Une modélisation du tissu cardiaque comme milieu à microdilatation : une étude numérique

Ces dernières années ont connu un regain d’intérêt pour la mécanique des milieux continus étendus dans le but de rendre plus fidèlement compte de phénomènes physiques se produisant à l’échelle microscopique, ou pour tenir compte de manière « explicite » de la microstructure du matériau. La théorie des milieux micromorphes de Eringen rentre dans ce cadre et permettrai d’analyser efficacement divers types de matériaux : des mousses, des milieux poreux, des tissus biologiques, etc. Dans sa généralité, le point matériel est doté de 12 degrés de liberté. Cependant, compte tenu de l’application envisagée et du mécanisme microscopique prédominant le modèle peut être simplifié avec comme conséquence une réduction du nombre de degré de liberté. Dans ce travail, nous utilisons la plus simple des particularisations de la théorie micromorphe pour modéliser le tissu cardiaque. Un tissu cardiaque sain est considéré comme un milieu à microdilatation. A l’issu d’un infarctus, les points matériels de la zone nécrosée perdent cette capacité. A l’aide d’un outil numérique spécifiquement dédié, nous analysons l’aptitude d’un tel modèle à décrire ce problème clinique. Les résultats obtenus sont conformes aux cas pratiques présentés dans la littérature

A simple solution procedure to 3D-piezoelectric problems: Isotropic BEM coupled with a point collocation method

International audienceThis paper presents a simple strategy allowing to adapt well established isotropic BEM approach for the solution of coupled problems with anisotropic material parameters. The method which is illustrated on the case of a piezoelectric material is based on the partition of the primary fields into complementary and particular parts. The complementary fields solve the isotropic form of the partial differential equation while particular fields are obtained by a point collocation of the strong form equation. Using the local radial point interpolation method, the effectiveness and accuracy of approach is demonstrated on some examples allowing a comparison with literature results

The local point interpolation–boundary element method (LPI–BEM) applied to the solution of mechanical 3D problem of a microdilatation medium

International audienceA numerical solution procedure of three-dimensional constrained microstretch (microdilatation) elastic problem is presented. The approach called local point interpolation–boundary element method (LPI–BEM) uses a partition of the kinematical variables into complementary and particular parts. The complementary fields are obtained by isotropic boundary element method. The particular integrals are determined by solving the corresponding strong form differential equations using local radial point interpolation. The effectiveness and accuracy of the approach are proven on some simple examples. The latter are also used in order to highlight some peculiarities and potentialities of such extended continuum mechanical approach

Etude des contraintes thermoelastiques dans les plaques perforees qui maintiennent les tubes de reaction d'un echangeur a faisceau tubulaire

SIGLECNRS T Bordereau / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Investigation of Elastic Constants of Polymer/Nanoparticles Composites Using the Brillouin Spectroscopy and the Mechanical Homogenization Modeling

International audienceA numerical model using homogenization techniques is proposed to simulate the evolution of elastic properties of nanocomposite polymer-nanoparticles, depending on the concentration of nanoparticles and the rigidity of the particle-matrix interface. To validate this model, it was confronted to several physical systems having different interface behavior, the nanocomposite systems: poly(vinylidene fluoride trifluoroethylene)/Al2O3 (alumina nanoparticles incorporated into copolymer of vinylidene difluoride and trifluoroethylene to form nanocomposite), PMMA/CNT (carbon nanotube/poly(methyl methacrylate) composite) and PMMA/SiO2 with nanoparticles with or without surface treatment of silanization. For all these systems, the Young's modulus (nanoparticles and matrix) has been obtained experimentally from the elastic modulus C-11 obtained by Brillouin spectroscopy. These macroscopic measurements coupled with the theoretical model allow a multiscale approach of the elastic behavior of nanocomposite systems, providing information on the global elastic properties of polymer-nanoparticle material, and also indications about the strength of physical and chemical bonds between the nanoparticles and the matrix. Our results validate the hypothesis of the crucial role of the interface module, provided by numerical simulation which shows that incorporation of nanoparticles may lead to a strengthening or a weakening of the matrix