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A three dimensional finite element method for biological active soft tissue formulation in cylindrical polar coordinates

Christian Bourdarias, Stéphane Gerbi, Jacques Ohayon (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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

Christian Bourdarias, Stéphane Gerbi, Jacques Ohayon (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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-field augmented Lagrangian formulation of unilateral contact problems with cohesive forces

David Doyen, Alexandre Ern, Serge Piperno (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We investigate unilateral contact problems with cohesive forces, leading to the constrained minimization of a possibly nonconvex functional. We analyze the mathematical structure of the minimization problem. The problem is reformulated in terms of a three-field augmented Lagrangian, and sufficient conditions for the existence of a local saddle-point are derived. Then, we derive and analyze mixed finite element approximations to the stationarity conditions of the three-field augmented Lagrangian....

A topological asymptotic analysis for the regularized grey-level image classification problem

Didier Auroux, Lamia Jaafar Belaid, Mohamed Masmoudi (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

The aim of this article is to propose a new method for the grey-level image classification problem. We first present the classical variational approach without and with a regularization term in order to smooth the contours of the classified image. Then we present the general topological asymptotic analysis, and we finally introduce its application to the grey-level image classification problem.

A two-fluid hyperbolic model in a porous medium

Laëtitia Girault, Jean-Marc Hérard (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The paper is devoted to the computation of two-phase flows in a porous medium when applying the two-fluid approach. The basic formulation is presented first, together with the main properties of the model. A few basic analytic solutions are then provided, some of them corresponding to solutions of the one-dimensional Riemann problem. Three distinct Finite-Volume schemes are then introduced. The first two schemes, which rely on the Rusanov scheme, are shown to give wrong approximations in some...

A unified analysis of elliptic problems with various boundary conditions and their approximation

Jérôme Droniou, Robert Eymard, Thierry Gallouët, Raphaèle Herbin (2020)

Czechoslovak Mathematical Journal

We design an abstract setting for the approximation in Banach spaces of operators acting in duality. A typical example are the gradient and divergence operators in Lebesgue-Sobolev spaces on a bounded domain. We apply this abstract setting to the numerical approximation of Leray-Lions type problems, which include in particular linear diffusion. The main interest of the abstract setting is to provide a unified convergence analysis that simultaneously covers (i) all usual boundary conditions, (ii)...

Currently displaying 1041 – 1060 of 9187