A comparison of numerical stability for ESPH and TLSPH for dynamic brittle fracture

Dynamic brittle fracture is a numerically challenging problem that involves crack nucleation, formation, propagation, and material fragmentation. In this work, we use two forms of Smoothed Particle Hydrodynamics (SPH), namely Eulerian SPH (ESPH) and Total Lagrangian SPH (TLSPH) augmented with the pseudo-spring or virtual-link analogy for seamless modelling of crack formation, subsequent propagation, and material fragmentation. Being particle-based in nature, SPH is naturally capable of capturing finite deformation in materials, and the pseudo-spring or virtual-link analogies provide modelling of multiple discrete cracks without any additional condition, such as visibility criteria. We simulate the crack branching and propagation in a brittle polymeric material subjected to biaxial tensile loading with a pre-existing central notch. The numerical results using ESPH and TLSPH agree with the previously published experimental and numerical results. We have also simulated the dynamic fragmentation of a cylinder and compared the results. This work shows the capability of both ESPH and TLSPH frameworks to model dynamic brittle fracture especially crack branching and curving. It is also observed that the ESPH and TLSPH frameworks present similar results for minor material deformation problems. However, the ESPH framework shows better stability and capability for finite material deformation problems.