Jihed Zghal

Predicting the maximum load that a (quasi-)brittle specimen can sustain, along with determining the correct crack path, is a crucial scientific and practical challenge. A natural approach to address this problem is to identify appropriate criteria. Strength and toughness criteria are well-suited for simple specimens with either no defects or an existing crack. However, when defects are present, the criteria become more complex and require more sophisticated approaches. Over the last few decades, numerous models have demonstrated their ability to predict both critical loads and crack paths effectively. Some of these models include the Thick Level Set (TLS) models (Moës et al., 2011; Zghal et al., 2018), Phase Field damage models (Miehe et al., 2010; Wu, 2017), Peridynamics (Diehl et al., 2022; Jafarzadeh et al., 2024), and more recently, the Lip Field damage model (Chevaugeon & Moës, 2022; Moës et al., 2022) ...

Phase Field damage model has been widely adopted over the past few decades, and it primarily builds on the foundational work of Ambrosio and Tortorelli (Ambrosio & Tortorelli, 1990). The excitement for this method within the mechanics community surged following the publication of Miehe’s influential work (Miehe et al., 2010). More recently, Wu proposed a unified formulation of the Phase Field model (Wu, 2017), enabling the treatment of different Phase Field versions, such as PF-AT1, PF-AT2, and PF-CZM ... This lecture will present a critical analysis of the Phase Field damage model. The first part will be dedicated to the PFDam tool, developed in the LEME laboratory on the FEniCS open-source computing platform. Then, various Phase Field damage models and resolution strategies will be compared within a quasi-static framework. In the final part, some preliminary results will be discussed from the extension of the PFDam tool to dynamic scenarios.