A. N. Guz

The physical fundamentals of the ultrasonic nondestructive stress analysis of solids

Theoretical and experimental works on acoustoelasticity are briefly generalized. Studies conducted and scientific results obtained at the S. P. Timoshenko Institute of Mechanics and E. O. Paton Institute of Electric Welding of the National Academy of Sciences of Ukraine are highlighted. Special features of these works and their difference from those of other authors are pointed out. The basic principles and laws governing the propagation of longitudinal, shear, and surface waves in bi- and triaxially stressed bodies are briefly stated with regard for the orthotropy and nonlinear properties of the material. The experimentally proven principles and laws for elastic waves propagating in initially stressed bodies are formulated. The physical fundamentals of the ultrasonic nondestructive technique for determining bi- and triaxial stresses in solids are described. The determination of bi- and triaxial residual stresses in specimens and structural members is demonstrated by examples. The basic principles of the related (dielectric and electromagnetic) methods for stress analysis of polymeric materials are stated. The application of the electromagnetic method to the stress analysis of some polymeric materials is considered

Constructing the Three-Dimensional Theory of Stability of Deformable Bodies

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

Description and Study of Some Nonclassical Problems of Fracture Mechanics and Related Mechanisms

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

Nanomaterials: on the Mechanics of Nanomaterials

The paper presents a brief historical sketch of nanotechnology and scientific analysis of nanoparticles, nanoformations, and nanomaterials. Certain aspects of the state of the art and promising trends in the nanomechanics of materials and relationships among macromechanics, mesomechanics, micromechanics, and nanomechanics are analyzed

The Three-Dimensional Theory of Stability of Fibrous and Laminated Materials

An analysis is made of the results of investigations into the internal and surface instability of fibrous and laminated composites within the framework of the piecewise-homogeneous model and the equations of the three-dimensional linearized theory of stability. The possible buckling modes of the reinforcing elements in composites with either an elastic (polymeric) or elastoplastic (metallic) matrix are studied. The reliability domains of applied approximate design models are determined and some applications of results on fracture (due to structural instability) of unidirectional composites are presented

On One Two-Level Model in the Mesomechanics of Compression Fracture of Cracked Composites

The article is devoted to a two-level model in the mesomechanics of compression fracture of composites with cracks. Consideration is given to fiber-laminated panels with an opening compressed along the fibers so that two cracks propagate from the opening edge in a direction perpendicular to the loading axis. The previous results obtained by the author in the three-dimensional theory of stability of deformable bodies and nonclassical fracture mechanics are used to create the above-mentioned two-level model

Establishing the Fundamentals of the Theory of Stability of Mine Workings

The fundamentals of the theory of stability of mine workings are analyzed. The theory is based on the linearized three-dimensional theory of stability of deformable bodies. Some results on horizontal and vertical mine workings and on underground closed cavities are analyzed

Mechanics of Curved Composites (Piecewise-Homogeneous Body Model)

A review is made of studies on the mechanics of curved composites carried out using the piecewise-homogeneous body model and the exact three-dimensional equations of the theory of elasticity and viscoelasticity. Relevant problem formulations and solution methods are considered and some typical results on the influence of structural distortion on the mechanical behavior of composites are analyzed. Subjects for near-term studies are proposed

Statics of laminated and fibrous composites with curved structures

A broad and detailed review is presented on problems of statics of mechanics of laminated and fibrous composite materials with curved structures. Studies are discussed which were carried out based on the piecewise-homogeneous body model using exact three-dimensional equations of deformable solid body mechanics. The classification was made according to the type of composite (laminated, fibrous), the form of bending in the structure of composites considered, the materials properties (isotropic, anisotropic), the properties of binder and filler, and their models (elastic, viscoelastic). The formulation of the problem is presented for laminated and fibrous composites with bent, curved structures. Two types of bending are distinguished according to the forms of reinforcing elements bending: (1) periodic; (2) local. For every type of bending, solution methods of corresponding problems are presented. Moreover, according to the form of the location of neighboring curved, bent layers, with respect to each other, two types of bending are distinguished—the monophasic and the antiphasic. Detailed presentation is given of some very significant specific results, illustrating the influence of reinforcing element bending on local distribution of stresses in every component of the composite material. Tables and graphs are presented from publications on this subject. Some applications are presented of results based on the piecewise-homogeneous body model in composite mechanics. In conclusion, some areas of future research are proposed. The situations presented prove the theoretical and practical importance of investigations discussed in the review. In the analysis of strength problems, in many cases information is needed on the local distribution of the stress-deformed state in every component of the composite material with bent, curved structures. Information of this type could be obtained only within the framework of the piecewise-homogeneous body model using exact three-dimensional equations of deformable solid body mechanics.

Dynamic problems of the mechanics of the brittle fracture of materials with initial stresses for moving cracks. 1. Problem statement and general relationships

This paper studies the brittle fracture of materials with initial stresses when the stresses act only along the cracks. Dynamic problems for moving cracks are considered when the plane crack infinite in one direction moves with constant velocity. General formulas are presented for compressible and incompressible elastic bodies with an arbitrary structure of elastic potentials. The stresses and displacements are presented as analytical functions of complex variables. Some general relationships may be used in order to obtain exact information on the singularity order of the crack tip for dynamical problems under consideration in the general formulation.