A variational minimization formulation for hydraulically induced fracturing in elastic-plastic solids

A variational modeling framework for hydraulically induced fracturing of elastic-plastic solids is developed in the present work. The developed variational structure provides a global minimization problem. While fracture propagation is modeled by means of a phase-field approach to fracture, plastic effects are taken into account by using a Drucker-Prager-type yield-criterion function. This yield-criterion function governs the plastic evolution of the fluid-solid mixture. Fluid storage and transport are described by a Darcy-Biot-type formulation. Thereby the fluid storage is decomposed into a contribution due to the elastic deformations and one due to the plastic deformations. Alocal return mapping scheme is used for the update of the plastic quantities. The global minimization structure demands a H(div)-conforming finite-element formulation. Furthermore this is combined with an enhanced-assumed-strain formulation in order to overcome locking phenomena arising from the plastic deformations. The robustness and capabilities of the presented framework will be shown in a sequence of numerical examples.