A Momentum-Conserving Implicit Material Point Method for Surface Energies with Spatial Gradients

TL;DR

This paper introduces a new implicit Material Point Method that accurately models surface energies with spatial gradients, enabling stable simulations of complex thermomechanical behaviors like Marangoni effects and contact angles.

Contribution

The paper presents a novel energy-based discretization for surface tension in MPM that captures surface gradients automatically and conserves momentum with a particle resampling approach.

Findings

Successfully simulates complex behaviors like Marangoni effects.

Achieves perfect conservation of linear and angular momentum.

Demonstrates robustness across diverse materials such as water, wine, and wax.

Abstract

We present a novel Material Point Method (MPM) discretization of surface tension forces that arise from spatially varying surface energies. These variations typically arise from surface energy dependence on temperature and/or concentration. Furthermore, since the surface energy is an interfacial property depending on the types of materials on either side of an interface, spatial variation is required for modeling the contact angle at the triple junction between a liquid, solid and surrounding air. Our discretization is based on the surface energy itself, rather than on the associated traction condition most commonly used for discretization with particle methods. Our energy based approach automatically captures surface gradients without the explicit need to resolve them as in traction condition based approaches. We include an implicit discretization of thermomechanical material coupling with a novel particle-based enforcement of Robin boundary conditions associated with convective heating. Lastly, we design a particle resampling approach needed to achieve perfect conservation of linear and angular momentum with AffineParticle-In-Cell (APIC) [Jiang et al. 2015]. We show that our approach enables implicit time stepping for complex behaviors like the Marangoni effect and hydrophobicity/hydrophilicity. We demonstrate the robustness and utility of our method by simulating materials that exhibit highly diverse degrees of surface tension and thermomechanical effects, such as water, wine and wax.