A phase field description for shear stress driven fracture: application to rocks and mining

  • Ramírez-Ganga, Javier (Universidad de Chile)
  • Estevez, Rafael (Université de Grenoble Alpes)
  • Bonnetier, Eric (Université de Grenoble Alpes)
  • Jofré, Alejandro (Universidad de Chile)
  • Ortega, Jaime (Universidad de Chile)
  • San Martín, Jorge (Universidad de Chile)

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Shear-driven fracture is a fundamental mechanism governing the deformation and failure of rocks, controlling processes such as fault initiation, shear banding, and the transition from intact rock to localized slip surfaces. Capturing these mechanisms numerically remains challenging due to strong mode II dominance, pressure-sensitive behavior, and the complex interaction between fracture and confinement. In this work, we present a phase-field formulation which allows to cover normal stress dominated to shear-driven fracture, with a single parameter. The approach is based on a variational framework in which a regularized fracture field is coupled to the elastic response of the solid. To model shear-dominated cracking while suppressing unphysical damage growth under compression, the fracture driving force is constructed from an energy decomposition to activate fracture primarily through shear and tensile components. By incorporating a modification in the Euler-Lagrange equations, inspired from Bonnetier et al. \cite{Paper1}, we tuned mode I dominated to shear dominated fracture while preventing damage under compression. This follows pioneering work and ideas proposed by Lancioni and Royer-Carfagni \cite{Paper2}, Miehe et al. \cite{Paper3}, review by Ambati et al. \cite{Paper4} and more recently Kumar et al. \cite{Paper5} and Haghdat and Santill\'an \cite{Paper6}, among other references. The formulation is shown able to capture the orientation for damage localization. This is examplified in the case study of a plate with a hole, with examples in tension and compression to highlight the model abilities. The proposed formulation will be discussed, and its implementation in FEniCS \cite{Paper7} briefly outlines. Selected simple configurations illustrate the proposed formulations, which is in particular tailored to rock mechanics and mining applications.