Failure of nonlinear microstructured solids by cohesive and contact instabilities

The prediction of failure onset in finitely strained nonlinear composite materials with periodic microstructure is a fundamental problem in the framework of nonlinear solid mechanics. The static and dynamic properties of these composite materials, also known as metamaterials due to their multifunctional properties obtained by tailoring their microstructure, could be affected by different failure mechanisms that can arise at microscale and then influence the whole structural behaviour. Among them, fracture, decohesion, instability and compression-induced contact, are those to be paid most attention to. To this end, it therefore essential to provide numerical models that are able to describe the structural behaviour of such metamaterials, combining computational efficiency and reliability in the expected results. In order to characterize the failure behaviour of periodically reinforced hyperelastic metamaterials, we present an innovative nonlinear homogenization scheme to evaluate the effects of the interfacial debonding contact arising from the onset of macro and micro instabilities. An enhanced cohesive-contact formulation has been introduced, adopting a special interface constitutive law and an accurate contact formulation in a finite strain continuum mechanics framework. Concerning the numerical results, different formulations for the cohesive-contact interfaces have been analytically developed and then introduced in the homogenization scheme in order to investigate how the critical load levels related to the primary instabilities and bifurcations are affected by the chosen formulation for the representation of the finite strain behaviour of the imperfect interfaces.