Negative Jacobian Free Simulations Using Principal Stretches

Abstract

Finite element (FE) simulations are prone to encountering negative Jacobians during the solving process. If nothing is done, the simulation can be brought to a halt, result in inverted elements or have undetermined behavior. We propose a solution that uses principal stretches as slack variables in a constrained minimization formulation and enforce them to always be positive. We show that our approach can never hit inverted configurations, thus being suitable for applications where inversion cannot be tolerated. We implement the method in 2D and show that it outperforms standard FE methods in stressful scenarios.