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

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 $\delta>0$. Moreover, we assume that the inclusion has a curvilinear rough boundary. We show that there exist three type of limiting problem as $\delta\to0$: $p>1$ – body with crack without interaction of its faces; $p=1$ – body with crack with adhesive interaction of its faces; $p\in[0,1)$ – homogeneous body (no crack).