|This paper presents a thorough analysis of potential-based and non-potential-based cohesive zone models (CZMs) under conditions of mixed-mode separation and mixed-mode over-closure. Problems are identified with the well established potential-based Xu–Needleman (XN) model and a number of new potential-based and non-potential-based models are proposed. It is demonstrated that incorrect weighting of the coupling terms in non-potential models can lead to the existence of a singularity under traction controlled conditions. It is also demonstrated that the potential-based models fail to capture a gradual change from mode II to mode I work of separation, as reported experimentally for traction controlled interface separation.
In a follow-on Part II companion paper a number of case studies are simulated, demonstrating that the theoretical findings of the present paper have significant implications for the finite element prediction of interface debonding.