A. A. Kaminskii

Study of the Deformation of Anisotropic Viscoelastic Bodies

A study is made of methods for solving linear viscoelastic problems on the basis of the Volterra concept — representation of irrational functions of integral operators as operator power series (analogues of Taylor series). It is pointed out that these series converge weakly. The results of development and substantiation of a new mathematical method for solution of the above problems are summarized. It is based on representing irrational functions of integral operators by operator continued fractions, which converge well. Solutions to certain linear viscoelastic problems for anisotropic bodies are given

Analyzing the Laws of Stable Subcritical Growth of Cracks in Polymeric Materials on the Basis of Fracture Mesomechanics Models. Theory and Experiment

The laws of stable crack growth are analyzed using fracture mesomechanics models for polymeric materials under long-term subcritical tension. A review is given of experimental and theoretical studies of crack-tip process zones. The studies were conducted using physical and mechanical methods and fracture mesomechanics models, allowing for the structural and rheological features of process zones. Theoretical and experimental results on the behavior of process zones are generalized and the theory of stable crack growth in viscoelastic polymers, which assumes the autonomy of the process zone during crack development, is justified

Tetragonal vanadates REVO4 (RE = Ln (Ce-Lu), Y)—a novel class of SRS-active crystals

The basic χ(3) nonlinear laser properties of tetragonal vanadates (YVO4, GdVO4, ErVO4, YbVO4, LuVO4, Y0.5Gd0.5VO4, and Gd0.5Lu0.5VO4), which represent a novel class of SRS-active crystals, are presented. The presence of combined χ(3) active phonon modes in the GdVO4 crystal at a cryogenic temperature (∼9 K) is reported.

Delayed Fracture of an Aging Viscoelastic Composite under Plane Strain

The theory of delayed fracture of cracked viscoelastic bodies and the method of continued fractions are used to study the problem on the delayed fracture of an unidirectional fibrous composite subjected to uniaxial tension under plane-strain conditions. The aging viscoelastic binder contains a mode I macrocrack, which is parallel to the fibers. The results of a numerical crack-resistance analysis of a composite whose aging properties are described by the Volterra operator with the Maslov–Arutyunyan kernel are presented. A convergence analysis is made of the expansion of an irrational function of the resolvent Volterra operator into a continued fraction.

Viscoelastic Deformation of a Reinforced Plate with a Crack

The deformation of a viscoelastic reinforced composite is studied. The composite has an axis of elastic symmetry and consists of transversally isotropic fibers and a viscoelastic matrix, which differ by the volume concentration and mechanical characteristics. The material is modeled by a transversely isotropic homogeneous linearly viscoelastic medium with some averaged characteristics. A plate fabricated from the composite in question is weakened by a through mode I crack and is subjected to constant tensile forces. The viscoelastic properties of the matrix material are described by a convolution operator. The Volterra principle is used to derive expressions for the viscoelastic characteristics and crack opening. The irrational function of the integral operator that describes the crack opening is expanded into an operator continued fraction and is represented as the sum of base operators

Delayed Fracture of a Laminated Viscoelastic Plate with a Through Crack under a Time-Dependent Load

The delayed fracture of a viscoelastic plate with a rectilinear mode I crack under a time-dependent load is studied. The plate is made of a laminated composite with an isotropic elastic reinforcing component and a viscoelastic matrix. The composite is modeled by an orthotropic homogeneous linearly viscoelastic medium with some averaged characteristics. To determine the viscoelastic characteristics of the composite, the Volterra principle and the method of continued fractions are used. The study is made within the framework of the theory of delayed fracture for viscoelastic bodies.

Study of the stress state near a corner point in simulating the initial plastic zone by slipbands

The stress state near a corner point in a homogeneous isotropic solid is investigated within the framework of a symmetric problem. The solid boundary near this point is stress-free. The initial plastic zone is modeled by two slipbands

The use of the “trident” model in the analysis of plastic zones near crack tips and corner points

The paper deals with calculation of a plastic zone near a crack tip in a homogeneous elastoplastic solid and near a corner point of the boundary of this solid. The calculations are conducted for a solid subject to plane strain and within the framework of models with plastic strips. It is shown that in comparison with the widely used model with two straight slip-lines, the process of plastic deformation is described by the “trident” model more accurately. The results of calculations of the plastic zone by the “trident” model that correspond to different stages of the development of plastic deformation are given for a crack of normal separation in a quasibrittle material.

Analysis of the Plastic Zone at a Corner Point by the Trident Model

The Wiener–Hopf method is used to analyze the plastic zone at a corner point by the model with three plastic lines of discontinuity.

One method of solution of problems in the linear theory of viscoelasticity for aging anisotropic materials

A method of solution of problems in the linear theory of viscoclasticity for aging anisotropic materials is discussed. The method is based on evaluation of irrational functions of nondiffcrence viscoelasticity operators using the theory of continued fractions. It is shown that operator-valued continuedS-fractions converge for a wide class of integral Voltcrra operators. Application of the method is illustrated by the evaluation of an irrational function of a linear combination of nondiffcrence-type resolvent operators obtained in the solution of a concrete problem of failure of an aging anisotropic viscoclastic body.