Modelling damage propagation and coupling of fluid flow and elasto-damage using smoothed particle hydrodynamics (SPH) method

In this paper, three simple test cases are presented to demonstrate the ability of the smoothed particle hydrodynamics (SPH) method to handle damage initiation and propagation in elastic solids, both with and without coupling to the fluid flow. In contrast to other approaches based on non-local damage models in the context of finite elements, SPH retains the local formulation of the damage model, while the non-local regularisation is achieved numerically by weighted interpolations. All governing equations for both fluid flow and solid mechanics with infinitesimal strain are discretised in the same SPH framework, together with a thermodynamics-based damage model with unilateral effects. This implementation is tested on a pre-cracked domain that is dynamically loaded in tension, leading to crack bifurcations or multiple bifurcations. It is shown that the number of secondary branches depends on the characteristic length h of the SPH method. For the case of a penny-shaped crack in a purely elastic medium loaded with a pressurised fluid, it is shown that the crack opening profile calculated with SPH is very close to the analytical quasi-static solution. Finally, a simple case of hydrofracking is simulated, and it is found that the critical fluid pressure required to initiate damage propagation is within 10% of the classical Griffith criterion. This paper concludes that the SPH method can be reliably used to simulate more complex phenomena, such as drainage within realistic pore geometries of Callovo-Oxfordian clay.