Continuum Foam

Abstract

We consider the simulation of dense foams composed of microscopic bubbles, such as shaving cream and whipped cream. We represent foam not as a collection of discrete bubbles, but instead as a continuum. We employ the Material Point Method (MPM) to discretize a hyperelastic constitutive relation augmented with the Herschel-Bulkley model of non-Newtonian viscoplastic flow, which is known to closely approximate foam behavior. Since large shearing flows in foam can produce poor distributions of material points, a typical MPM implementation can produce non-physical internal holes in the continuum. To address these artifacts, we introduce a particle resampling method for MPM. In addition, we introduce an explicit tearing model to prevent regions from shearing into artificially-thin, honey-like threads. We evaluate our method's efficacy by simulating a number of dense foams, and we validate our method by comparing to real-world footage of foam.

A material point method for thin shells with frictional contact

“…The motion of the grid is then interpolated to the particles to update the Lagrangian state without ever actually moving grid nodes. Our approach is ultimately very similar to other MPM methods that define forces from a notion of potential energy [Daviet and Bertails-Descoubes 2016;Jiang et al 2015;Klár et al 2016;Stomakhin et al 2013;Yue et al 2015] and particularly . We briefly discuss aspects common to the approach of and discuss our novel modifications needed for subd shells in more detail.…”

“…A number of recent approaches have used hybrid Lagrangian and Eulerian views to simplify collision and contact treatment. Examples include simulation of elastoplastic solids using an Eulerian view of the governing physics [Fan et al 2013[Fan et al , 2014Levin et al 2011;Li et al 2013], using MPM [Daviet and Bertails-Descoubes 2016;Klár et al 2016;Narain et al 2010;Stomakhin et al 2013;Yue et al 2015;Zhu and Bridson 2005] and using Particle-In-Cell [McAdams et al 2009]. Other hybrid approaches have been used successfully for solid/fluid coupling [Jiang et al , 2015Teng et al 2016] and for crowds [Golas et al 2014;Narain et al 2009].…”

A Generalized Interpolation Material Point Method for Shallow Ice Shelves. 1: Shallow Shelf Approximation and Ice Thickness Evolution

“…Although this approach risks some artificial diffusion, it may be negligible if reinitialization is infrequent. However, more sophisticated schemes are also available that reinitialize material points locally as needed, while minimizing artificial diffusion (e.g., Yue et al, 2015).…”

Animation of crack propagation by means of an extended multi-body solver for the material point method

“…It was later introduced to computer graphics by Stomakhin et al (2013) with their work on snow. Ram et al (2015) and Yue et al (2015) modified their method to simulate viscoplastic materials like foam. Stomakhin et al (2014) added a heat solver to simulate phase change of materials.…”

“…Klar et al (2016) and Daviet and Bertails-Descoubes (2016) used MPM together with a DruckerPrager plasticiy model to simulate sand and other granular materials. Yue et al (2015) complemented MPM with a particle re-sampling scheme to handle potential non-uniform particle distributions due to high shearing strain. Jiang et al (2015) proposed to track a locally affine transformation on each particle that would enable conservation of angular momentum; an improvement over the normally used PIC/FLIP [Zhu and Bridson (2005)] update scheme.…”