Stability of solids with interfaces

Stability, in the sense of limits to the uniqueness of solutions to quasi-static boundary value problems, is investigated for two semi-infinite solids bonded along a planar interface. The interface is characterized by a traction-displacement jump relation, so that dimensional considerations introduce a characteristic length. Stability is addressed in terms of the existence of certain stationary waves. Complex variable methods are exploited to obtain an explicit solution when the interface instability precedes bulk localization. Particular cases are analyzed that illustrate a range of behaviors. Under certain conditions, a minimum wavelength for the instability mode is predicted that is at least one to two orders of magnitude larger than the interface constitutive characteristic length. A post-bifurcation analysis, carried out for linear elastic material behavior, shows how the instability plays a role in the transition from a uniform mode of separation to crack-like behavior. The results obtained suggest a mechanism for the size dependence of the failure mode.