Potential-based versus non potential-based cohesive models accounting for loading and unloading with application to sliding elastic laminates

A rigorous unified perspective of cohesive zone models is presented, including and comparing potential-based and non potential-based formulations, and encompassing many of the known examples studied in literature. The main novelty of the work consists in the natural inclusion of loading and unloading effects in a general mixed-mode framework, incorporated through an intrinsic construction of energy densities or tensions. The proposed mathematical investigation identifies and proves the limitations of variational models with respect to non-variational ones, the latter yielding a feasible description of real instances in all relevant situations and regimes. This validates existing empirical and numerical observations. An application to a mechanical process of two elastic laminates sliding one on each other along their cohesive interface is finally analyzed, and existence results in both potential-based and non potential-based versions are obtained, extending previous contributions.