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

development of a stabilised petrov galerkin formulation for conservation laws in lagrangian fast solid dynamics a stabilised second order finite element methodology is presented for the numerical simulation of a mixed conservation law formulation in fast solid dynamics the mixed formulation where the unknowns are linear momentum deformation gradient and total energy can be cast in the form of a system of first order hyperbolic equations the difficulty associated with locking effects commonly encountered in standard pure displacement formulations is addressed by treating the deformation gradient as one of the primary variables the formulation is first discretised in space by using a stabilised petrov galerkin pg methodology derived through the use of variational work conjugate principles the semi discretised system of equations is then evolved in time by employing a total variation diminishing runge kutta tvd rk time integrator the formulation achieves optimal convergence e g second order with linear interpolation with equal orders in velocity or displacement and stresses in contrast with the displacement based approach this paper defines a set of appropriate stabilising parameters suitable for this particular formulation where the results obtained avoid the appearance of non physical spurious zero energy modes in the solution over a long term response we also show that the proposed pg formulation is very similar and under certain conditions identical to the well known two step taylor galerkin 2tg a series of numerical examples are presented in order to assess the performance of the proposed algorithm the new formulation is proven to be very efficient in nearly incompressible and bending dominated scenarios

many component limit of the quantum potts model abstract the q component quantum potts model is solved exactly in the limit q the resulting free energy and its first partial derivatives order parameters are shown to be identical to the corresponding mean field expressions taken in the same limit

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

on the existence and profile of nodal solutions for a two dimensional elliptic problem with large exponent in nonlinearity we study the existence of nodal solutions to the boundary value problem u u p 1u in a bounded smooth domain in ir with homogeneous dirichlet boundary condition when p is a large exponent we prove that for p large enough there exist at least two pairs of solutions which change sign exactly once and whose nodal lines intersect the boundary of

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

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

a stability study of some mixed finite elements for large deformation elasticity problems we consider the finite elasticity problem for incompressible materials proposing a simple bidimensional problem for which we provide an indication on the solution stability furthermore we study the stability of discrete solutions obtained by means of some well known mixed finite elements and we present several numerical experiments

a uniform deformation gradient hexahedron element with artificial hourglass control an 8 noded linear hexahedron element for large strain hyperelastic analysis is presented in this paper the element is based on a constant deformation gradient interpolation and is formulated using a mixed variational principle of the hu washizu type volumetric and isochoric components of the deformation are treated independently to ensure the correct evaluation of the element volume a simple procedure to control the propagation of spurious hourglass deformation modes is also discussed this is based on the addition of artificial hourglass forces which vanish under constant deformation gradient conditions thereby ensuring that the element passes a non linear version of the patch test applications in the field of neo hookean materials and superplastic forming processes are also considered

w1 p quasiconvexity and variational problems for multiple integrals abstract variational problems for the multiple integral i u g u x dx where r m and u r n are studied a new condition on g called w1 p quasiconvexity is introduced which generalizes in a natural way the quasiconvexity condition of c b morrey it being shown in particular to be necessary for sequential weak lower semicontinuity of i in w 1 p r n and for the existence of minimizers for certain related integrals counterexamples are given concerning the weak continuity properties of jacobians in w 1 p r n p n m an existence theorem for nonlinear elastostatics is proved under optimal growth hypotheses

steady vortex patches near a rotating flow with constant vorticity in a planar bounded domain abstract in this paper we study the possible equilibrium states of the 2d incompressible euler equations in a bounded domain by solving a suitable minimization problem we prove existence of a new type of steady euler flows in which the vorticity vanishes on a finite number of compact sets of small diameter and is a positive constant elsewhere the locations of those small compact sets are determined by the geometry of the domain

a new framework for large strain electromechanics based on convex multi variable strain energies finite element discretisation and computational implementation abstract in gil and ortigosa 2016 gil and ortigosa introduced a new convex multi variable framework for the numerical simulation of electro active polymers eaps in the presence of extreme deformations and electric fields this extends the concept of polyconvexity to strain energies which depend on non strain based variables the consideration of the new concept of multi variable convexity guarantees the well posedness of generalised gibbs energy density functionals and hence opens up the possibility of a new family of mixed variational principles the aim of this paper is to present as an example the finite element implementation of two of these mixed variational principles these types of enhanced methodologies are known to be necessary in scenarios in which the simpler displacement potential based formulation yields non physical results such as volumetric locking bending and shear locking pressure oscillations and electro mechanical locking to name but a few crucially the use of interpolation spaces in which some of the unknown fields are described as piecewise discontinuous across elements can be used in order to efficiently condense these fields out this results in mixed formulations with a computational cost comparable to that of the displacement potential based approach yet far more accurate finally a series of very challenging numerical examples are presented in order to demonstrate the accuracy robustness and efficiency of the proposed methodology

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 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

a 2 d coupled bem fem simulation of electro elastostatics at large strain the numerical simulation of nonlinear electro elastostatics is considered in this work using the coupled boundary and finite element method the objective of the work is to properly simulate the deformation of an electroelastic body undergoing large deformation subjected to electric stimulations in the case where the surrounding space has significant influence on the electric field inside the body finite elements are used to model the nonlinear electroelastic body in which both mechanical nonlinearity and electrical nonlinearity are taken into account boundary elements are used to model the surrounding space and account for the large deformation of the boundary of the body

vortex rings in a cylinder and rearrangements on demontre l existence d une solution faible au probleme de valeur limite pour un tourbillon annulaire stationnaire dans un fluide parfait s ecoulant le long d un tube infini de section circulaire

euler evolution for singular initial data and vortex theory we study the evolution of a two dimensional incompressible ideal fluid in a case in which the vorticity is concentrated in small disjoint regions of the physical space we prove for short times a connection between this evolution and the vortex model

a mixed enhanced formulation tetrahedral finite elements this paper considers the solution of problems in three dimensional solid mechanics using tetrahedral finite elements a formulation based on a mixed enhanced treatment involving displacement pressure and volume effects is presented the displacement and pressure are used as nodal quantities while volume effects and enhanced modes belong to individual elements both small and finite deformation problems are addressed and sample solutions are given to illustrate the performance of the formulation copyright 2000 john wiley sons ltd

numerical modelling of non linear electroelasticity the numerical modelling of non linear electroelasticity is presented in this work based on well established basic equations of non linear electroelasticity a variational formulation is built and the finite element method is employed to solve the non linear electro mechanical coupling problem numerical examples are presented to show the accuracy of the implemented formulation copyright 2006 john wiley sons ltd

an approach to symmetrization via polarization we prove that the steiner symmetrization of a function can be approximated in l p r n by a sequence of very simple rearrangements which are called polarizations this result is exploited to develop elementary proofs of many inequalities including the isoperimetric inequality in euclidean space in this way we also obtain new symmetry results for solutions of some varia tional problems furthermore we compare the solutions of two boundary value problems one of them having a polarized geometry and we show some point wise inequalities between the solutions this leads to new proofs of well known functional inequalities which compare the solutions of two elliptic or parabolic problems one of them having a steiner symmetrized geometry the method also allows us to investigate the case of equality in the inequalities roughly speaking we prove that the equality sign is valid only if the original problem has the symmetrized geometry

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 uniform strain hexahedron and quadrilateral with orthogonal hourglass control the treatment of zero energy modes which arise due to one point integration of first order isoparametric finite elements is addressed a method for precisely isolating these modes for arbitrary geometry is developed two hourglass control schemes viscous and elastic are presented and examined in addition a convenient one point integration scheme which analytically integrates the element volume and uniform strain modes is presented

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

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

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

the importance of the exact satisfaction of the incompressibility constraint in nonlinear elasticity mixed fems versus nurbs based approximations in the present paper we investigate the capability of finite element methods to correctly reproduce the stability range of finite strain problems in the incompressible regime to this end we develop a numerical scheme obtained combining a stream function formulation with an isogeometric nurbs approach which is able to sharply estimate the stability limits of the continuous problem using such a method we show a pair of benchmark problems on which various well known finite element methods largely fail in approximating the correct stability range

improved versions of assumed enhanced strain tri linear elements for 3d finite deformation problems abstract improved three dimensional tri linear elements for finite deformation problems are developed based on an assumed enhanced strain methodology which in the linear regime incorporates the classical method of incompatible modes as a particular case three crucial modifications of a recently proposed element which reduces to wilson s brick in the linear regime are introduced to prevent locking response in distorted configurations and to maintain proper rank while preserving excellent performance in bending dominated and localization problems i a modified quadrature rule ii an additional enhancement of the divergence term and iii a modification of the isoparametric shape function derivatives for the three dimensional problem moreover these modified shape function derivatives are shown to improve the performance of the standard tri linear brick in distorted configurations in addition a strategy is described to circumvent the memory storage requirements in the static condensation procedure of the enhanced strain parameters the excellent performance of the improved methodology is illustrated in representative numerical simulations

a vertex centred finite volume jameson schmidt turkel jst algorithm for a mixed conservation formulation in solid dynamics a vertex centred finite volume algorithm is presented for the numerical simulation of fast transient dynamics problems involving large deformations a mixed formulation based upon the use of the linear momentum the deformation gradient tensor and the total energy as conservation variables is discretised in space using linear triangles and tetrahedra in two dimensional and three dimensional computations respectively the scheme is implemented using central differences for the evaluation of the interface fluxes in conjunction with the jameson schmidt turkel jst artificial dissipation term the discretisation in time is performed by using a total variational diminishing tvd two stage runge kutta time integrator the jst algorithm is adapted in order to ensure the preservation of linear and angular momenta the framework results in a low order computationally efficient solver for solid dynamics which proves to be very competitive in nearly incompressible scenarios and bending dominated applications

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

a velocity stress mixed stabilized nodal finite element for elastodynamics analysis and computations with strongly and weakly enforced boundary conditions abstract a new nodal mixed finite element is proposed for the simulation of linear elastodynamics and wave propagation problems in time domain our method is based on equal order interpolation discrete spaces for both the velocity or displacement and stress or strain tensor variables the mixed form is derived using either the velocity stress or velocity strain pair of unknowns the latter being instrumental in extensions of the method to nonlinear mechanics the proposed approach works equally well on hexahedral or tetrahedral grids and for this reason it is suitable for time domain engineering applications in complex geometry the peculiarity of the proposed approach is the use of the rate form of the stress update equation which yields a set of governing equations with the structure of a non dissipative space time friedrichs system we complement standard traction boundary conditions for the stress with strongly and weakly enforced boundary conditions for the velocity or displacement weakly enforced boundary conditions are particularly suitable when considering complex geometrical shapes because they do not require dedicated data structures for the imposition of the boundary degrees of freedom but rather they utilize the structure of the variational formulation we also show how the framework of weakly enforced boundary conditions can be used to develop variational forms for multi domain simulations of heterogeneous media a complete analysis including stability and convergence proofs is included in the case of a space time variational approach a series of computational tests are used to demonstrate and verify the performance of the proposed approach

desingularization of vortices for the euler equation we study the existence of stationary classical solutions of the incompressible euler equation in the planes that approximate singular stationary solutions of this equation the construction is performed by studying the asymptotics of equation varepsilon 2 delta u varepsilon u varepsilon q frac kappa 2 pi log frac 1 varepsilon p with dirichlet boundary conditions and q a given function we also study the desingularization of pairs of vortices by minimal energy nodal solutions and the desingularization of rotating vortices

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

n vortex equilibria for ideal fluids in bounded planar domains and new nodal solutions of the sinh poisson and the lane emden fowler equations we prove the existence of equilibria of the n vortex hamiltonian in a bounded domain omega subset mathbb r 2 which is not necessarily simply connected on an arbitrary bounded domain we obtain new equilibria for n 3 or n 4 if has an axial symmetry we obtain a symmetric equilibrium for each n in mathbb n we also obtain new stream functions solving the sinh poisson equation delta psi rho sinh psi in with dirichlet boundary conditions for 0 small the stream function psi rho induces a stationary velocity field v rho solving the euler equation in on an arbitrary bounded domain we obtain velocitiy fields having three or four counter rotating vortices if has an axial symmetry we obtain for each n a velocity field v rho that has a chain of n counter rotating vortices analogous to the mallier maslowe row of counter rotating vortices in the plane our methods also yield new nodal solutions for other semilinear dirichlet problems in particular for the lane emden fowler equation delta u u p 1 u in with p large

a family of mixed finite elements for the elasticity problem a new mixed finite element formulation for the equations of linear elasticity is considered in the formulation the variables approximated are the displacement the unsymmetric stress tensor and the rotation the rotation act as a lagrange multiplier introduced in order to enforce the symmetry of the stress tensor based on this formulation a new family of both two and three dimensional mixed methods is defined optimal error estimates which are valid uniformly with respect to the poisson ratio are derived finally a new postprocessing scheme for improving the displacement is introduced and analyzed

a first order hyperbolic framework for large strain computational solid dynamics part i total lagrangian isothermal elasticity abstract this paper introduces a new computational framework for the analysis of large strain fast solid dynamics the paper builds upon previous work published by the authors gil et al 2014 48 where a first order system of hyperbolic equations is introduced for the simulation of isothermal elastic materials in terms of the linear momentum the deformation gradient and its jacobian as unknown variables in this work the formulation is further enhanced with four key novelties first the use of a new geometric conservation law for the co factor of the deformation leads to an enhanced mixed formulation advantageous in those scenarios where the co factor plays a dominant role second the use of polyconvex strain energy functionals enables the definition of generalised convex entropy functions and associated entropy fluxes for solid dynamics problems moreover the introduction of suitable conjugate entropy variables enables the derivation of a symmetric system of hyperbolic equations dual of that expressed in terms of conservation variables third the new use of a tensor cross product 61 greatly facilitates the algebraic manipulations of expressions involving the co factor of the deformation fourth 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 as an example a polyconvex mooney rivlin material is used and for completeness the eigen structure of the resulting system of equations is studied to guarantee the existence of real wave speeds finally a series of numerical examples is presented in order to assess the robustness and accuracy of the new mixed methodology benchmarking it against an ample spectrum of alternative numerical strategies including implicit multi field fraeijs de veubeke hu washizu variational type approaches and explicit cell and vertex centred finite volume schemes

on 3 d coupled bem fem simulation of nonlinear electro elastostatics abstract in this work the numerical simulation of nonlinear electro elastostatics is considered with a special focus on the influence of the free space surrounding an electro sensitive body the influence of the free space on the electric field and on the deformation field inside an electro sensitive body can become highly important for many materials and can change profoundly the simulation results in order to take into account this influence the free space must be simulated by using for example the finite element method fem or the boundary element method bem a coupled bem fem approach is employed here to exploit the advantage of the finite element method in solving nonlinear problems and the advantage of the boundary element method in dealing with infinite domains numerical studies using this approach show that for materials with low electric permittivity the free space can have a huge impact on the simulated electric and deformation fields the same observation is expected for the general case of nonlinear electro elasticity and nonlinear electro viscoelasticity and constitutes the direction for future works

concentrating solutions for a planar elliptic problem involving nonlinearities with large exponent abstract we consider the boundary value problem u u p 0 in a bounded smooth domain in r 2 with homogeneous dirichlet boundary condition and p a large exponent we find topological conditions on which ensure the existence of a positive solution u p concentrating at exactly m points as p in particular for a nonsimply connected domain such a solution exists for any given m 1

a stabilised petrov galerkin formulation for linear tetrahedral elements in compressible nearly incompressible and truly incompressible fast dynamics a mixed second order stabilised petrov galerkin finite element framework was recently introduced by the authors lee et al 2014 46 the new mixed formulation written as a system of conservation laws for the linear momentum and the deformation gradient performs extremely well in bending dominated scenarios even when linear tetrahedral elements are used yielding equal order of convergence for displacements and stresses in this paper this formulation is further enhanced for nearly and truly incompressible deformations with three key novelties first a new conservation law for the jacobian of the deformation is added into the system providing extra flexibility to the scheme second a variationally consistent petrov galerkin stabilisation methodology is derived third an adapted fractional step method is presented for both incompressible and nearly incompressible materials in the context of nonlinear elastodynamics for completeness and ease of understanding these three improvements are presented both in small and large strain regimes studying the eigenstructure of the resulting systems a series of numerical examples are presented in order to demonstrate the robustness of the enhanced methodology with respect to the work previously published by the authors

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100