A domain decomposition method for solving a Helmholtz-like problem in elasticity based on the Wilson nonconforming element
A frictionless contact algorithm for deformable bodies
This article is devoted to the presentation of a new contact algorithm for bodies undergoing finite deformations. We only address the kinematic aspect of the contact problem, that is the numerical treatment of the non-intersection constraint. In consequence, mechanical aspects like friction, adhesion or wear are not investigated and we restrict our analysis to the simplest frictionless case. On the other hand, our method allows us to treat contacts and self-contacts, thin or non-thin structures...
A frictionless contact algorithm for deformable bodies*
This article is devoted to the presentation of a new contact algorithm for bodies undergoing finite deformations. We only address the kinematic aspect of the contact problem, that is the numerical treatment of the non-intersection constraint. In consequence, mechanical aspects like friction, adhesion or wear are not investigated and we restrict our analysis to the simplest frictionless case. On the other hand, our method allows us to treat contacts and self-contacts, thin or non-thin structures...
A generalization of Signorini's perturbation method suggested by two problems of Grioli
A geometrically nonlinear analysis of laminated composite plates using a shear deformation theory
A shear deformation theory is developed to analyse the geometrically nonlinear behaviour of layered composite plates under transverse loads. The theory accounts for the transverse shear (as in the Reissner Mindlin plate theory) and large rotations (in the sense of the von Karman theory) suitable for simulating the behaviour of moderately thick plates. Square and rectangular plates are considered: the numerical results are obtained by a finite element computational procedure and are given for various...
A model of neck formation on a rod under tension.
A multiplicative Schwarz method and its application to nonlinear acoustic-structure interaction
A new Schwarz method for nonlinear systems is presented, constituting the multiplicative variant of a straightforward additive scheme. Local convergence can be guaranteed under suitable assumptions. The scheme is applied to nonlinear acoustic-structure interaction problems. Numerical examples validate the theoretical results. Further improvements are discussed by means of introducing overlapping subdomains and employing an inexact strategy for the local solvers.
A nonlinear model for inextensible rods as a low energy Γ-limit of three-dimensional nonlinear elasticity
A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry
We prove that the critical points of the 3d nonlinear elasticity functional on shells of small thickness h and around the mid-surface S of arbitrary geometry, converge as h → 0 to the critical points of the von Kármán functional on S, recently proposed in [Lewicka et al., Ann. Scuola Norm. Sup. Pisa Cl. Sci. (to appear)]. This result extends the statement in [Müller and Pakzad, Comm. Part. Differ. Equ.33 (2008) 1018–1032], derived for the case of plates when . The convergence holds provided...
A note on convergence of low energy critical points of nonlinear elasticity functionals, for thin shells of arbitrary geometry
We prove that the critical points of the 3d nonlinear elasticity functional on shells of small thickness h and around the mid-surface S of arbitrary geometry, converge as h → 0 to the critical points of the von Kármán functional on S, recently proposed in [Lewicka et al., Ann. Scuola Norm. Sup. Pisa Cl. Sci. (to appear)]. This result extends the statement in [Müller and Pakzad, Comm. Part. Differ. Equ.33 (2008) 1018–1032], derived for the case of plates when . The convergence holds provided...
A note on weak approximation of minors
A Numerical Method for Detecting Singular Minimizers.
A numerical method for detecting singular minimizers of multidimensional problems in nonlinear elasticity.
A quasistatic bilateral contact problem with friction for nonlinear elastic materials.
A quasistatic unilateral contact problem with slip-dependent coefficient of friction for nonlinear elastic materials.
A short remark on energy functionals related to nonlinear Hencky materials.
A theoretical approach to the problem of the most dangerous initial deflection shape in stability type structural problems
The author introduces a global measure of initial deflection given by the energy norm. Solving the formulated minimization problem with a subsidiary condition the most dangerous initial deflection shape is obtained. The theoretical results include a wide range of stability type structural problems.
A three dimensional finite element method for biological active soft tissue formulation in cylindrical polar coordinates
A hyperelastic constitutive law, for use in anatomically accurate finite element models of living structures, is suggested for the passive and the active mechanical properties of incompressible biological tissues. This law considers the passive and active states as a same hyperelastic continuum medium, and uses an activation function in order to describe the whole contraction phase. The variational and the FE formulations are also presented, and the FE code has been validated and applied to describe...
A three dimensional finite element method for biological active soft tissue Formulation in cylindrical polar coordinates
A hyperelastic constitutive law, for use in anatomically accurate finite element models of living structures, is suggested for the passive and the active mechanical properties of incompressible biological tissues. This law considers the passive and active states as a same hyperelastic continuum medium, and uses an activation function in order to describe the whole contraction phase. The variational and the FE formulations are also presented, and the FE code has been validated and applied to describe...
A two-dimensional variational model for the equilibrium configuration of an incompressible, elastic body with a three-well elastic potential.