post processing stage without adding any source of artificial stiffness specifically an arc length newton raphson method has been employed in conjunction with a ratio of the material parameters for void and solid regions of 1 0 12

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

a computational framework for polyconvex large strain elasticity abstract this paper presents a novel computational formulation for large strain polyconvex elasticity the formulation based on the original ideas introduced by schroder et al 2011 introduces the deformation gradient the fibre map its adjoint the area map and its determinant the volume map as independent kinematic variables of a convex strain energy function compatibility relationships between these variables and the deformed geometry are enforced by means of a multi field variational principle with additional constraints this process allows the use of different approximation spaces for each variable the paper extends the ideas presented in schroder et al 2011 by introducing conjugate stresses to these kinematic variables which can be used to define a generalised convex complementary energy function and a corresponding complementary energy principle of the hellinger reissner type where the new conjugate stresses are primary variables together with the deformed geometry both compressible and incompressible or nearly incompressible elastic models are considered a key element to the developments presented in the paper is the new use of a tensor cross product presented for the first time by de boer 1982 page 76 which facilitates the algebra associated with the adjoint of the deformation gradient for the numerical examples quadratic interpolation of the displacements piecewise linear interpolation of strain and stress fields and piecewise constant interpolation of the jacobian and its stress conjugate are considered for compressible cases in the case of incompressible materials two formulations are presented first continuous quadratic interpolation for the displacement together with piecewise constant interpolation for the pressure and second linear continuous interpolation for both displacement and pressure stabilised via a petrov galerkin technique

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

density of defects and spatial entropy in extended systems abstract we consider a distribution of defects in the spatial structures of nonlinear fields for some classes of lattice systems it is shown that a critical density of defects is inversely proportional to a logarithm of a nonlinearity energy pumping the relation between the density of defects and the topological entropy of spatial structures of the field is also obtained

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

statistical mechanics of probabilistic cellular automata we investigate the behavior of discrete time probabilistic cellular automata pca which are markov processes on spin configurations on ad dimensional lattice from a rigorous statistical mechanics point of view in particular we exploit whenever possible the correspondence between stationary measures on the space time histories of pcas on d and translation invariant gibbs states for a related hamiltonian on d 1 this leads to a simple large deviation formula for the space time histories of the pca and a proof that in a high temperature regime the stationary states of the pca are gibbsian we also obtain results about entropy fluctuations and correlation inequalities and demonstrate uniqueness of the invariant state and exponential decay of correlations in a high noise regime we discuss phase transitions in the low noise or low temperature regime and review toom s proof of nonergodicity of a certain class of pcas

a computational framework for large strain nearly and truly incompressible electromechanics based on convex multi variable strain energies the series of papers published by gil and ortigosa gil and ortigosa 2016 ortigosa and gil 2016 0000 introduced a new convex multi variable variational and computational framework for the numerical simulation of electro active polymers eaps in scenarios characterised by extreme deformations and or extreme electric fields building upon this body of work five key novelties are incorporated in this paper first a generalisation of the concept of multi variable convexity to energy functionals additively decomposed into isochoric and volumetric components this decomposition is typical of nearly and truly incompressible materials group which represents the majority of the most relevant eaps second convexification or regularisation strategies are applied to a priori non convex multi variable isochoric functionals to yield physically meaningful convex multi variable functionals third based on the mixed variational principles introduced in gil and ortigosa 2016 in the context of compressible electro elasticity a novel extended hu washizu mixed variational principle for nearly and truly incompressible scenarios is presented from the computational standpoint a static condensation procedure is applied in order to condense out the element wise extra fields the resulting formulation having a comparable cost to the more standard three field displacement potential pressure mixed formulation fourth the computational framework for the three field mixed variational principle in nearly and truly incompressible scenarios is also presented in this case the novelty resides in the consideration of convex multi variable energy functionals ultimately this leads to the definition of new tangent operators for the helmholtz s energy functional in the specific context of incompressible electro elasticity fifth a petrov galerkin stabilisation technique is applied on the three field formulation for the circumvention of the ladyz enskaja babus ka brezzi lbb condition enabling the use of linear tetrahedral finite elements for the interpolation of the unknowns of the problem finally a series of challenging numerical examples is presented in order to provide an exhaustive comparison of the different variational formulations presented in this paper

a constructive approach of invariants of behavior laws with respect to an infinite symmetry group application to a biological anisotropic hyperelastic material with one fiber family abstract in this paper six new invariants associated with an anisotropic material made of one fiber family are calculated by presenting a systematic constructive and original approach this approach is based on the development of mathematical techniques from the theory of invariants definition of the material symmetry group definition of the generalized reynolds operator calculation of an integrity basis for invariant polynomials comparison between the new constructed invariants and the classical ones

a first order hyperbolic framework for large strain computational solid dynamics part ii total lagrangian compressible nearly incompressible and truly incompressible elasticity abstract in part i of this series bonet et al 2015 introduced a new computational framework for the analysis of large strain isothermal fast solid dynamics where a mixed set of total lagrangian conservation laws was presented in terms of the linear momentum and an extended set of strain measures namely the deformation gradient its co factor and its jacobian the main aim of this paper is to expand this formulation to the case of nearly incompressible and truly incompressible materials the paper is further enhanced with three key novelties first the use of polyconvex nearly incompressible strain energy functionals enables the definition of generalised convex entropy functions and associated entropy fluxes two variants of the same formulation can then be obtained namely conservation based and entropy based depending on the unknowns of the system crucially the study of the eigenvalue structure of the system is carried out in order to demonstrate its hyperbolicity and thus obtain the correct time step bounds for explicit time integrators second the development of a stabilised petrov galerkin framework is presented for both systems of hyperbolic equations that is when expressed in terms of either conservation or entropy variables third an adapted fractional step method built upon the work presented in gil et al 2014 is presented to extend the range of applications towards the incompressibility limit finally a series of numerical examples are presented in order to assess the applicability and robustness of the proposed formulation the overall scheme shows excellent behaviour in compressible nearly incompressible and truly incompressible scenarios yielding equal order of convergence for velocities and stresses

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

a polyconvex framework for soft biological tissues adjustment to experimental data the main goal of this contribution is to provide a simple method for constructing transversely isotropic polyconvex functions suitable for the description of biological soft tissues the advantage of our approach is that only a few parameters are necessary to approximate a variety of stress strain curves and to satisfy the condition of a stress free reference configuration a priori in the framework of polyconvexity the proposed polyconvex stored energies are embedded into the concept of structural tensors and the representation theorems for isotropic tensor functions are utilized as an example the medial layer of a human abdominal aorta is investigated modeled by some of the proposed polyconvex functions and compared with experimental data hereby the economic fitting to experimental data and hence the easy handling of the functions is shown

a new framework for large strain electromechanics based on convex multi variable strain energies variational formulation and material characterisation abstract following the recent work of bonet et al 2015 this paper postulates a new convex multi variable variational framework for the analysis of electro active polymers eaps in the context of reversible nonlinear electro elasticity this extends the concept of polyconvexity ball 1976 to strain energies which depend on non strain based variables introducing other physical measures such as the electric displacement six key novelties are incorporated in this work first a new definition of the electro mechanical internal energy is introduced expressed as a convex multi variable function of a new extended set of electromechanical arguments crucially this new definition of the internal energy enables the most accepted constitutive inequality namely ellipticity to be extended to the entire range of deformations and electric fields and in addition to incorporate the electro mechanical energy of the vacuum and hence that for ideal dielectric elastomers as a degenerate case second a new extended set of variables work conjugate to those characterising the new definition of multi variable convexity is introduced in this paper third both new sets of variables enable the definition of novel extended hu washizu type of mixed variational principles which are presented in this paper for the first time in the context of nonlinear electro elasticity fourth some simple strategies to create appropriate convex multi variable energy functionals in terms of convex multi variable invariants by incorporating minor modifications to a priori non convex multi variable functionals are also presented fifth a tensor cross product operation de boer 1982 used in bonet et al 2015 to facilitate the algebra associated with the adjoint of the deformation gradient tensor is incorporated in the proposed variational electro mechanical framework leading to insightful representations of otherwise complex algebraic expressions finally under a characteristic experimental setup in dielectric elastomers the behaviour of a convex multi variable constitutive model capturing some intrinsic nonlinear effects such as electrostriction is numerically studied

a highly accurate 1st and 2nd order differentiation scheme for hyperelastic material models based on hyper dual numbers abstract in this paper we propose a numerical scheme for the calculation of stresses and corresponding consistent tangent moduli for hyperelastic material models which are derived in terms of the first and second derivatives of a strain energy function this numerical scheme provides a compact model independent framework which means that once the framework is implemented any other hyperelastic material model can be incorporated by solely modifying the energy function the method is based on the numerical calculation of strain energy derivatives using hyper dual numbers and thus referred to as hyper dual step derivative hdsd the hdsd does neither suffer from roundoff errors nor from truncation errors and is thereby a highly accurate method with high stability being insensitive to perturbation values furthermore it enables the calculation of derivatives of arbitrary order this is a great advantage compared to other numerical approaches as e g the finite difference approximation which is highly sensitive with respect to the perturbation value and which thus only yields accurate approximations for a small regime of perturbation values another alternative the complex step derivative approximation enables highly accurate derivatives for a wide range of small perturbation values but it only provides first derivatives and is thus not able to calculate stresses and moduli at once in this paper representative numerical examples using an anisotropic model are provided showing the performance of the proposed method in detail an introductory example shows the insensitivity with respect to the perturbation values and the higher accuracy compared to the finite difference scheme furthermore examples demonstrate the robustness and simple implementation of the hdsd scheme in finite element software it turns out that the higher accuracy compared with other approaches can still be achieved in reasonable computing time

fkg inequalities in cellular automata and coupled map lattices abstract we review conditions for the preservation of the fkg fortuin kasteleyn ginibre inequalities in cellular automata and coupled map lattices in addition conditions are derived on the transition probabilities for n state probabilistic cellular automata which insure monotonicity and preservation of fkg inequalities this can be used for example to prove normal fluctuation and large deviations theorems for these systems a number of examples of probabilistic cellular automata and coupled map lattices that preserve positive correlations are presented and the implications of fkg inequalities are discussed

time dependent fibre reorientation of transversely isotropic continua finite element formulation and consistent linearization transverse isotropy is realized by one characteristic direction for instance the fibre direction in fibre reinforced materials commonly the characteristic direction is assumed to be constant but in some cases for instance in the constitutive description of biological tissues liquid crystals grain orientations within polycrystalline materials or piezoelectric materials as well as in optimization processes it proves reasonable to consider reorienting fibre directions various fields can be assumed to be the driving forces for the reorientation process for instance mechanical electric or magnetic fields in this work we restrict ourselves to reorientation processes in hyper elastic materials driven by principal stretches the main contribution of this paper is the algorithmic implementation of the reorientation process into a finite element framework therefore an implicit exponential update of the characteristic direction is applied by using the rodriguez formula to express the exponential term the non linear equations on the local and on the global level are solved by means of the newton raphson scheme accordingly the local update of the characteristic direction and the global update of the deformation field are consistently linearized yielding the corresponding tangent moduli through implementation into a finite element code and some representative numerical simulations the fundamental characteristics of the model are illustrated copyright 2007 john wiley sons ltd

a generalized orthotropic hyperelastic material model with application to incompressible shells in the present paper a new orthotropic hyperelastic constitutive model is proposed which can be applied to the numerical simulation of a wide range of anisotropic materials and particularly biological soft tissues the model represents a non linear extension of the orthotropic st venant kirchhoff material and is described in each principal material direction by an arbitrary isotropic tensor function coupled with the corresponding structural tensor in the special case of isotropy this constitutive formulation reduces to the valanis landel hypothesis and may therefore be considered as its generalization to the case of orthotropy constitutive relations and tangent moduli of the model are expressed in terms of eigenvalue bases of the right cauchy green tensor c and obtained for the case of distinct and coinciding eigenvalues as well for the analysis of shells the model is then coupled with a six five in incompressible case parametric shell kinematics able to deal with large strains as well as finite rotations the application of the developed finite shell element is finally illustrated by a number of numerical examples copyright 2001 john wiley sons ltd

a new mixed finite element based on different approximations of the minors of deformation tensors finite element formulations for arbitrary hyperelastic strain energy functions that are characterized by a locking free behavior for incompressible materials a good bending performance and accurate solutions for coarse meshes need still attention therefore the main goal of this contribution is to provide an improved mixed finite element for quasi incompressible finite elasticity based on the knowledge that the minors of the deformation gradient play a major role for the transformation of infinitesimal line area and volume elements as well as in the formulation of polyconvex strain energy functions a mixed finite element with different interpolation orders of the terms related to the minors is developed due to the formulation it is possible to condensate the mixed element formulation at element level to a pure displacement form examples show the performance and robustness of the element

variational inequalities for fuzzy mappings ii in this paper we establish the equivalence between the variational inequalities for fuzzy mappings and the wiener hopf equations for fuzzy mappings we use this equivalence to suggest a number of new iterative algorithms for solving the variational inequalities for fuzzy mappings we also study the convergence criteria of these iterative algorithms the auxiliary principle technique is used to study the existence of a solution of the variational inequality for fuzzy mappings and to suggest a novel and innovative iterative algorithm for computing the approximate solution the results proved in this paper represent an improvement of previously known results

a variational approach for materially stable anisotropic hyperelasticity abstract in this work we propose an anisotropic stored energy function which satisfies a priori the legendre hadamard condition which is strongly related to the material stability of the constitutive equations in the linearized case this condition implies positive wave speeds the legendre hadamard condition plays also an important role for the local existence of solutions in the neighborhood of stationary points we apply the proposed hyperelastic energies to soft tissues and compare the formulation with existing models which have been used for the calculation of medial collateral ligament and arterial walls in our numerical and analytical investigations we discuss the distribution of wave speeds for a sequence of deformation states containing some essential stress strain characteristics of the compared models

implementation of incremental variational formulations based on the numerical calculation of derivatives using hyper dual numbers abstract in this paper novel implementation schemes for the automatic calculation of internal variables stresses and consistent tangent moduli for incremental variational formulations ivfs describing inelastic material behavior are proposed ivfs recast inelasticity theory as an equivalent optimization problem where the incremental stress potential within a discrete time interval is minimized in order to obtain the values of internal variables in the so called multilevel newton raphson method for the inelasticity theory this minimization problem is typically solved by using second derivatives with respect to the internal variables in addition to that to calculate the stresses and moduli further second derivatives with respect to deformation tensors are required compared with classical formulations such as the return mapping method the ivfs are relatively new and their implementation is much less documented furthermore higher order derivatives are required in the algorithms demanding increased implementation efforts therefore even though ivfs are mathematically and physically elegant their application is not standard here novel approaches for the implementation of ivfs using hdns of second and higher order are presented to arrive at a fully automatic and robust scheme with computer accuracy the proposed formulations are quite general and can be applied to a broad range of different constitutive models which means that once the proposed schemes are implemented as a framework any other dissipative material model can be implemented in a straightforward way by solely modifying the constitutive functions these include the helmholtz free energy function the dissipation potential function and additional side constraints such as e g the yield function in the case of plasticity its uncomplicated implementation for associative finite strain elasto plasticity and performance is illustrated by some representative numerical examples

on a tensor cross product based formulation of large strain solid mechanics abstract this paper describes in detail the formulation of large strain solid mechanics based on the tensor cross product originally presented by r de boer 1982 and recently re introduced by bonet et al 2015a and bonet et al 2015b the paper shows how the tensor cross product facilitates the algebra associated with the area and volume maps between reference and final configurations these maps together with the fibre map make up the fundamental kinematic variables in polyconvex elasticity the algebra proposed leads to novel expressions for the tangent elastic operator which neatly separates material from geometrical dependencies the paper derives new formulas for the spatial and material stress and their corresponding elasticity tensors these are applied to the simple case of a mooney rivlin material model the extension to transversely isotropic material models is also considered

a new parameter identification method of soft biological tissue combining genetic algorithm with analytical optimization the main goal of this paper is to provide simple parameter identification process for most of hyperelastic constitutive laws in biomechanics of soft tissues the advantage of our approach lies on its rapidity and effectiveness by reducing analytically the number of parameters to identify in the model during the identification procedure with the use of genetic algorithms the search for an adequate initial guess point is avoided and the space solution of the objective function is reduced to meet only parameters that cannot be calculated analytically as an example we focus on models that predict arterial wall behaviour such as laws based on fung s type energy function holzapfel 2006 14 and holzapfel et al 2000 model 15 our approach is applied on uniaxial extension tests and the results are compared with available data in the literature

a new computational framework for electro activation in cardiac mechanics abstract this paper presents a novel computational framework for the numerical simulation of the electromechanical response of the myocardium during the cardiac cycle the paper presents the following main novelties 1 two new mixed formulations tailor made for active stress and active strain coupling approaches have been developed and used in conjunction with two different ionic models namely bueno orovio et al 2008 and ten tusscher et al 2004 taking as a reference the mixed formulations introduced by bonet et al 2015 in the context of nonlinear elasticity the proposed formulations include as unknown fields the geometry and the transmembrane potential and possibly a lagrange multiplier enforcing weakly the incompressibility constraint as well as the deformation gradient tensor its cofactor its determinant the gradient of the transmembrane potential and their respective work conjugates the finite element implementation of these formulations is shown in this paper where a static condensation procedure is presented in order to yield an extremely competitive computational approach 2 a comprehensive and rigorous study of different ionic models i e bueno orovio and ten tusscher and electromechanical activation couplings i e active strain and active stress has been carried out 3 an analytical and numerical analysis of the possible loss of ellipticity and polyconvexity of one of the most widely used constitutive models in the context of cardiac mechanics is carried out in this paper putting forward possible polyconvexifications of the existing model 4 in addition an invariant representation of guccione s constitutive model is proposed finally a series of numerical examples are included in order to demonstrate the applicability and robustness of the proposed formulations

iterative algorithm for generalized quasi variational like inclusions with fuzzy mappings in banach spaces in this paper we introduce and study a class of generalized quasi variational like inclusions with fuzzy mappings in real banach spaces and show its equivalence with a class of relations using this equivalence we suggest and analyze an iterative algorithm for finding the approximate solution of this class of inclusions further we prove the existence of solution of this class of inclusions and discuss the convergence criteria of iterative sequences generated by the iterative algorithm

traffic assignment model with fuzzy level of travel demand an efficient algorithm based on quasi logit formulas abstract the place of fuzzy concepts in traffic assignment ta models has been studied in recent literature keeping fuzzy level of travel demand in mind we propose a new ta model in which the travel costs of links are depended on their congestion from the results of such fuzzy ta model network planners are able to estimate the number of travelers on network links by using zero one variables the proposed model is transformed into a crisp mixed integer problem with respect to path flow variables in order to produce the logit flows from this problem damberg et al algorithm is modified then the level of certainty is maximized and perceived travel delays are minimized for a fixed certainty degree the obtained solution which is named the fuzzy equilibrium flow satisfies a quasi logit formula similar to ordinary expression of the logit route choice model eventually we examine the quality of different path enumeration techniques in the proposed model

on an alternative modelling of distributed fibre directions abstract the main contribution of this work is the introduction of an alternative approach for the fast and accurate modelling of distributed fibre directions this method employs a quadrature rule which uses the sample vectors of the fibre orientation distribution function as integration points thus the computation time is drastically reduced compared to the classic angular integration method whereas the accuracy remains the same the effective stress converges with increasing numbers of integration further studies on different sets of sample vectors reveal a dependency of the effective second and fourth moment of the orientation distribution function on the choice of the integration points and their initial position by means of two example deformations with two different free energy densities the accuracy of the alternative method is clearly depicted over the complete range of fibre distributions it is worth mentioning that the method is not restricted to rotationally symmetric distributions and it is able to incorporate all five irreducible invariants of transverse isotropy the application of the alternative method to the numerical example of an arterial layer simulation by means of the fe method reveals drastic differences to the established modelling approaches

a new framework for large strain electromechanics based on convex multi variable strain energies conservation laws hyperbolicity and extension to electro magneto mechanics abstract this work is the third on a series of papers by gil and ortigosa gil and ortigosa 2016 ortigosa and gil 2016 on the development of a new computational framework for the analysis of electro active polymers where the concept of polyconvexity ball 1976 is extended to the case of electro magneto mechanical energy functionals specifically four key novelties are incorporated in this paper firstly a new set of first order hyperbolic equations is presented in the context of nonlinear electro magneto elasticity including conservation laws for all the fields of the extended set of arguments which determine the convex multi variable nature of the internal energy secondly the one to one and invertible relationship between this extended set and its associated entropy conjugate set enables the definition of a generalised convex entropy function resulting in the symmetrisation of the system when expressed in terms of the entropy variables thirdly this paper shows that after careful analysis of the eigenvalue structure of the system the definition of multi variable convexity in gil and ortigosa 2016 leads to positive definiteness of the electro magneto acoustic tensor therefore multi variable convexity ensures the satisfaction of the legendre hadamard condition hence showing that the speeds of propagation of acoustic and electro magnetic waves in the neighbourhood of a stationary point are real finally under a characteristic experimental set up for electrostrictive dielectric elastomers a study of the material stability of convex and non convex multi variable constitutive models is carried out

stochastic modeling and identification of a hyperelastic constitutive model for laminated composites abstract in this paper we investigate the construction and identification of a new random field model for representing the constitutive behavior of laminated composites here the material is modeled as a random hyperelastic medium characterized by a spatially dependent stochastic and anisotropic strain energy function the latter is parametrized by a set of material parameters modeled as non gaussian random fields from a probabilistic standpoint the construction is first achieved by invoking information theory and the principle of maximum entropy constraints related to existence theorems in finite elasticity are in particular accounted for in the formulation the identification of the parameters defining the random fields is subsequently addressed this issue is attacked as a two step problem where the mean model is calibrated in a first step by imposing a match between the linearized model and nominal values proposed in the literature the remaining parameters controlling the fluctuations are next estimated by solving an inverse problem in which principal component analysis and the maximum likelihood method are combined the whole framework is illustrated considering an experimental database where multi axial measurements are performed on a carbon epoxy laminate this work constitutes a first step towards the development of an integrated framework that will support decision making under uncertainty for the design certification and qualification of composite materials and structures

a nonlinear elimination preconditioned inexact newton method for heterogeneous hyperelasticity we propose and study a nonlinear elimination preconditioned inexact newton method for the numerical simulation of diseased human arteries with a heterogeneous hyperelastic model we assume the arte

on referential and spatial formulations of inverse elastostatic analysis abstract there are two families of element formulation for inverse elastostatic analysis in the literature they employ different computation procedures at the element and material levels it has been suggested that one of them can preserve material library while the other requires redeveloping the material functions in this article we show that these two formulations are completely equivalent under certain conditions both can preserve the material library while under other conditions neither can we show that the modification of material functions is caused by the need of updating material symmetry in the inverse solution process several theoretical results were obtained while establishing the equivalence including an identity relating the inverse and forward tangent tensors for isotropic materials a comprehensive documentation of these two formulations is provided

a new invariant based method for building biomechanical behavior laws application to an anisotropic hyperelastic material with two fiber families abstract in this article we present a general constructive and original approach that allows us to calculate the invariants associated with an anisotropic hyperelastic material made of two families of collagen fibers this approach is based on mathematical techniques from the theory of invariants definition of the material symmetry group analytical calculation of a set of generators using the noether s theorem analytical calculation of an integrity basis comparison between the proposed invariants and the classical ones

from pca s to equilibrium systems and back stationary measures for probabilistic cellular automata pca s ind dimensions give rise to space time histories whose statistics may naturally be described by gibbs states ind 1 dimensions for an interaction energy obtained from the pca in this note we study the converse question do all gibbs states for this correspond to statistical space time histories for the pca our main result states that the answer is yes at least for translation invariant or periodic gibbs states thus ergodicity questions for pca s can at least partially be formulated as questions of uniqueness of gibbs states

a large strain finite element formulation for biological tissues with application to mitral valve leaflet tissue mechanics this paper presents a finite element formulation suitable for large strain modeling of biological tissues and uses this formulation to implement an accurate finite element model for mitral valve leaflet tissue first an experimentally derived strain energy function is obtained from literature this function is implemented in finite elements using the mixed pressure displacement formulation a modification is made to aid in maintaining positive definiteness of the stiffness matrix at low strains the numerical implementation is shown to be accurate in representing the analytical model of material behavior the mixed formulation is useful for modeling of soft biological tissues in general and the model presented here is applicable to finite element simulation of mitral valve mechanics

analysis of thin shells using anisotropic polyconvex energy densities in this contribution the numerical framework for the simulation of anisotropic thin shells is presented on the basis of polyconvex strain energy functions the nonlinear shell theory is based on the reissner mindlin kinematic along with inextensible director vectors for the variational framework we consider a three field variational functional taking into account independent displacements enhanced strains and stress resultants where the latter field is eliminated by the evaluation of some orthogonality conditions the iterative enforcement of the zero normal stress condition at the integration points allows consideration of arbitrary three dimensional constitutive equations due to the fact that we are interested in fiber reinforced materials we consider an additive structure of the energy decoupled in an isotropic part for the matrix and a superposition of transversely isotropic parts for the fiber families for the representation of the anisotropy we use the concept of structural tensors and formulate the strain energy function in terms of principal and mixed invariants of the right cauchy green tensor and the structural tensor in order to guarantee the existence of minimizers we focus on polyconvex strain energy functions the anisotropy effect is documented in several representative examples