Potential-based versus non potential-based cohesive models accounting for loading and unloading with application to sliding elastic laminates

Francesco Freddi; Filippo Riva; Francesco Freddi; Filippo Riva

doi:10.3934/mine.2025017

Mathematics in Engineering

2025, Volume 7, Issue 3: 406-438. doi: 10.3934/mine.2025017

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Research article

Potential-based versus non potential-based cohesive models accounting for loading and unloading with application to sliding elastic laminates

Francesco Freddi ¹,
Filippo Riva ^{2
,
,}

1.
Università degli Studi di Parma, Dipartimento di Ingegneria e Architettura, Parco Area delle Scienze, 181/A, 43124, Parma, Italy
2.
Università Commerciale Luigi Bocconi, Dipartimento di Scienze delle Decisioni, via Roentgen 1, 20136 Milano, Italy

Received: 17 March 2025 Revised: 19 June 2025 Accepted: 20 June 2025 Published: 26 June 2025

A rigorous unified perspective of cohesive zone models is presented, including and comparing potential-based and non potential-based formulations, and encompassing many of the 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.
- cohesive interface,
- potential-based model,
- non potential-based model,
- loading and unloading regimes
Citation: Francesco Freddi, Filippo Riva. Potential-based versus non potential-based cohesive models accounting for loading and unloading with application to sliding elastic laminates[J]. Mathematics in Engineering, 2025, 7(3): 406-438. doi: 10.3934/mine.2025017

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Abstract

A rigorous unified perspective of cohesive zone models is presented, including and comparing potential-based and non potential-based formulations, and encompassing many of the 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.

References

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