Root rotations and root displacements in bimaterial layers and thin films

An elasticity technique to derive compliance coefficients describing crack tip root rotations and displacements in end-loaded, bimaterial, isotropic and orthotropic layers has been recently proposed in Ustinov and Massabò (Int. J. Solids Struct., 2022). The coefficients define the boundary conditions which account for the near tip deformations when using beam (plate) theories to describe the detached layers. The coefficients, collected into 6x6 compliance matrices, relate crack tip kinematic variables describing relative displacements and rotations between the detached and intact parts, and six elementary crack tip loadings, which combine to describe general end loadings. The steps necessary to use the coefficients in the solution of statically determined problems, when the forces acting on the layer are known through equilibrium, is presented here with reference to classical fracture mechanics specimens