Asymptotic modeling of curvilinear narrow inclusions with rough boundaries in elastic bodies: case of a soft inclusion

Abstract

Within the framework of two-dimensional elasticity theory,
a heterogeneous body with a narrow inclusion lying strictly inside the
body is considered. It is assumed that the elastic properties of inclusion
and its width depend on the small parameter > 0. Moreover, we assume
that the inclusion has a curvilinear rough boundary. We show that there
exist three type of limiting problem as ! 0: p > 1 body with crack
without interaction of its faces; p = 1 body with crack with adhesive
interaction of its faces; p 2 [0; 1) homogeneous body (no crack).