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We present an adaptively updated Lagrangian Material Point Method (A‐ULMPM) to alleviate non‐physical artifacts, such as the cell‐crossing instability and numerical fracture, that plague state‐of‐the‐art Eulerian formulations of MPM, while still allowing for large deformations that arise in fluid simulations. A‐ULMPM spans MPM discretizations from total Lagrangian formulations to Eulerian formulations. We design an easy‐to‐implement physics‐based criterion that allows A‐ULMPM to update the reference configuration adaptively for measuring physical states, including stress, strain, interpolation kernels and their derivatives. For better efficiency and conservation of angular momentum, we further integrate the APIC [JSS*15] and MLS‐MPM [HFG*18] formulations in A‐ULMPM by augmenting the accuracy of velocity rasterization using both the local velocity and its first‐order derivatives. Our theoretical derivations use a nodal discretized Lagrangian, instead of the weak form discretization in MLS‐MPM [HFG*!!18], and naturally lead to a "modified" MLS‐MPM in A‐ULMPM, which can recover MLS‐MPM using a completely Eulerian formulation. A‐ULMPM does not require significant changes to traditional Eulerian formulations of MPM, and is computationally more efficient since it only updates interpolation kernels and their derivatives during large topology changes. We present end‐to‐end 3D simulations of stretching and twisting hyperelastic solids, viscous flows, splashing liquids, and multi‐material interactions with large deformations to demonstrate the efficacy of our new method. [ABSTRACT FROM AUTHOR]

We propose a Lagrangian particle‐based formulation for simulating deformation, fracture, and diffusion in thin membranelike structures, such as aluminium foil, rubbery films, and seaweed flakes. We integrate our model with diffusion processes and derive a unified framework for simulating deformation‐diffusion coupled phenomena, which is applied to provide realistic heterogeneity induced by the diffusion process to fracture patterns. To the best of our knowledge, our work is the first to simulate the complex fracture patterns of single‐layered membranes in computer graphics and introduce heterogeneity induced by the diffusion process, which generates more geometrically rich fracture patterns. Our end‐to‐end 3D simulations show that our deformation‐diffusion coupling framework captures detailed fracture growth patterns in thin membranes due to both in‐plane and out‐of‐plane motions, producing realistically wrinkled slit edges, and heterogeneity introduced due to diffusion. [ABSTRACT FROM AUTHOR]

Abstract: We present an efficient solver for monolithic two‐way coupled simulation of rigid bodies with incompressible fluids that is robust to poor conditioning of the coupled system in the presence of large density ratios between the solid and the fluid. Our method leverages ideas from the theory of Domain Decomposition, and uses a hybrid combination of direct and iterative solvers that exploits the low‐dimensional nature of the solid equations. We observe that a single Multigrid V‐cycle for the fluid equations serves as a very effective preconditioner for solving the Schur‐complement system using Conjugate Gradients, which is the main computational bottleneck in our pipeline. We use spectral analysis to give some theoretical insights behind this observation. Our method is simple to implement, is entirely assembly‐free besides the solid equations, allows for the use of large time steps because of the monolithic formulation, and remains stable even when the iterative solver is terminated early. We demonstrate the efficacy of our method on several challenging examples of two‐way coupled simulation of smoke and water with rigid bodies. To illustrate that our method is applicable to other problems, we also show an example of underwater bubble simulation. [ABSTRACT FROM AUTHOR]