Axisymmetric response of a bi-material full-space reinforced by an interfacial thin film

Analytical treatment of a linear elastic isotropic bi-material full-space reinforced by an interfacial thin film under axisymmetric normal loading is addressed. The thin film is modeled as an extensible membrane perfectly bonded to the half-spaces. By virtue of Love’s potential function and Hankel integral transform, elastic fields of the system are explicitly written in the form of semi-infinite line integrals. The analytical results are verified by the special cases corresponding to the surface stiffened half-space and classical bi-material problem. The limiting cases of reinforced homogeneous full-space and inextensible membrane are presented and discussed. The proposed formulation is also applicable for studying reinforced auxetic materials with negative Poisson’s ratio. The surface/interface effect on the elastic responses of two perfectly bonded half-spaces is also simulated by assigning equivalent surface elastic constant to the membrane stiffness. Effects of thin film stiffness, material properties, loading depth, and surface/interface effect are studied by some numerical examples.