Abstract This paper proposes a novel method that enhances the optimization‐based elastic body solver. The proposed method tackles the element inversion problem, which is prevalent in the prediction‐projection approach for numerical simulation of elastic bodies. At the prediction stage, our method alleviates inversions such that the subsequent projection solver can benefit in stability and efficiency. To prevent excessive suppression of predicted inertial motion when alleviating, we introduce a velocity decomposition method and adapt only the non‐rigid motion while preserving the rigid motion, that is, linear and angular momenta. Thanks to the respected inertial motion in the prediction stage, our method produces lively motions while keeping the entire simulation more stable. The experiments demonstrate that our alleviation method successfully stabilizes the simulation and improves the efficiency particularly when large deformations hamper the solver.

Abstract This paper proposes a novel method for simulating hyperelastic solids with Smoothed Particle Hydrodynamics (SPH). The proposed method extends the coverage of the state‐of‐the‐art elastic SPH solid method to include different types of hyperelastic materials, such as the Neo‐Hookean and the St. Venant‐Kirchoff models. To this end, we reformulate an implicit integration scheme for SPH elastic solids into an optimization problem and solve the problem using a general‐purpose quasi‐Newton method. Our experiments show that the Limited‐memory BFGS (L‐BFGS) algorithm can be employed to efficiently solve our optimization problem in the SPH framework and demonstrate its stable and efficient simulations for complex materials in the SPH framework. Thanks to the nature of our unified representation for both solids and fluids, the SPH formulation simplifies coupling between different materials and handling collisions.

Abstract In general, it is not easy to simulate an elastic body that undergoes large deformations. Especially when its elements are inverted or tangled, that is, when its vertices penetrate its polygons, simulation often fails. In this paper, we propose a simple yet highly effective method for alleviating the inversion problems of elastic bodies. Our experiments made with typical optimization‐based solvers demonstrate that the proposed method successfully stabilizes the solvers and produces visually plausible motions. We believe that our method can be widely adopted by a variety of state‐of‐the‐art elastic‐body simulators thanks to its simplicity.

This paper proposes a novel energy-momentum conserving integration method. Adopting Projective Dynamics, the proposed method extends its unconstrained minimization for time integration into the constrained form with the position-based energy-momentum constraints. This resolves the well-known problem of unwanted dissipation of energy and momenta without compromising the real-time performance and simulation stability. The proposed method also enables users to directly control the energy and momenta so as to easily create the vivid deformable and global motions they want, which is a fascinating feature for many real-time applications such as virtual/augmented reality and games.