An analysis is made of the results obtained in the three-dimensional linearized theory of elastic waves propagating in initially stressed solids. Consideration is given to surface waves along planar and curvilinear boundaries and interfaces, waves in layers and cylinders, waves in composite materials, waves in hydroelastic systems, and dynamic problems for moving loads. The results were obtained in exact formulations.

Elastic waves in bodies with initial (residual) stresses

An analysis of research available on the problem under consideration shows that at this time: a) Wave propagation in unbounded, bounded, and composite laminar bodies with homogeneous initial states has been studied sufficiently extensively; b) methods to determine the third-order elastic constants have been developed on the basis of existing theories; c) an ultrasonic nondestructive method to determine the stress in solids has been developed, where the stresses averaged over the bulk of the body are determined. In light of the above, in the authors' opinion, the following should be considered the most urgent questions for further investigations on the problem: a) the investigation of wave propagation regularities in bodies with inhomogeneous initial states (it is hence important to execute quantitative and qualitative analyses of the phenomenon); b) development of an ultrasonic nondestructive method of determining the stress in the near surface layers of a solid, which will afford a possibility of determining not only the membrane stresses but also the bending stresses; c) an investigation of the wave propagation regularities in fibrous composites with initial stresses.

Elastic waves in bodies with initial stresses

The construction of the three-dimensional linearized theory of stability of deformable bodies (TLTSDB) is analyzed. Historical aspects, the statement of the problem, basic relations, general results, and some specific problems are outlined

Constructing the three-dimensional theory of stability of deformable bodies

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

Establishing fundamentals of the mechanics of nanocomposites

Some nonclassical problems of fracture mechanics that have been analyzed by the author and his collaborators at the Institute of Mechanics (Kiev) during the past thirty years are considered in brief

A. N. Guz

Papers

Comment on the book by A. N. Guz', stability of elastic bodies under finite deformations, Izd-vo Naukova Dumka, Kiev (1973)