Potential-based and non-potential-based cohesive zone formulations under mixed-mode separation and over-closure. Part I: Theoretical analysis

摘要: Abstract This paper presents a thorough analysis of potential-based and non-potential-based cohesive zone models (CZMs) under conditions mixed-mode separation over-closure. Problems are identified with the well established Xu–Needleman (XN) model number new proposed. It is demonstrated that derivation traction–separation relationships from potential function can result in non-physical repulsive normal tractions instantaneous negative incremental energy dissipation displacement controlled monotonic when work tangential exceeds separation. A modified (MP) proposed so which occur be controlled. The MP also provides an additional benefit correct penalisation over-closure, contrast to XN model. In order fully eliminate problem CZM (NP1) shown provide physically realistic behaviour Noting form equations differ for mode I II XN, NP1 models, (NP2) near mode-independent achieved separation, while correctly penalising Following NP2 model, coupling based on magnitude considered (SMC model). final part performance each traction investigated by numerically inverting equations. Separation paths reveal strong bias toward exhibits towards Interestingly, high degree sensitivity conditions, its independence conditions. incorrect weighting terms non-potential lead existence singularity Finally, it fail capture gradual change as reported experimentally interface follow-on Part companion case studies simulated, demonstrating theoretical findings present have significant implications finite element prediction debonding.