Elasticity Tensor Identification in Elastic Body with Thin Inclusions: Non-coercive Case

Alexander Khludnev () and Alexander Rodionov ()
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Alexander Khludnev: Lavrentyev Institute of Hydrodynamics of the RAS
Alexander Rodionov: Saint-Petersburg State Marine Technical University

Journal of Optimization Theory and Applications, 2023, vol. 197, issue 3, No 6, 993-1010

Abstract: Abstract In the paper, we analyze problems of elasticity tensor identification for an elastic body with incorporated thin elastic and rigid inclusions in a non-coercive case. The inclusions are assumed to be delaminated from the surrounding elastic body, thus forming interfacial cracks. We consider inequality-type boundary conditions at the crack faces with unknown set of a contact to provide a mutual non-penetration between the crack faces. The considered problems are characterized by unknown displacement field and elasticity tensor. A formulation of identification problems includes an additional information, which can be found from a measurement. A solution existence of these problems is proved.

Keywords: Elastic body; Thin inclusion; Crack; Variational inequality; Non-coercive boundary value problem; Inverse problem; 35J88; 49J40 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10957-023-02216-1

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