Eulerian solid simulation with contact

Abstract

Simulating viscoelastic solids undergoing large, nonlinear deformations in close contact is challenging. In addition to inter-object contact, methods relying on Lagrangian discretizations must handle degenerate cases by explicitly remeshing or resampling the object. Eulerian methods, which discretize space itself, provide an interesting alternative due to the fixed nature of the discretization. In this paper we present a new Eulerian method for viscoelastic materials that features a collision detection and resolution scheme which does not require explicit surface tracking to achieve accurate collision response. Time-stepping with contact is performed by the efficient solution of large sparse quadratic programs; this avoids constraint sticking and other difficulties. Simulation and collision processing can share the same uniform grid, making the algorithm easy to parallelize. We demonstrate an implementation of all the steps of the algorithm on the GPU. The method is effective for simulation of complicated contact scenarios involving multiple highly deformable objects, and can directly simulate volumetric models obtained from medical imaging techniques such as CT and MRI.

A material point method for thin shells with frictional contact

“…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].…”

“…It is more difficult to impose and resolve collision constraints over subd and NURBS surfaces than it is over triangle meshes with linear interpolation (see Eischen et al[1996], Thomaszewski et al[2006], and Lu and Zhang[2014]). Recently, approaches that utilize a hybrid Lagrangian/Eulerian view of the physics have been developed for collision and contact with elastic solids [Fan et al 2013[Fan et al , 2014Levin et al 2011;Li et al 2013;McAdams et al 2009]. While Lagrangian methods require separate modeling for collision/contact resolution, Eulerian methods naturally resolve collision and contact through the elasticity physics.…”

A polynomial particle-in-cell method

“…We note that Levin et al have developed a number of methods that make use of the inverse flow map [Fan et al 2013;Levin et al 2011;Teng et al 2016].…”

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

“…Due to the particles in MPM being meshless, contact is often resolved on the grid, and any Eularian contact method can be used. Levin et al (2011) resolves contact of overlapping Eularian grids by formulating the problem by the principle of least constraints. A similar approach was employed by Fan et al (2013), who uses this Eularian formulation to simulate contact for a Lagrangian mesh.…”

“…18. Alternatively, another Eularian contact algorithm, like the one presented in Levin et al (2011), could be employed instead.…”