Instability issues in microstructured solids embedding cohesive and contact interfaces

This work presents a theoretical study regarding the failure onset in finitely strained nonlinear composite materials characterized by a periodic microstructure. The microscopic instability mechanism is studied by means of an innovative nonlinear homogenization scheme, taking into account cohesive and contact effects at discontinuity interfaces. Numerical investigations are conducted on a periodic microstructure, whose behavior is described via a hyperelastic constitutive law for a Neo-Hookean solid. Within the context of finite strain continuum mechanics, the theoretical framework is developed by incorporating a continuum contact mechanics model, coupled with a class of irreversible cohesive traction-separation laws, accounting for unilateral contact and decohesion at discontinuity interfaces. The governing equations of the equilibrium problem are derived, both in finite and incremental forms. Different formulations are employed for the cohesive/contact interfaces, in order to evaluate the critical load factors when either single or double edges debonding are triggered at the imperfect interfaces due to the applied loading conditions.