Coupled total- and semi-Lagrangian peridynamics for modelling fluid-driven fracturing in solids

This paper presents a novel computational approach for modelling fluid-driven fracturing in quasi-brittle solids using peridynamics. The approach leverages a rigorous coupling of the total -and semi-Lagrangian formulations of peridynamics. Specifically, the total-Lagrangian formulation, whch is based on classical peridynamics theory used for modelling fractures in solids, is combined with the semi-Lagrangian formulation to solve the Navier-Stokes equation using a non-local differential operator for weakly compressible fluid flow. The proposed approach offers a unified peridynamics-based framework that enables simulations of a wide range of fluid-driven fracturing problems in solids. The framework can model the solid as either an ordinary or non-ordinary material and quantify the fluid with different equations of state. To prevent unphys-ical inter-penetration, a fluid-solid interaction scheme that assumes fictitious fluid points in the solid domain is proposed to quantify the forces at the fluid-solid interface. The proposed computational approach is validated through simulations of several classic problems, including the dam break and the Kristianovich-Geertsma-de Klerk (KGD) problem. The predictive capability of the proposed approach is further demonstrated by numerical examples of fractures induced by fluid injection in sandstone, which reasonably capture the fracture patterns compared to experimental results. The presented approach offers an alternative to explicit modelling of fluid-driven fracturing processes and may find wide and useful applications to a variety of industrial and geophysical processes.