Abstract
Inspired by bio-medical applications, a new mathematical model of the equilibrium of a heterogeneous Timoshenko plate with two thin rigid inclusions connected by a hinge joint is studied. It is assumed that one inclusion is not delaminated from the plate’s elastic matrix, while the second inclusion is delaminated on both sides, thus generating two cracks. Nonlinear conditions of the non-penetration type are imposed on the delaminated cracks. The existence of a variational solution to the delamination problem is established based on the Weierstrass theorem. Optimality conditions characterizing the solution in the domain, as well as on the curves describing the cracks and the inclusion, are derived in the form of a primal-dual system. For its solution, a semi-smooth Newton algorithm is provided rigorously and tested numerically.