ElastoMonolith: A monolithic optimization-based liquid solver for contact-aware elastic-solid coupling

Abstract

Simultaneous coupling of diverse physical systems poses significant computational challenges in terms of speed, quality, and stability. Rather than treating all components with a single discretization methodology (e.g., smoothed particles, material point method, Eulerian grid, etc.) that is ill-suited to some components, our solver, ElastoMonolith, addresses three-way interactions among standard particle-in-cell-based viscous and inviscid fluids, Lagrangian mesh-based deformable bodies, and rigid bodies. While prior methods often treat some terms explicitly or in a decoupled fashion for efficiency, often at the cost of robustness or stability, we demonstrate the effectiveness of a strong coupling approach that expresses all of the relevant physics within one consistent and unified optimization problem, including fluid pressure and viscosity, elasticity of the deformables, frictional solid-solid contact, and solid-fluid interface conditions. We further develop a numerical solver to tackle this difficult optimization problem, incorporating projected Newton, an active set method, and a transformation of the inner linear system matrix to ensure symmetric positive definiteness. Our experimental evaluations show that our framework can achieve high quality coupling results that avoid artifacts such as volume loss, instability, sticky contacts, and spurious interpenetrations.