CD-MPM: continuum damage material point methods for dynamic fracture animation

We present two new approaches for animating dynamic fracture involving large elastoplastic deformation. In contrast to traditional mesh-based techniques, where sharp discontinuity is introduced to split the continuum at crack surfaces, our methods are based on Continuum Damage Mechanics (CDM) with a variational energy-based formulation for crack evolution. Our first approach formulates the resulting dynamic material damage evolution with a Ginzburg-Landau type phase-field equation and discretizes it with the Material Point Method (MPM), resulting in a coupled momentum/damage solver rooted in phase field fracture: PFF-MPM. Although our PFF-MPM approach achieves convincing fracture with or without plasticity, we also introduce a return mapping algorithm that can be analytically solved for a wide range of general non-associated plasticity models, achieving more than two times speedup over traditional iterative approaches. To demonstrate the efficacy of the algorithm, we also develop a Non-Associated Cam-Clay (NACC) plasticity model with a novel fracture-friendly hardening scheme. Our NACC plasticity paired with traditional MPM composes a second approach to dynamic fracture, as it produces a breadth of organic, brittle material fracture effects on its own. Though NACC and PFF can be combined, we focus on exploring their material effects separately. Both methods can be easily integrated into any existing MPM solver, enabling the simulation of various fracturing materials with extremely high visual fidelity while requiring little additional computational overhead.