Published Paper

Inserted: 5 mar 2025
Last Updated: 1 jul 2025

Journal: Mathematics in Engineering
Volume: 7
Number: 3
Pages: 406-438
Year: 2025
Doi: https://doi.org/10.3934/mine.2025017

Abstract:

A rigorous unified perspective of cohesive zone models is presented, including and comparing potential-based and non potential-based formulations, and encompassing known examples studied in literature. The main novelty of the work consists in the natural inclusion of loading and unloading effects in a general mixed-mode framework, incorporated through an intrinsic construction of energy densities or tensions. The proposed mathematical investigation identifies and proves the limitations of variational models with respect to non-variational ones, the latter yielding a feasible description of real instances in all relevant situations and regimes. This validates existing empirical and numerical observations. An application to a mechanical process of two elastic laminates sliding one on each other along their cohesive interface is finally analyzed, and existence results in both potential-based and non potential-based versions are obtained, extending previous contributions.

Keywords: Cohesive interface, potential-based model, non potential-based model, loading and unloading regimes

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