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We propose In-Timestep Remeshing, a fully coupled, adaptive meshing algorithm for contacting elastodynamics where remeshing steps are tightly integrated, implicitly, within the timestep solve. Our algorithm refines and coarsens the domain automatically by measuring physical energy changes within each ongoing timestep solve. This provides consistent, degree-of-freedom-efficient, productive remeshing that, by construction, is physics-aware and so avoids the errors, over-refinements, artifacts, per-example hand-tuning, and instabilities commonly encountered when remeshing with timestepping methods. Our in-timestep computation then ensures that each simulation step's output is both a converged stable solution on the updated mesh and a temporally consistent trajectory with respect to the model and solution of the last timestep. At the same time, the output is guaranteed safe (intersection- and inversion-free) across all operations. We demonstrate applications across a wide range of extreme stress tests with challenging contacts, sharp geometries, extreme compressions, large timesteps, and wide material stiffness ranges - all scenarios well-appreciated to challenge existing remeshing methods. 

Simulating stiff materials in applications where deformations are either not significant or else can safely be ignored is a fundamental task across fields. Rigid body modeling has thus long remained a critical tool and is, by far, the most popular simulation strategy currently employed for modeling stiff solids. At the same time, rigid body methods continue to pose a number of well known challenges and trade-offs including intersections, instabilities, inaccuracies, and/or slow performances that grow with contact-problem complexity. In this paper we revisit the stiff body problem and present ABD, a simple and highly effective affine body dynamics framework, which significantly improves state-of-the-art for simulating stiff-body dynamics. We trace the challenges in rigid-body methods to the necessity of linearizing piecewise-rigid trajectories and subsequent constraints. ABD instead relaxes the unnecessary (and unrealistic) constraint that each body's motion be exactly rigid with a stiff orthogonality potential, while preserving the rigid body model's key feature of a small coordinate representation. In doing so ABD replaces piecewise linearization with piecewise linear trajectories. This, in turn, combines the best of both worlds: compact coordinates ensure small, sparse system solves, while piecewise-linear trajectories enable efficient and accurate constraint (contact and joint) evaluations. Beginning with this simple foundation, ABD preserves all guarantees of the underlying IPC model we build it upon, e.g., solution convergence, guaranteed non-intersection, and accurate frictional contact. Over a wide range and scale of simulation problems we demonstrate that ABD brings orders of magnitude performance gains (two- to three-orders on the CPU and an order more when utilizing the GPU, obtaining 10, 000× speedups) over prior IPC-based methods, while maintaining simulation quality and nonintersection of trajectories. At the same time ABD has comparable or faster timings when compared to state-of-the-art rigid body libraries optimized for performance without guarantees, and successfully and efficiently solves challenging simulation problems where both classes of prior rigid body simulation methods fail altogether. 

We propose a new model and algorithm to capture the high-definition statics of thin shells via coarse meshes. This model predicts global, fine-scale wrinkling at frequencies much higher than the resolution of the coarse mesh; moreover, it is grounded in the geometric analysis of elasticity, and does not require manual guidance, a corpus of training examples, nor tuning of ad hoc parameters. We first approximate the coarse shape of the shell using tension field theory, in which material forces do not resist compression. We then augment this base mesh with wrinkles, parameterized by an amplitude and phase field that we solve for over the base mesh, which together characterize the geometry of the wrinkles. We validate our approach against both physical experiments and numerical simulations, and we show that our algorithm produces wrinkles qualitatively similar to those predicted by traditional shell solvers requiring orders of magnitude more degrees of freedom.