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This study presents a micromechanics model based on the variational asymptotic method for unit cell homogenization (VAMUCH) to predict the effective elastic properties of a continuous fuzzy fiber-reinforced composite material. The constructional feature of the fuzzy fiber-reinforced composite (FFRC) proposed in [S.I. Kundalwal, M.C. Ray, "Effective properties of a novel continuous fuzzy-fiber reinforced composite using the method of cells and the finite element method", European Journal of Mechanics A/Solids 36 (2012) 191-203] is that uniformly aligned carbon nanotubes (CNTs) are radially grown on the surface of the horizontal carbon fibers. The effective elastic properties of the fuzzy fiber-reinforced composite estimated by the variational asymptotic method have been compared with those predicted by the finite element based micromechanics approach (FEA) and the method of cells (MOC) approach reported in the previous reference. It has been also observed that the transverse effective properties of such a composite material are significantly improved due to the radial growing of CNTs on the surface of the carbon fiber. It is shown that two 2D unit cells can be successfully used within the VAMUCH for the intuitive prediction of the full effective 3D anisotropic properties of such FFRC. This lead to a reduced computational expenditure in comparison to the three 3D unit cells used in the FEA reported in the above reference.

We investigate the effect of various spherical nanoparticles in a polymer matrix on dispersion, chain dimensions and entanglements for ionic nanocomposites at dilute and high nanoparticle loading by means of molecular dynamics simulations. The nanoparticle dispersion can be achieved in oligomer matrices due to the presence of electrostatic interactions. We show that the overall configuration of ionic oligomer chains, as characterized by their radii of gyration, can be perturbed at dilute nanoparticle loading by the presence of charged nanoparticles. In addition, the nanoparticle’s diffusivity is reduced due to the electrostatic interactions, in comparison to conventional nanocomposites where the electrostatic interaction is absent. The charged nanoparticles are found to move by a hopping mechanism., Polymers, 10 (9), ISSN:2073-4360

International audience; On passe en revue les progrès récents réalisés sur une méthode sans maillage qui ne discrétise que les frontières. L'idée est de résoudre l'EDP dans le domaine par la méthode des séries de Taylor. Quatre points-clé sont discutés: le traitement des conditions aux limites, les techniques de raccord entre polynômes de degré élevé, les procédures pour obtenir la solution générale d'une EDP quelconque et l'efficacité numérique de la méthode.

International audience; New bridging techniques are introduced to match high degree polynomials. This permits piecewise resolutions of elliptic partial differential equations (PDEs) in the framework of a boundary meshless method introduced recently. This new meshless method relies on the computation of Taylor series approximations deduced from the PDE, the shape functions being high degree polynomials. In this way, the PDE is solved quasi-exactly inside the subdomains so that only discretization of the boundary and the interfaces are needed, which leads to small size matricial problems. The bridging techniques are based on the introduction of Lagrange multipliers and a set of collocation points on the boundary and the interfaces. Several numerical applications establish that the method is robust and permits an exponential convergence with the degree.