A general two-stage initialization for sag-free deformable simulations

Ours Fig. 1. An example deformable object simulation prepared using (top-row) naive initialization that treats the given initial shape as the rest shape, which leads to sagging with gravity, and (bottom-row) our initialization that preserves the given initial shape by treating it as the intended shape in static equilibrium under gravity. The two initialization methods produce qualitatively similar animations, while ours maintains the initial shape prior to collisions with the torus. Simulations are generated using FEM with corotated linear elasticity material [Sifakis and Barbic 2012].

Initializing simulations of deformable objects involves setting the rest state of all internal forces at the rest shape of the object. However, often times the rest shape is not explicitly provided. In its absence, it is common to initialize by treating the given initial shape as the rest shape. This leads to sagging, the undesirable deformation under gravity as soon as the simulation begins. Prior solutions to sagging are limited to specific simulation systems and material models, most of them cannot handle frictional contact, and they require solving expensive global nonlinear optimization problems.

We introduce a novel solution to the sagging problem that can be applied to a variety of simulation systems and materials. The key feature of our approach is that we avoid solving a global nonlinear optimization problem by performing the initialization in two stages. First, we use a global linear optimization for static equilibrium. Any nonlinearity of the material definition is handled in the local stage, which solves many small local problems efficiently and in parallel. Notably, our method can properly handle frictional contact orders of magnitude faster than prior work. We show that our approach can be applied to various simulation systems by