The Thick Level Set (TLS) damage model for an adequate transition to fracture

The TLS model was designed to allow for a smooth transition to fracture. It belongs to the family of the non-local damage models and thus introduces a length. The twist in the TLS is that it incorporates geometrical aspects: the shape of the localization zone is located by a level set.
So far, most of the efforts have been concentrated to quasi-brittle fracture. After restating the motivations for the new model, we review the results obtained in these past 5 years. Among other topics the following issues will be addressed:

• Predictive capabilities for crack onsets at notches.
• Capability of the model to reproduce properly size effects
• Theoretical issues regarding boundary conditions (with practical consequences!)
• Capability of the model to take into account concurrent local and non-local developments of damage.
• Comparison with other non-local damage models
• Relationships with the cohesive zone model
• Possibilities offered by the TLS for ductile failure
A set of open issues will also be discussed.

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References
Moës, N., Stolz, C., Bernard, P.-E., & Chevaugeon, N. (2011). A level set based model for damage growth : the thick level set approach. International Journal For Numerical Methods in Engineering, 86, 358–380.
Parrilla Gómez, A., Moës, N., & Stolz, C. (2015). Comparison between thick level set (TLS) and cohesive zone models. Advanced Modeling and Simulation in Engineering Sciences, 2(1), 18. doi:10.1186/s40323-015-0041-9
Moës, N., Stolz, C., & Chevaugeon, N. (2014). Coupling local and non-local damage evolution with The Thick Level Set model. Advanced Modelling and Simulation in Engineering Sciences, 2(16), 21.
Cazes, F., & Moës, N. (2015). Comparison of a Phase-Field model and of a Thick Level Set model for brittle and quasi-brittle fracture. International Journal for Numerical Methods in Engineering, 103, 114–143. doi:10.1002/nme