Abstract: The paper is concerned with an equilibrium problem for 2D elastic body with a thin elastic Timoshenko inclusion and a thin rigid inclusion. The elastic inclusion is assumed to be delaminated from the elastic body thus forming an interfacial crack with the matrix. Inequality type boundary conditions are imposed at the crack faces to prevent a mutual penetration. A connection between two inclusions at a given point is characterized by a positive damage parameter. Existence of solutions of the problem considered is proved, and different equivalent formulations of the problem are analyzed; junction conditions at the connection point are found. A convergence of solutions as the damage parameter tends to zero and to infinity as well as the rigidity parameter of the elastic inclusion tends to infinity is analyzed. An analysis of the limit models is performed. A solution existence of an inverse problem for finding the damage and rigidity parameters is proved provided that an additional information concerning the derivative of the energy functional with respect to the delamination length is given.

Cite: Khludnev A.M. , Popova T.S.
On junction problem with damage parameter for Timoshenko and rigid inclusions inside elastic body
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik. 2020. V.100. N8. 202000063 . DOI: 10.1002/zamm.202000063 WOS Scopus OpenAlex

Identifiers:

Web of science:	WOS:000537941600001
Scopus:	2-s2.0-85085942137
OpenAlex:	W3033404218

Citing:

DB	Citing
Scopus	13
OpenAlex	9
Web of science	7

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