TY - JOUR

T1 - T-shape inclusion in elastic body with a damage parameter

AU - Khludnev, Alexander

N1 - Funding Information: The work is supported by Mathematical Center in Akademgorodok, Russia under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. Publisher Copyright: © 2021 Elsevier B.V. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/9

Y1 - 2021/9

N2 - We consider an equilibrium problem for a 2D elastic body with a thin elastic T-shape inclusion. A part of the inclusion is delaminated from the elastic body forming a crack between the inclusion and the surrounding elastic body. Inequality type boundary conditions are imposed at the crack faces preventing interpenetration between the crack faces. The model is characterized by a damage parameter. This parameter is responsible for connection at the junction points between different parts of the considered structure. Dependence of solutions on the damage parameter is investigated, in particular, a passage to infinity and to zero is analyzed. Inverse problems are considered provided that the damage parameter and Lamé parameters of the elastic body are unknown. In this case, a displacement of the tip point of the inclusion is assumed to be known. A solution existence of the inverse problems is proved.

AB - We consider an equilibrium problem for a 2D elastic body with a thin elastic T-shape inclusion. A part of the inclusion is delaminated from the elastic body forming a crack between the inclusion and the surrounding elastic body. Inequality type boundary conditions are imposed at the crack faces preventing interpenetration between the crack faces. The model is characterized by a damage parameter. This parameter is responsible for connection at the junction points between different parts of the considered structure. Dependence of solutions on the damage parameter is investigated, in particular, a passage to infinity and to zero is analyzed. Inverse problems are considered provided that the damage parameter and Lamé parameters of the elastic body are unknown. In this case, a displacement of the tip point of the inclusion is assumed to be known. A solution existence of the inverse problems is proved.

KW - Crack

KW - Elastic body

KW - Inverse problem

KW - Non-penetration condition

KW - T-shape inclusion

KW - Variational inequality

UR - http://www.scopus.com/inward/record.url?scp=85102321269&partnerID=8YFLogxK

UR - https://elibrary.ru/item.asp?id=46754374

U2 - 10.1016/j.cam.2021.113540

DO - 10.1016/j.cam.2021.113540

M3 - Article

AN - SCOPUS:85102321269

VL - 393

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

M1 - 113540

ER -