Lavrentyev Institute of Hydrodynamics of RAS, and Novosibirsk State University, Novosibirsk 630090, Russia.
Philos Trans A Math Phys Eng Sci. 2022 Nov 14;380(2236):20210360. doi: 10.1098/rsta.2021.0360. Epub 2022 Sep 26.
The article concerns a junction problem for two-dimensional elastic body with a thin elastic inclusion and a volume rigid inclusion. It is assumed that the inclusions have a common point. A delamination of the thin inclusion from the surrounding elastic body is assumed thus forming an interfacial crack. Constraint-type boundary conditions are imposed at the crack faces to prevent interpenetration between the faces. Moreover, a connection between the crack faces is characterized by a positive damage parameter. Limit transitions are justified as the damage parameter tends to infinity and to zero. In addition to this, a transition to limit is analysed as a rigidity parameter of the thin inclusion tends to infinity. Limit models are investigated. In particular, junction conditions at the common point are found for all cases considered. This article is part of the theme issue 'Non-smooth variational problems and applications'.
本文研究了二维弹性体中带有薄弹性夹杂和体刚性夹杂的连接问题。假设夹杂有一个公共点。薄夹杂从周围弹性体中分层，形成界面裂纹。在裂纹面上施加约束型边界条件，以防止面之间的贯穿。此外，通过一个正的损伤参数来描述裂纹面之间的连接。当损伤参数趋于无穷大或零，极限过渡得到证明。此外，当薄夹杂的刚性参数趋于无穷大时，也对极限过渡进行了分析。研究了极限模型。特别地，对所有考虑的情况，找到了公共点的连接条件。本文是“非光滑变分问题及其应用”主题的一部分。
