Corotational simulation of deformable solids

Abstract

The classical formulation of large displacement visco-elasticity requires the geometrically nonlinear Green tensor. Keeping track of the rotational part of strain permits alternative formulations, that allow the tensor to stay linear, and at the same time maintaining rotational invariance. We replace a recently proposed heuristical warping technique by the application of the polar decomposition. The polar decomposition exactly extracts rotations, thus enhances stability and accuracy. We combine it with a hierarchical finite element basis, which allows us to compute accurate rotations from a coarse level nonlinear simulation and use them with corotated tensors for finer detail.