Multiscale modeling in the mechanics of materials: Cohesion, interfacial interactions, inclusions and defects

The models of media with multiscale effects axe constructed based on the variational formalism. The internal interactions are determined by kinematic constraints of general character. These models take into account the superficial effects and internal interactions similar to interatomic forces of coupling. The models of media with a continuous field of defects of various types are considered. Descriptions of the media with defects, cohesion field models as a special case of the Cosserat models are considered. This paper is devoted to the consideration of disperse composite materials reinforced by nanoparticles. For numerical simulation, the new efficient block analytical-numerical method is developed oriented to the general case of solving problems in complex-shaped 2D and 3D domains. As an example of numerical investigation of the interfacial interactions in heterogeneous media, the medium with inclusions is considered.