ИСТИНА

An approach to modeling of nonlinear elastic materials with nanoinclusions is proposed. The model developed within the framework of the mechanics of deformable solids takes into account that deformations are finite. It is assumed that regions with special properties (v-regions) are originated around nanoinclusions. The typical size of these regions is comparable with the size of nanoinclusions. Note that v-regions may be neglected for inclusions that are larger in size than nanoinclusions. The theory of repeated superposition of large deformations is required for the solution of specific problems. To illustrate the approach, a representative problem of stretching a nonlinear elastic solid with interacting spheroidal inclusions under finite strains is considered. The numerical results for this representative problem are presented. The solution is obtained using the special-purpose finite-element code "Superposition" developed by the authors. In order to determine the boundaries of v-regions, one must choose a criterion that gives the shape of these regions or the rule of definition of this shape. Some of such criteria are considered. Use of non-local criteria [1] for this purpose is discussed. The existence of v-regions around nanoinclusions changes the mechanical behavior of materials. The effective properties of nanocomposites undergoing finite strains may be estimated by combining the proposed approach with the homogenization techniques described in [2,3].