Revisiting the hydromechanical formulation of a micromechanics-based phase-field model for poro-elastoplastic media

Abstract

Even for tension-dominated fracture propagation, porous materials may deform plastically adjacent to the propagating fracture. As is common for porous materials, existing phase-field models typically employ a non-associative flow rule for plasticity, and a Helmholtz free energy based on strain and fluid pressure. This work revisits the hydromechanically coupled formulation of the phase-field model for fracture in poro-elastoplastic media by analyzing the strength surface and fracture driving force. Our analyses show that these common choices of flow rule and free energy will lead to a discontinuous strength surface across the tension-compression transition. A non-associative flow rule introduces a jump at the strength surface, while treating fluid pressure-rather than fluid content-as the independent variable in the Helmholtz free energy omits a coupling term from the phase-field driving force, also breaking continuity. Incorporating an associative Drucker-Prager flow rule and this omitted coupling term ensures a continuous strength surface and the accurate fracture driving force. The proposed model exhibits improved accuracy in hydromechanical responses when compared against the analytical solution of the Kristianovich-Geertsma-de Klerk hydraulic fracturing benchmark. Numerical simulations of hydraulic fracturing and biaxial compression in poro-elastoplastic media show that the model can reproduce both shear-dominated fractures induced by mechanical disturbance and tension-dominated fractures driven by fluid injection in saturated porous media.