Vol 217, No 3 (2016)

We study the development of plastic strains localized on the surface of a rigid fiber with square cross section in a perfect elastoplastic matrix. Two identical interface cracks originate from the opposite vertices of the fiber. The strains are caused by a shear load parallel to one of the diagonals of the fiber connecting the origins of the cracks. It is shown that, in the case where the length of an interface crack does not exceed a half of the length of the fiber edge, the plastic strains can be localized only on the inclusion–matrix interface. For the cracks shorter than the half length of the fiber edge, we determine the dependence of lengths of the strips of plastic exfoliation on the load. It is shown that the plastic strips cannot completely cover the surface of the fiber on the continuation of the crack.

We consider a mathematical model of elastic body with thin inclusion or coating in the form of a thin elastic shell. It is shown that the corresponding Steklov–Poincaré operator of the mathematical model possesses the properties guaranteeing the existence and uniqueness of a weak solution of the boundary-value problem. We propose a method of solution based on the domain decomposition algorithm with the use of the boundary-element and finite-element methods. We prove the convergence of the iterative domain decomposition method and present the results of numerical experiments.

We study the processes of thermodiffusion with regard for the decay of a substance in a two-phase randomly inhomogeneous layered strip. The statement of a contact-boundary-value problem is formulated on the basis of the theory of binary systems with conditions of perfect contact for temperature and imperfect conditions for concentration. The system of equations of thermodiffusion of decaying particles is obtained for the entire body. The system of integrodifferential equations equivalent to the source contact boundary-value problem is formulated. Its solution is constructed by the method of successive approximations. The random fields of temperature and concentration of decaying particles are found in the form of Neumann series. The conditions of absolute and uniform convergence of the series are established. The procedure of averaging of the random fields is carried out over the ensemble of phase configurations with uniform distribution function.

On the basis of the variational problem of classical thermoelasticity for three-dimensional bodies of small thickness, we formulate the corresponding variational problem of nonstationary thermoelasticity for shells compliant to shears and compression. The reduction of dimensionality of the original problem is attained by using the Galerkin semidiscretization and the Timoshenko–Mindlin hypotheses on the linearity of variations of displacements and temperature along the thickness of the shell. The problem is formulated in terms of the vector of elastic displacements and rotations of the normal, temperature, and its gradient defined on the middle surface of the shell. The case of quasistatic problem for which the conditions of correctness are established is analyzed in more detail. The results of the finite-element analysis of the problem of thermoelasticity for a steel plate subjected to the action of thermal and force loads are presented.