A new framework for the formulation and validation of cohesive mixed-mode delamination models

A new framework for the formulation and validation of interface cohesive models for mixed mode I- mode II delamination with variable mode-ratio is presented. The approach is based on a free energy decomposition driven by the identification of three main damage modes in the tensile plane of normal and shear tractions and leads to models thermodynamically consistent for any loading path. A model with a bilinear traction-separation law is developed in detail within the proposed framework. The con- sidered model requires a limited number of easily identifiable parameters: the traction-separation laws in the pure modes with their fracture energies, plus two phenomenological parameters, responsible for the mixed-mode interaction between the mode I and mode II failure modes, that directly affect the shape of the damage activation locus, namely an exponent and a constitutive parameter, the latter geometrically defined as an internal angle. The overall fracture energy at any mode-ratio is an outcome of the model, without the need to introduce any empirical laws, and depends on the actually followed loading path. A rigorous validation protocol, including consistency, accuracy and evolutionary tests is proposed and used for the model validation. Several tests proposed in the literature, along different proportional and non- proportional loading paths, with application to the simulation of pure and mixed-mode tests for a variety of composite materials, are considered obtaining in all cases, consistent and accurate results.