A partially debonded circular elastic inhomogeneity with an incompressible liquid inclusion occupying the debonded section

We study the plane strain problem associated with a circular isotropic elastic inhomogeneity partially debonded from an infinite isotropic elastic matrix subjected to uniform remote in-plane stresses. The debonded portion of the circular interface is occupied by an incompressible liquid inclusion. A closed-form solution to the problem is derived by solving a Riemann-Hilbert problem with discontinuous coefficients and by imposing the incompressibility condition of the liquid inclusion. An elementary explicit expression for the internal uniform hydrostatic tension within the liquid inclusion is obtained. A hydrostatic far-field load will not induce any singular stress field and the entire circular interface remains perfect.

Automated summary

This paper studies the debonding problem between a circular isotropic elastic inhomogeneity and an elastic matrix, where the debonded portion is filled with an incompressible liquid. A closed-form solution is derived by solving a Riemann-Hilbert problem and imposing the incompressibility condition. An explicit expression for the internal stress within the liquid is obtained.