This study investigates the challenge of unrealistic stress predictions that arise when associating cohesive interface energy with standard linear elasticity, building upon findings in [1]. We focus on anti-plane elasticity under mode III loading, leveraging the Linear Elastic Fracture Mechanics (LEFM) solution [2]. The traditional approach can lead to situations where predicted stress components exceed the fracture strength of the material.

To address this, we incorporate a relaxed bulk energy approach from [3]. This approach utilizes a quadratic law for small strains, transitioning to linear growth upon reaching a critical strain threshold specific to the material. This modification ensures a well-posed problem, paving the way for a viable solution.

We validate our approach through numerical simulations showcasing crack nucleation and propagation along a predefined path. The results show adherence to the stress yield condition, supporting the effectiveness of our methodology in overcoming the limitations of the traditional approach.

Reference

[1] Marigo, J.-J., ”Modelling of fracture by cohesive force models: A path to pursue”, European Journal of Mechanics - A/Solids, 102, 105088, (2023).
[2] Abdelmoula, R., Marigo, J.-J., Weller, T., ”Construction d'une loi de fatigue à partir d'un modèle de forces cohésives : cas d'une fissure en mode III”, Comptes Rendus Mécanique, 337, 53-59, (2009).
[3] Braides, A., Buttazzo, G., and Bouchitté, G., ”Relaxation results for some free discontinuity problems”, Journal für die reine und angewandte Mathematik, 458, 1-18, (1995).