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Joshuah Wolper presented us two new approaches to animating dynamic fracture involving large elastoplastic deformation.
Joshuah Wolper presented us two new approaches to animating dynamic fracture involving large elastoplastic deformation. In contrast to traditional mesh-based techniques, the methods of his team are based on Continuum Damage Mechanics (CDM).
Intro
My name’s Joshuah Wolper and I’m a soon-to-be third-year Ph.D. student here at the University of Pennsylvania! I’m a PA native, I grew up in the Lehigh Valley and went on to do my undergrad at Swarthmore College for a B.S. in engineering and a B.A. in Computer Science. Now, at UPenn, I’m centering my studies on physical simulation techniques for elastoplastic effects with a focus on augmenting the material point method (MPM), which has been used recently both for scientific computing (avalanche study and prediction in Gaume et al. 2018) and production level animation (snow in Frozen). This is actually my first primary authored work, so I’m still at the beginning of developing a narrow research area, but fracture still has many questions to answer so that is quickly becoming the focus!
My co-authors are:
- Yu Fang — second year Ph.D. student and has his own paper in SIGGRAPH 2019
- Minchen Li — second year Ph.D. student and also has his own paper in SIGGRAPH 2019
- Jiecong Lu –digital media design sophomore and our awesome rendering guy
- Ming Gao — post-doc at Penn with Prof. Jiang
- Chenfanfu Jiang — our incredible advisor and mentor with 4 works at this SIGGRAPH
We are all living and working in Philadelphia. Only through this close group collaboration were we able to crank out the breadth of works we have at this year’s SIGGRAPH! It’s truly a humbling experience working with these guys, everyone has a specialty and their passion is so palpable in their work. We are a relatively nascent group here at Penn with Professor Jiang starting in fall 2017 (the same year I did) and Yu, Minchen, and Ming joining us this past fall! We aim to reinvigorate the CG research coming out of Penn with this group, and we are, I think, off to a great start!
CDM & FM Differences
In the engineering community, fracture approaches are typically grouped into two categories: fracture mechanics (FM) and continuum damage mechanics (CDM).
FM uses a discrete, geometric representation of cracks and as such is contingent on the underlying meshes; key considerations include determining where to physically fracture, determining closest nodes, splitting them, reskinning surfaces, etc. Many approaches to fracture use FM because it pairs very nicely with finite element methods, which are, again, very popular; newer techniques like XFEM solve many meshing issues and are the best of the best in FM techniques (within graphics).
In contrast, CDM focuses on representing a crack through a continuum representation of the material. This is a little abstract, but in the context of MPM, where the material is represented by thousands of particles, we can track a crack by adjusting a variable on each particle that is near the crack. This allows the rest of the physics to treat the crack as disconnected material, even though the crack is not geometrically there or “modeled.” This is best illustrated where a bunny is represented as a collection of particles, and each particle has a damage variable (in this case we call damage the “phase”: high damage is red, healthy material is blue) that varies based on the physics we are solving.
To give this some context, we had to develop a new constitutive model (used to compute elastic forces of the material) that allows us to feed these damage variables into the computation of the elastic forces. The cool result of this pairing is that if a particle is “damaged” it feels very little of the elastic forces from the particles around it, allowing it to separate from them despite not being distinctly modeled as a “crack.”
This idea of softening/weakening material points such that they can separate from the continuum body is the core of our two distinct approaches to fracture animation:
- a phase-field based MPM augmentation (PFF-MPM) that solves for a field of damage variables in a non-local manner
- and a new plasticity model (NACC) that allows for dynamic fracture through plastic projection alone (no “damage” involved).
Better Simulation: CDM or FM?
I would personally say that all of the additional complications of the CDM approach (continuum representation, damage variable fields, local and global damage solvers, etc.) are pretty equivalent to those of FM (mesh resolution and subsequent dependence, remeshing and crack representation, node splitting schemes, etc.). I actually find CDM easier to reason about because the geometry is amorphous by nature; it’s just a body of particles interacting like cells or atoms rather than a mesh with sharp discontinuities. Accuracy is tricky to talk about because it really depends:
- FM methods are only as accurate as the meshes are
- CDM methods typically get better accuracy with higher resolution discretizations.
Building Fracture
We have two distinct approaches to fracture in this work:
- a damage based phase field fracture material point method (PFF-MPM)
- and a new plasticity scheme called Non-Associated Cam Clay (NACC).
PFF-MPM is a coupled damage and momentum solver that performs all the usual computations of MPM but alternates (within one simulation step) between solving the damage of the material and solving the momentum of the material. This approach is the one that requires our new constitutive model and in turn, this allows cracks to form through weakening the elastic forces present on particles near cracks. Phase field fracture theory allows us to solve for the damage in a global manner (considering the whole material rather than local swathes of it), and then we use the damage variables to determine how weak or strong the surrounding elastic forces should be. When clumps of particles with high damage experience tension forces, they begin to separate, forming cracks! See the data flow in paper Fig. 13 to see the key differences between MPM and PFF-MPM highlighted.
Conversely, our second approach to fracture is purely a plasticity model. As such, it is effectively vanilla MPM with a new return mapping scheme and new plasticity model, adding very little computation time to MPM. NACC is a modification of an existing yield surface used recently for avalanche prediction (CCC in Gaume et al. 2018) and allows cracks to form simply through modeling the plasticity of the material. Plasticity modeling begins with a “yield surface,” which is a space of admissible stresses for a given particle or element. Plastic projection refers to computing the stress of a given particle, and then, if it is outside the yield surface, “returning” it to the surface in a physically realistic way. The magnitude and direction of this projection dictate how much the particle will harden/soften and how much energy is absorbed into plastic deformation rather than absorbed or emitted as elastic energy.
Each time we project a particle’s stress to the surface, we update the hardening parameter for that particle, and this hardening, in turn, changes the size and shape of the yield surface for that particle. Through tracking the hardening in this way, we allow cracks to form naturally wherever the material is weaker (softer) and to stay solid where it is hardened. In essence, it is very similar to our other technique because cracks form again through the weakening of the inter-particle elastic forces. Though NACC may seem simpler than PFF-MPM, it shouldn’t be discounted, as it’s arguably easier to tune parameters for and produced some of our favorite visual results!
Organic Material Fracture
The funny thing about physical simulation is that even once you have all this rigor and theory in place, getting the right material effects is an endeavor in itself; the final result comes down to choosing good starting geometry, tuning the parameters of your method, and then, of course, rendering it to look believable! For the organic material demos like the pumpkin and watermelon, we actually found that NACC was easier to tune to get this supple, yet firm effect that we wanted.
See paper Fig. 16 and Fig. 10 to see the breadth of material effects possible through just tuning the parameters themselves within NACC (Fig. 16) and PFF-MPM (Fig. 10)! As for PFF-MPM, we found it excelled more at ductile examples (fracture with plastic deformation at the interface) and struggled with brittle (sharp cracks) ones. Brittle fracture, in general, is actually quite difficult for methods like MPM, especially when paired with the “smeared” crack approach of CDM because it simply does not produce clean interfaces.
Advantages of CDM Approach
The main difference between the procedural approaches used by games and offline simulation approaches such as ours is that we value different things in the final result. Games have the difficult challenge of making fracture look as good as possible as fast as possible, often caring more for speed than visual fidelity. This means that games typically use geometric approaches to fracture (rather than physically based ones) including pre-baking the crack into the asset, tessellating the volume at runtime for simple fractures, etc. Conversely, we focus on physically based approaches and as such, we favor visual fidelity and accuracy over speed. For reference, one single frame of the bread demo takes 5.5 minutes to process, and that’s just the simulation (no rendering). The advantages of our approach include not only the very high visual fidelity but also the very high accuracy due to the underlying theory; notably, highly accurate models are often adopted and used even in the fields of scientific computing to model large-scale natural phenomena. Another key advantage of our methods over procedural ones is that an artist can tune the many parameters to get just the right effect for a shot, making it a strong tool for production level animation!
Bread Tearing Experiment
The bread really did turn out awesomely: we picked a great starting geometry of a bread slice and added 11.5 million particles inside the volume, so it is an extremely high-resolution sim! We used PFF-MPM for the bread because we wanted to control the beautifully intricate tear in the middle, and this was much more difficult to achieve with the parameters in NACC. This allowed us to also get a gorgeous phase-colored bread so you can distinctly see where the bread has high damage and see the cracks forming in real time when you play the video. The rendering was tricky, but Jacky had some great ideas for extruding a crust outwards from the bread and coloring it accordingly. I would say my personal favorite results were the organic ones, like the pumpkin and watermelon smashes, due to the intricate debris sprays that have so much impact to them; you can feel those smashes! We used NACC plasticity for both: we visualize the hardening parameter for the pumpkin in one of our demos which is really cool to watch, and the watermelon smash is actually a multi-material sim with a stiffer “rind” material and a more pliable inner “meat” material.
I think that the jello bar twist is also one of the most striking demos, due to the see-through rendering that allows you to see the fractures in even more detail and earlier on in the sim! That was another PFF-MPM demo that truly shows just how much detail we get at the fractured surfaces, especially compared with the traditional MPM bar twist (top of Fig. 4) which simply allows the bar to twist and twist, staying intact.
Conclusion & Plans
I would absolutely love to see our methods used both in film/VFX and in scientific computing! I’m so excited by the dual application of MPM approaches because they can be used either to create these beautiful natural effects in major motion pictures (Frozen and Moana recently) or to model large-scale natural phenomena like the aforementioned avalanche paper! There is still, of course, room for further study and improvement such as through better parameter interfaces for artists seeking specific effects. I’d really love to see this type of sim in interactive media like games, but of course, that’s very far away, if on the horizon at all. ?
Thanks so much for reading and to 80 Level for this interview! You can come see our work in detail this July at SIGGRAPH 2019!
You can also download and read the full research here. Please feel free to discuss your thoughts on this project.