Establishing fundamentals of the mechanics of nanocomposites

The paper proposes a basic approach to study the mechanical properties of nanocomposite materials with polymer matrix and the deformation of nanocomposites and structural members made of them. The notions of homogenization and continualization are discussed with reference to nanocomposite materials. Four main tasks for nanocomposite mechanics are defined: (i) description of the properties of nanoformations, (ii) description of the properties of the matrix (binder), (iii) description of phenomena at the matrix-nanoformations interfaces, and (iv) determination of the effective properties of nanocomposites to change over to the mechanics of structural members. Particular attention is given to the interface conditions between the matrix and reinforcement. The role of lower and upper bound estimates is pointed out. The basic models of linear or nonlinear micro- and nanocomposites are considered. These models are used in a numerical analysis. The analysis makes it possible to observe and describe the peculiarities of the processes of fracture, deformation, and wave propagation in nanocomposite materials with polymer matrix. The numerical results are presented in the form of plots.