Shape and topology sensitivity analysis for cracks in elastic bodies on boundaries of rigid inclusions

Alexander Khludnev (1) , Andre Novotny (2) , Jan Sokolowski (3) , Antoni Zochowski (4)

1 Lavryentyev Institute of Hydrodynamics
2 LNCC / MCT - Laboratorio Nacional de Computação Cientifica [Rio de Janeiro]
3 IECN - Institut Élie Cartan de Nancy
4 IBS PAN - Systems Research Institute [Warsaw]

We consider a 3D elastic body with a rigid inclusion and a crack located at the boundary of the inclusion. It is assumed that non-penetration conditions are imposed at the crack faces which do not allow the opposite crack faces to penetrate each other. We analyze the variational formulation of the problem and provide shape and topology sensitivity analysis of the solution.

Mots clés: Rigid inclusion; crack growth; contact condition; shape sensitivity analysis; topological derivatives

Domaines: Equations aux dérivées partielles [math.AP]

Alexander Khludnev, Andre Novotny, Jan Sokolowski, Antoni Zochowski. Shape and topology sensitivity analysis for cracks in elastic bodies on boundaries of rigid inclusions. 2008. ⟨hal-00335565⟩