International audienceIn a nanostructured material, the interface to volume ratio is so high that the interface energy, which is usually negligible with respect to the bulk energy in solid mechanics, can no longer be neglected. The interfaces in a number of nanomaterials can be appropriately characterized by the coherent interface model. According to the latter, the displacement vector field is continuous across an interface in a medium while the traction vector field across the same interface is discontinuous and must satisfy the Laplace-Young equation. The present work aims to elaborate an efficient numerical approach to dealing with the interface effects described by the coherent interface model and to determining the size-dependent effective elastic moduli of nanocomposites. To achieve this twofold objective, a computational technique combining the level set method and the extended finite element method is developed and implemented. The numerical results obtained by the developed computational technique in the two-dimensional context are compared and discussed with respect to the relevant exact analytical solutions used as benchmarks. The computational technique elaborated in the present work is expected to be an efficient tool for evaluating the overall sizedependent elastic behaviour of nanomaterials and nanosized structures

The theory of first strain gradient elasticity (SGE) is widely used to model size and non-local effects observed in materials and structures. For a material whose microstructure is centrosymmetric, SGE is characterized by a sixth-order elastic tensor in addition to the classical fourth-order elastic tensor. Even though the matrix form of the sixth-order elastic tensor is well-known in the isotropic case, its complete matrix representations seem to remain unavailable in the anisotropic cases. In the present paper, the explicit matrix representations of the sixth-order elastic tensor are derived and given for all the 3D anisotropic cases in a compact and well-structured way. These matrix representations are necessary to the development and application of SGE for anisotropic materialsComment: Journal of the Mechanics and Physics of Solids (2013) (Accepted

Eshelby's results and formalism for an elastic circular or spherical inhomogeneity embedded in an elastic infinite matrix are extended to the thermal conduction phenomenon with a Kapitza's interface thermal resistance between matrix and inclusions. Closed-form expressions are derived for the generalized Eshelby's interior and exterior conduction tensor fields and localization tensor fields in the case where the matrix and inclusion phases have the most general anisotropy. Unlike the relevant results in elasticity, the generalized Eshelby's conduction tensor fields and localization tensor fields inside circular and spherical inhomogeneities are shown to remain uniform even in the presence of Kapitza's interface thermal resistance. With the help of these results, the size-dependent overall thermal conduction properties of composites are estimated by using the dilute, Mori-Tanaka, self-consistent and generalized self-consistent models. The analytical estimates are finally compared with numerical results delivered by the finite element method. The approach elaborated and results provided by the present work are directly applicable to other physically analogous transport phenomena, such as electric conduction, dielectrics, magnetism, diffusion and flow in porous media, and to the mathematically identical phenomenon of anti-plane elasticity.

Flexoelectricity is due to the electric polarization generated by a non-zero strain gradient in a dielectric material without or with centrosymmetric microstructure. It is characterized by a fourth-order tensor, referred to as flexoelectric tensor, which relates the electric polarization vector to the gradient of the second-order strain tensor. This paper solves the fundamental problem of determining the number and types of all possible rotational symmetries for flexoelectric tensors and specifies the number of independent material parameters contained in a flexoelectric tensor belonging to a given symmetry class. These results are useful and even indispensable for experimentally identifying or theoretically/numerically estimating the flexoelectric coefficients of a dielectric material.