The main physical laws of thermal–plastic deformation and fatigue damage accumulation processes in polycrystalline structural alloys under various regimes of cyclic thermal–mechanical loading are considered. Within the framework of mechanics of damaged media, a mathematical model is developed that describes thermal–plastic deformation and fatigue damage accumulation processes under low-cycle loading. The model consists of three interrelated parts: relations defining plastic behavior of the material, accounting for its dependence on the failure process; evolutionary equations describing damage accumulation kinetics; a strength criterion of the damaged material. The plasticity model based on the notion of yield surface and the principle of orthogonality of the plastic strain vector to the yield surface is used as defining relations. This version of defining equations of plasticity describes the main effects of the deformation process under monotone cyclic, proportional and nonproportional loading regimes. The version of kinetic equations of damage accumulation is based on introducing a scalar parameter of damage degree and energy principles, and account for the main effects of nucleation, growth and merging of microdefects under arbitrary regimes of low-cycle loading. The strength criterion of the damaged material is based on reaching a critical value of the damage degree. The results of numerically modeling cyclic thermal–plastic deformation and fatigue damage accumulation in heat-resistant alloys (Nimonic 80A, Haynes 188) under combined thermal–mechanical loading are presented. Special attention is paid to the issues of modeling the processes of cyclic thermal–plastic deformation and fatigue damage accumulation for complex deformation processes accompanied by the rotation of the main stress and strain tensor areas. It is shown that the present damaged medium model accurately enough for engineering purposes describes the processes of cyclic isothermal and nonisothermal deformation and fatigue damage accumulation under combined thermal–mechanical loading and makes it possible to evaluate low-cycle fatigue life of heat-resistant alloys under arbitrary deformation trajectories.

This paper presents the results of mathematical and discrete modeling of linear dynamics problems for three-dimensional viscoelastic and porous elastic bodies. The employed methods and approaches are based on formulating boundary integral equations solved using boundary elements. The model of a standard viscoelastic body is employed as the viscoelastic model. The properties of porous elastic materials are described using the full Biot model with four basic functions. Examples of numerical solutions of the problems are compared with known results of solutions.

The present paper is dedicated to numerical solving of three dimensional boundary-value problems in poroviscoelastic formulation. The poroviscoelastic formulation is treated as a combination of...

The action of a non-stationary force on a deformed porous-elastic die rigidly interacting with a porous-elastic half-space is analyzed in a 3D formulation, using BEM in combination with the integral Laplace transform. The displacement and flow responses are constructed. The displacement responses are used to demonstrate the effect of formation of Raleigh wave. Keywords: boundary element, porous-elastic material, half-space, 3D formulation, deformed die, non-stationary dynamics. Рассматривается в трехмерной постановке численное решение задачи методом граничного элемента в сочетании с интегральным преобразованием Лапласа о действии нестационарной силы на деформируемый пористо-упругий штамп, жестко взаимодействующий с пористо-упругим полупространством. Построены отклики перемещений и потока. На откликах перемещений продемонстрирован эффект формирования волны Рэлея. Ключевые слова: граничный элемент, пористо-упругий материал, полупространство, трехмерная постановка, деформируемый штамп, нестационарная динамика.