. Existence, uniqueness and regularity theory is developed for a general initial-boundary-value problem for a system of partial differential equations which describes the Biot consolidation model in poroelasticity as well as a coupled quasistatic problem in thermoelasticity. Additional effects of secondary consolidation and pore fluid exposure on the boundary are included. This quasi-static system is resolved as an application of the theory of linear degenerate evolution equations in Hilbert space, and this leads to a precise description of the dynamics of the system. 1. Introduction We shall consider a system modeling diffusion in an elastic medium in the case for which the inertia effects are negligible. This quasi-static assumption arises naturally in the classical Biot model of consolidation for a linearly elastic and porous solid which is saturated by a slightly compressible viscous fluid. The fluid pressure is denoted by p(x; t) and the displacement of the structure by u(x; t). ...

Various formulations of the equations of motion for both finiteand infinite-dimensional constrained Lagrangian dynamical systems are studied. The different formulations correspond to different ways of enforcing constraints through multiplier fields. All the formulations considered are posed on ambient spaces whose members are not restricted to satisfy constraint equations, but each formulation is shown to possess an invariant set on which the constraint equations and physical balance laws are satisfied. The stability properties of the invariant set within its ambient space differ in each of the cases. For the model problem of linearized incompressible elastodynamics, we study three formulations and establish the well-posedness of one formulation corresponding to a homogeneous, isotropic material body with a specified traction on its boundary. 1 Introduction In this article we study formulations of the equations of motion for Lagrangian dynamical systems whose configuration space can b...

Abstract. The evaluation of the traction exerted by a cell on a planar substrate is here considered as an inverse problem: shear stress is calculated on the basis of the measurement of the deformation of the underlying gel layer. The adjoint problem of the direct two-dimensional plain stress operator is derived by a suitable minimization requirement. The resulting coupled systems of elliptic partial differential equations (the direct and the adjoint problem) are solved by a finite element method and tested vs. experimental measures of displacement induced by a fibroblast cell traction. Introduction. The study of the basic mechanisms of cell migration has received a tremendous increment in the last few years. Cell locomotion occurs through a very complex interaction that involves, among others, actin polymerization, matrix degradation, chemical signaling, adhesion and pulling on substrate and fibers [12]. All these ingredients concur not only in single cell migration but also in collective

Implicit time integration schemes that inherit the conservation laws of total energy, linear and angular momentum are considered for initial boundary-value problems in finite-deformation elastodynamics. Conserving schemes are constructed for general hyperelastic material models, both compressible and incompressible, and are formulated in a way that is independent of spatial discretization. Three numerical examples for Ogden-type material models, implemented using a finite element discretization in space, are given to illustrate the performance of the proposed schemes. These examples show that, relative to the standard implicit mid-point rule, the conserving schemes exhibit superior numerical stability properties without a compromise in accuracy. Key words: numerical integration, nonlinear elastodynamics, incompressible elasticity, integral preservation 1 Introduction In this article we consider energy and momentum conserving time discretization schemes for general initial boundary-valu...

apport de recherche N 0249-6399Asymptotic expansion of the solution of Maxwell’s equations in polygonal plane domains