Asymptotic justification of the models of thin inclusions in an elastic body in the antiplane shear problem

E. M. Rudoy ; H. Itou ; N. P. Lazarev

Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 1, pp. 103-119.

Résumé

The equilibrium problem for an elastic body having an inhomogeneous inclusion with curvilinear boundaries is considered within the framework of antiplane shear. We assume that there is a power-law dependence of the shear modulus of the inclusion on a small parameter characterizing its width. We justify passage to the limit as the parameter vanishes and construct an asymptotic model of an elastic body containing a thin inclusion. We also show that, depending on the exponent of the parameter, there are the five types of thin inclusions: crack, rigid inclusion, ideal contact, elastic inclusion, and a crack with adhesive interaction of the faces. The strong convergence is established of the family of solutions of the original problem to the solution of the limiting one.

Détail

Keywords: asymptotic analysis, antiplane shear, inhomogeneous elastic body, thin rigid inclusion, thin elastic inclusion, crack. .

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