Phase-field fracture 2.0: "New formulation!", "Extra strength!"

Blaise Bourdin (McMaster)

Monday, November 10, 11:30 (HH312)

Crack propagation in brittle materials can be described in terms of trade-off between a bulk and surface energies, characterized by a material's fracture toughness (Griffith, 1921; Francfort and Marigo, 1998). Crack nucleation, however, is a much more complex process involving fracture toughness, material strength, i.e. the range of stresses a material can sustain while deforming elastically, and complex scale effects. 

Phase-field models of fracture (Bourdin et al., 2000; Bourdin et al., 2008) have become ubiquitous due to their ability to account for complex fracture patterns in a wide range of materials and multi-physics settings. When seen as gradient damage models (Pham et al., 2011; Marigo et al., 2016), they properly account for tensile crack nucleation only (Tanné et al., 2018; Kumar et al., 2020). 

A case can be made that crack nucleation cannot be accounted for in variational models based on Griffith-like surface energy and it has been suggested that one needs to renounce to the variational nature of the models (Lopez-Pamies et al., 2025). Instead, I will propose a new approach using a cohesive energy depending on the crack opening. Unlike existing models, this approach is capable of handling arbitrary strength surfaces and cohesive energies, and behaves in a Griffith-like manner for "large" crack openings.

In this talk, I will present the proposed model and its properties, including a postulated "sharp interface" limit, its properties, and its numerical implementation.

This is a joint work with J.-J. Marigo (Institut Polytechnique de Paris, France), C. Maurini (Sorbonne Université, France), and C. Zolesi (Institut Polytechnique de Paris, France).