Exploring dynamic contact of soft solids with an Eulerian phase-field approach

Abstract

Dynamic contact of soft solids plays a role in many applications, from biomechanical impacts to manufacturing processes. Traditional Lagrangian methods often struggle with large deformations and rapidly evolving contact interfaces. Fully Eulerian approaches for solid–solid contact have remained few and contributions are mostly from the fluid–structure interaction community. In this work, we extend our previous Eulerian phase-field framework for static contact to solid dynamics. Our formulation employs multiple Eulerian fields – a phase-field for interface capturing, a reference map to model elasticity, and separate velocity fields for each body – to describe the state of different solids on a fixed mesh. Contact is resolved implicitly through a penalty-based approach that uses the overlap of phase-fields. Temporal integration is performed using the generalized-$\alpha$ method. Numerical examples demonstrate that translating the contact formulation to the dynamic case is straight-forward and that the total energy is well-conserved.