Integrating Peridynamics to Material Point Method for Modelling Solids and Fracture Dynamics in High Velocity Impact.

Abstract

The desire for graphical methods to intuitively handle elastoplastic materials has grown hand in hand with the advances made in computer Graphics. Simulating physical materials with dynamic movements to photorealistic resolution is still one of the most crucial and challenging topics, especially involving fractures. Material Point Method (MPM) presents a strong approach for animating elastoplastic materials due to its natural support for arbitrarily large topological deformations and intrinsic collision handling. However, the partial derivative based MPM brings underlying instability issue of handling discontinuous particle distributions and requires computationally expensive treatments to separate broken pieces. The objective of this thesis is to pro- pose a novel MPM solver for robustly and intuitively animating scenarios containing fractures. We are inspired by Peridynamics (PD) which is oriented toward deformations with discontinuities. This study exploits the PD within the MPM scheme to mitigate the difficulties inherent in handling fractures. First, we propose an integral-based MPM by adopting a PD integral energy density function to the MPM weak form and following the standard MPM discretization scheme. Novel elastic, plastic, viscoelastic and fracture models encoding PD bond concepts are designed as constitutive models. The integral-based MPM out-weighs the differential-based MPM in both accuracy and stability. To efficiently model myriad fragments with a MPM solver (especially in high speed impact scenarios), our second contribution is to formulate a rigorous coupling governing equation which integrates the state-based PD within the MPM scheme (Superposition- based MPM) that features an automatic fractures modelling scheme. In SPB-MPM, PD evolves as a result of failure evolution in critical regions while the MPM derives entire problem domain. Giving a low-overhead PD computation to the MPM, this method allows for simulating a breadth of fracture effects, including ductile and brittle fractures. The prominent features at high strain rate in high velocity impact are unattainable through general constitutive models. Our third contribution is to introduce a shock wave effects model and a metallic plastic model which are designed to capture the intricate and characteristic impact behaviours. We simulate a number of representative impact scenarios, including organic fruits, metallic materials and multi-material deformable objects, demonstrating the efficacy of our models.