Elastoplastic equilibrium of composite with a rigid linear inclusion (Q2754713)

A homogeneous isotropic solid (plate) contains a rigid rod-shaped inclusion and undergoes tension at infinity in the direction parallel to the inclusion. It is assumed that near the inclusion tips, plasticity zones are formed. They can be modelled by plastic strips along the interface. The authors use this model to represent plasticity zones by thin layers of ideally plastic material, and thus to reduce the problem to a mixed boundary value problem of elasticity for a body with a rigid inclusion and with transverse shear cracks along the interface around the inclusion tip. The elastic problem is solved by Kolosoff-Muskhelishvili technique. After elastic solution, the lengths of plastic strips are determined from the condition that stresses are finite near the crack tip.