title: ÐÐ¸Ð»Ð°ÑÐ°ÑÐ¸Ð¾Ð½Ð½ÑÐµ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ñ Ð² ÑÐ¿ÑÑÐ³Ð¾Ð¼ ÐºÐ»Ð¸Ð½Ðµ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Dilatation inclusions in an elastic wedge
Creators: name: ÐÑÐ´ÐºÐ¸Ð½Ð°, ÐÐ°Ð½Ð½Ð°
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2021
Subjects: Ð­Ð½ÐµÑÐ³ÐµÑÐ¸ÑÐµÑÐºÐ¸Ðµ ÑÐ¸ÑÑÐµÐ¼Ñ
Ð¢Ð²ÐµÑÐ´ÑÐµ ÑÐµÐ»Ð°
Ð´Ð¸Ð»Ð°ÑÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ Ð½Ð¸ÑÑ
ÐºÐ»Ð¸Ð½
ÑÐ²Ð¾Ð±Ð¾Ð´Ð½Ð°Ñ Ð¿Ð¾Ð²ÐµÑÑ Ð½Ð¾ÑÑÑ
Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð¸Ðµ ÐÐµÐ»Ð»Ð¸Ð½Ð°
dilatation line
wedge
free surface
Mellin transform

description: Ð Ð°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð½Ð¾-Ð´ÐµÑÐ¾ÑÐ¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ð³Ð¾ ÑÐ¾ÑÑÐ¾ÑÐ½Ð¸Ñ Ð² ÑÐ¿ÑÑÐ³Ð¾-Ð¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾Ð¼ ÐºÐ»Ð¸Ð½Ð¾Ð²Ð¸Ð´Ð½Ð¾Ð¼ ÑÐµÐ»Ðµ Ñ Ð´Ð¸Ð»Ð°ÑÐ°ÑÐ¸Ð¾Ð½Ð½ÑÐ¼Ð¸ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸ÑÐ¼Ð¸. ÐÐºÑÑÐ°Ð»ÑÐ½Ð¾ÑÑÑ ÑÐ°Ð±Ð¾ÑÑ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÑÐµÑÑÑ ÑÐµÐ¼, ÑÑÐ¾ Ð½Ð° ÑÑÑÐºÐµ Ð¼ÐµÑÐ°Ð½Ð¸ÐºÐ¸ Ð´ÐµÑÐ¾ÑÐ¼Ð¸ÑÑÐµÐ¼Ð¾Ð³Ð¾ ÑÐ²ÐµÑÐ´Ð¾Ð³Ð¾ ÑÐµÐ»Ð° Ð¸ ÑÐ¸Ð·Ð¸ÐºÐ¸ ÑÐ²ÐµÑÐ´Ð¾Ð³Ð¾ ÑÐµÐ»Ð° Ð²ÐµÐ´ÐµÑÑÑ Ð¿Ð¾Ð¸ÑÐº Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸Ñ ÑÐµÑÐµÐ½Ð¸Ð¹ Ð³ÑÐ°Ð½Ð¸ÑÐ½ÑÑ Ð·Ð°Ð´Ð°Ñ ÑÐµÐ¾ÑÐ¸Ð¸ ÑÐ¿ÑÑÐ³Ð¾ÑÑÐ¸ Ð´Ð»Ñ Ð´ÐµÑÐµÐºÑÐ¾Ð², Ð¿Ð¾Ð²ÐµÐ´ÐµÐ½Ð¸Ðµ ÐºÐ¾ÑÐ¾ÑÑÑ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÑÐµÑ ÑÐ¸Ð·Ð¸ÐºÐ¾-Ð¼ÐµÑÐ°Ð½Ð¸ÑÐµÑÐºÐ¸Ðµ ÑÐ²Ð¾Ð¹ÑÑÐ²Ð° ÑÐ¾Ð²ÑÐµÐ¼ÐµÐ½Ð½ÑÑ ÑÐ²ÐµÑÐ´Ð¾ÑÐµÐ»ÑÐ½ÑÑ Ð½Ð°Ð½Ð¾Ð³ÐµÑÐµÑÐ¾ÑÑÑÑÐºÑÑÑ. Ð¢ÐµÐ¾ÑÐµÑÐ¸ÑÐµÑÐºÐ°Ñ Ð¸ Ð¿ÑÐ°ÐºÑÐ¸ÑÐµÑÐºÐ°Ñ Ð·Ð½Ð°ÑÐ¸Ð¼Ð¾ÑÑÑ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² ÑÐ¾ÑÑÐ¾Ð¸Ñ Ð² ÑÐ¾Ð¼, ÑÑÐ¾ Ð²Ð¿ÐµÑÐ²ÑÐµ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¾ Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ Ð³ÑÐ°Ð½Ð¸ÑÐ½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ ÑÐµÐ¾ÑÐ¸Ð¸ ÑÐ¿ÑÑÐ³Ð¾ÑÑÐ¸ Ð¾ Ð´Ð¸Ð»Ð°ÑÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¼ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ð¸ Ð² Ð²Ð¸Ð´Ðµ Ð±ÐµÑÐºÐ¾Ð½ÐµÑÐ½Ð¾ ÑÐ¾Ð½ÐºÐ¾Ð¹ ÑÐ¿ÑÑÐ³Ð¾Ð¹ Ð¿ÑÑÐ¼Ð¾Ð¹ Ð½Ð¸ÑÐ¸ Ð² ÑÐ¿ÑÑÐ³Ð¾-Ð¾Ð´Ð½Ð¾ÑÐ¾Ð´Ð½Ð¾Ð¼ ÐºÐ»Ð¸Ð½Ð¾Ð²Ð¸Ð´Ð½Ð¾Ð¼ ÑÐµÐ»Ðµ. ÐÐ¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ ÑÑÐ¾ ÑÐµÑÐµÐ½Ð¸Ðµ Ð¼Ð¾Ð¶ÐµÑ ÑÐ»ÑÐ¶Ð¸ÑÑ Ð¾ÑÐ½Ð¾Ð²Ð¾Ð¹ Ð´Ð»Ñ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ð¸Ñ Ð°Ð½Ð°Ð»Ð¾Ð³Ð¸ÑÐ½ÑÑ ÑÐµÑÐµÐ½Ð¸Ð¹ Ð´Ð»Ñ ÑÐ¸Ð»Ð¸Ð½Ð´ÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð²ÐºÐ»ÑÑÐµÐ½Ð¸Ð¹ Ñ Ð¿ÑÐ¾Ð¸Ð·Ð²Ð¾Ð»ÑÐ½ÑÐ¼ Ð¿Ð¾Ð¿ÐµÑÐµÑÐ½ÑÐ¼ ÑÐµÑÐµÐ½Ð¸ÐµÐ¼. Ð­ÑÐ¾ Ð¾ÑÐºÑÑÐ²Ð°ÐµÑ ÑÐ¸ÑÐ¾ÐºÐ¸Ðµ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ÑÑÐ¸ Ð´Ð»Ñ ÑÐ°Ð·Ð²Ð¸ÑÐ¸Ñ ÐºÐ¾Ð½ÑÐ¸Ð½ÑÐ°Ð»ÑÐ½ÑÑ Ð¼Ð¾Ð´ÐµÐ»ÐµÐ¹, Ð¾Ð¿Ð¸ÑÑÐ²Ð°ÑÑÐ¸Ñ Ð·Ð°ÑÐ¾Ð¶Ð´ÐµÐ½Ð¸Ðµ Ð¸ ÑÐ°Ð·Ð²Ð¸ÑÐ¸Ðµ Ð´ÐµÑÐµÐºÑÐ¾Ð² Ð½Ð° ÑÑÐ°Ð´Ð¸Ð¸ ÑÐµÐ»Ð°ÐºÑÐ°ÑÐ¸Ð¸ Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð¸Ð¹ Ð½ÐµÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²Ð¸Ñ Ð¸ ÑÐµÑÐ¼Ð¾ÑÐ¿ÑÑÐ³Ð¸Ñ Ð½Ð°Ð¿ÑÑÐ¶ÐµÐ½Ð¸Ð¹ Ð² ÑÐµÐ°Ð»ÑÐ½ÑÑ Ð¿ÑÐ¸Ð±Ð¾ÑÐ½ÑÑ ÑÐ²ÐµÑÐ´Ð¾ÑÐµÐ»ÑÐ½ÑÑ ÑÑÑÑÐºÑÑÑÐ°Ñ ÑÐ¾ÑÐ¾Ð½Ð¸ÐºÐ¸, ÑÐ»ÐµÐºÑÑÐ¾Ð½Ð¸ÐºÐ¸ Ð¸ Ð¾Ð¿ÑÐ¾ÑÐ»ÐµÐºÑÑÐ¾Ð½Ð¸ÐºÐ¸.
description: The work is devoted to the study of the stress-strain state in an elastically homogeneous wedge-shaped body with dilatation inclusions. The relevance of the work is due to the fact that, at the junction of the mechanics of deformable solids and the solid-state physics, the search for analytical solutions to the boundary value problems in the theory of elasticity for defects, the behavior of which determines the physical and mechanical properties of modern solid-state nanoheterostructures, is carried out. The theoretical and practical significance of the results obtained lies in the fact that, for the first time, an analytical solution of the boundary-value problem in the theory of elasticity on a dilatation inclusion in the form of an infinitely thin elastic straight thread in an elastically homogeneous wedge -shaped body was obtained. It is shown that this solution can serve as a basis for constructing similar solutions for cylindrical inclusions with an arbitrary cross section. This opens up wide opportunities for the development of continual models describing the nucleation and development of defects at the stage of relaxation of misfit stresses and thermoelastic stresses in real solid-state device structures of photonics, electronics, and optoelectronics.