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On the problem of a thin rigid inclusion embedded in a Maxwell material

On the problem of a thin rigid inclusion embedded in a Maxwell material Thumbnail


Abstract

We consider a plane viscoelastic body, composed of Maxwell material, with a crack and a thin rigid inclusion. The statement of the problem includes boundary conditions in the form of inequalities, together with an integral condition describing the equilibrium conditions of the inclusion. An equivalent variational statement is provided and used to prove the uniqueness of the problem’s solution. The analysis is carried out in respect of perfect and non-perfect bonding of the rigid inclusion. Additional smoothness properties of the solutions, namely the existence of the time derivative, are also established.

Acceptance Date Jun 15, 2016
Publication Date Aug 4, 2016
Publicly Available Date Mar 28, 2024
Journal Zeitschrift fur angewandte Mathematik und Physik
Print ISSN 0044-2275
Publisher Springer Verlag
DOI https://doi.org/10.1007/s00033-016-0700-9
Keywords viscoelasticity, crack, rigid inclusion, variational inequality, inequality-type boundary conditions,
non-penetration condition
Publisher URL http://link.springer.com/article/10.1007/s00033-016-0700-9

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