Simulating fracture in brittle objects and thin shell objects for visual effects

Abstract

This doctoral thesis presents a series of studies focused on simulating fractures within various objects. In the context of fracture simulation, it is crucial to address collision detection and contact handling, including self-contact, particularly when employing mesh-based methods. However, these methods necessitate the discretization of the domain using volumetric meshes, as opposed to surface meshes commonly used in computer graphics applications. For the sake of simplicity and efficiency, material point method (MPM) is employed for more straightforward discretization. MPM also facilitates automatic contact due to its hybrid Lagrangian/Eulerian representation. Nevertheless, the continuum assumption of MPM prevents the representation of cracks as discontinuities. Additionally, the intricate behaviors of real-world fractures, such as dynamic bifurcation and merging, require sophisticated explicit geometry processing methods.

To address these challenges, a novel approach is proposed to implicitly simulate arbitrary non-manifold cracks by monitoring the evolution of a scalar phase field. The simulation encompasses two categories of commonly encountered objects: brittle objects and codimensional thin shell objects.

For brittle objects, a combination of elastodynamic continuum mechanical models and rigid-body methods is utilized. The global dynamic motion of fragments is captured through a rigid-body solver. The impacts computed by this solver, including contact forces and durations, are then integrated into the MPM framework to update the phase field. This approach enables the extraction of a non-manifold crack surface from the phase field, facilitating accurate and robust modeling of material fragment volumes to enhance fast and rigid shatter effects. To faithfully replicate the natural patterns of brittle fracture surfaces, fracture details are introduced, incorporating particle damage-time to guide localized perturbations of the crack surface with artistic control.

Regarding thin shell objects, a hybrid Lagrangian/Eulerian continuum shell formulation is introduced to facilitate arbitrary fracturing. The geometry of thin shell objects is described using Non-Uniform Rational Basis-Spline (NURBS) surfaces. The kinematics is simplified using a Kirchhoff-Love shell model, followed by compression and shearing in the normal direction. A coherent crack surface is extracted from the evolving phase field within the co-dimensional manifold. To capture the pronounced discon tinuities of interpolated field quantities near the crack, a moving least squares (MLS) approximation is applied. To address complex surface geometries, a novel NURBS patch coupling method is presented, ensuring arbitrary order continuity across the interface.

In summary, the dissertation addresses the intricate challenges of fracture simulation. It thoroughly investigates brittle object fracture and thin-shell object fracture to achieve generality. The study proposes several innovative approaches to tackle the issues encountered during the simulation process.