Small perturbations of an interface for elastostatic problems

Jihene Lagha (1) , Faouzi Triki (2) , Habib Zribi (3)

1 FST - Faculté des Sciences Mathématiques, Physiques et Naturelles de Tunis
2 EDP - Equations aux Dérivées Partielles
3 Department of Mathematics, College of Sciences, Saudi Arabia

We consider the Lamé system for an elastic medium consisting of an inclusion embedded in a homogeneous background medium. Based on the field expansion method (FE) and layer potential techniques, we rigorously derived the asymptotic expansion of the perturbed displacement field due to small perturbations in the interface of the inclusion. We extend these techniques to determine a relationship between traction-displacement measurements and the shape of the object and derive an asymptotic expansion for the perturbation in the elastic moments tensors (EMTs) due to the presence of small changes in the interface of the inclusion.

Mots clés: elastic moment tensors; boundary integral method; Small perturbations; interface problem; Lamé system; asymptotic expansions

Domaines: Equations aux dérivées partielles [math.AP]

Jihene Lagha, Faouzi Triki, Habib Zribi. Small perturbations of an interface for elastostatic problems. Mathematical Methods in the Applied Sciences, 2017, 40 (10), pp.3608-3636 ⟨10.1002/mma.4249⟩. ⟨hal-01462842⟩