On junction problem with damage parameter for Timoshenko and rigid inclusions inside elastic body

A. M. Khludnev, T. S. Popova

Результат исследования: Научные публикации в периодических изданияхстатья

Аннотация

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.

Язык оригиналаанглийский
Номер статьиe202000063
Число страниц17
ЖурналZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
Том100
Номер выпуска8
Ранняя дата в режиме онлайн5 июн 2020
DOI
СостояниеОпубликовано - 1 авг 2020

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