Animation of crack propagation by means of an extended multi-body solver for the material point method

Highlights

• New N-body collision algorithm for the material point method framework.

• Dynamic crack propagation algorithm using multi-body solver and particle constraints.

• Example contact and tearing scenarios are provided as results.

Abstract

We propose a multi-body solver that extends the Material Point Method (MPM) to simulate cracks in computer animation. We define cracks as the intersection between pieces of bodies created by a pre-fracture process and held together by massless particle constraints (glue particles). These pieces are simulated using a MPM multi-body solver extended by us to efficiently handle N-body collisions. Benefits of the present work include (1) low computational overhead compared to a normal MPM algorithm; (2) good scaling in three dimensions due to our use of sparse grids for background computations; (3) allowing for an easy and controllable setup phase to simulate a desired material failure mode, which is especially useful for computer animation.

Introduction

Some of the most interesting natural phenomena involve material fracture, and it is a vital ingredient in simulations where realism is desired. Hence, algorithms for object breakage using various simulation techniques are a topic of high level of interest, both for engineering applications and for computer graphics and animation. Specifically for simulations using the material point method (MPM) by [1], simulation of fracture via crack propagation appear to have been mostly discussed in the engineering literature with a focus on numerical accuracy. The aim of these works is different from what is needed for animation applications, where simulation speed and art directability are prioritized. In the present paper we present an algorithm for fracture that provides attractive features for use in computer graphics while only adding a small overhead over regular MPM simulation.

The MPM method is increasingly relevant for simulations of materials due to improvements in hardware and algorithms. It has proven useful in simulations involving large deformations, where the approach of combining meshless particles with a fixed computational background grid provides a robust framework. Both viscoelastic and viscoplastic materials have been simulated with impressive results. The MPM has also been used for other materials like rubber and sponges, which can undergo large elastic deformations. Inherent to the method is that these materials will break naturally if the stress is too high at any particular location. Normally, a simulated material is homogeneous and isotropic. This is often not the case for their real-world counterpart, as small weaknesses and local inconsistencies are important features for how a crack propagates through a medium. Such irregularities could be introduced in the simulation by modifying the parameters that govern the constitutive model on a per-particle basis or by jittering the particles in their initial configuration, but doing so in a way that both conserves the original collective behavior of the material while achieving the desired break point is difficult.

In the present work, we extend MPM by defining a crack via pre-fracturing of a specimen into different bodies, which are bound together by particle constraints scattered on the crack surface. We call these particles glue particles, and their role is to hold the object fragments connected until they break and a crack is formed. The focus of this paper is on simulation of bodies with a single crack, and where the crack propagation is dominated by an opening mode. The pieces from a fractured body are allowed to interact freely in the simulation, and we also present an extension to the contact algorithm by [2] to allow for arbitrarily many colliding bodies in the same solver.

The rest of the paper is organized as follows. A review of related works is discussed in 2. In Section 3 we present the extended contact algorithm, which is utilized for the crack algorithm in Section 4. Simulations based on the two algorithms will be shown in Section 5, followed by a discussion in Section 6 that points out current artefacts and limitations. Final conclusions then follow in Section 7.