Many complexities emerge in solving problems that intermingle the mechanical behaviors of solids and fluids, complexities which challenge the common simulation methodologies for fluid-only or solid-only problems. Two specific topics of interest in our group are simulating fluid-structure interaction (FSI), and simulating solids undergoing fluid-like levels of plastic strain.

FSI must mitigate a challenge in computational perspective; solid constitutive relations require local information on the total deformation state, which is natural to calculate on a Lagrangian mesh (e.g. finite-element methods) and fluids with their often extreme levels of shear and mixing are amenable to simulation on an Eulerian grid (e.g. finite-difference -volume methods). To address this dichotomy, we have created a novel, fully-Eulerian, simulation method for largely-deforming solids, exploiting a surrogate vectorial quantity called the reference map.  Our Reference Map Technique discretizes the new field, enabling the modeling of both fluid and solid domains on a single fixed grid using a level-set formulation to track the interface and direct the continuity conditions. The resulting method is fast and robust. It has found use in computer graphics and is being applied in nuclear fuel rod simulation. Using the distance-functions defined by the level-set fields of each object, contact detection is simplified, enabling simulation of multiple fluid and solid phases interacting all on a single finite-difference grid.

On the other hand, motivated by challenges in simulating granular continua, we have developed tools to simulate solids whose yield properties admit extreme levels of plastic flow. We are adopting a meshless simulation approach that is able to capture quasi-rigid zones together with highly deforming ones without the common pitfalls of finite-element entanglement or the constitutive constraints of many fluid solvers. In the case of granular media, our home-coded Material Point Method (MPM) algorithm can handle enormous distortions while implementing our recently proposed trans-phase granular constitutive model. In so doing, it captures the constitutive behavior and transition rules for all common granular phases, i.e. gas-like "open" material, dense-packed static subyield material, and dense viscoplastic flowing media. This level of generality enables continuum modeling of problems that might normally be considered outside the realm of continuum simulation. For example, we have recently shown the ability to solve the full process of granular impact and penetration as a continuum problem. Solutions obtained match many different aspects of experimentally obtained data, such as intrusion distance, force propagation on impact, grain flow fields around the intruder, and splashing of the grains at the free surface.

The trans-phase MPM modeling approach has recently been hybridized with the particle-by-particle discrete element method (DEM) to produce a multi-scale model that aims at capturing the accuracy of DEM where needed with the ease and speed of MPM everywhere else.  The adpativity of the approach let's us model tricky parts of the domain --- such as zones near walls or free-surfaces, or shear-bands --- with "real" grains, to deliver DEM level precision but without the computational cost.          

External collaborators:

Chris Rycroft (Harvard)
Dan Negrut (U Wisconsin, Madison)
Eitan Grinspun (U Toronto)
Sachith Dunatunga
  (Green Hills Software)

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Simulations of multiphase solid/fluid problems using the Reference Map Technique. The algorithm uses only a fixed Cartesian background grid. Top: Stirring and settling of 20 rubber objects submerged in fluid. Colors are pressure, fluid velocity visualized with point-markers, and solid deformation visualized through post-processed score lines. Bottom:   Reference Map Technique with internal actuation of the soft solids to produce swimming. Colors show vorticity.

The movies above are continuum simulations of flowing granular media using our trans-phase constitutive model. Visible points are not grains, but rather the marker points for our meshless solver. Colors indicate plastic strain-rate. Top: Continuum simulation of a solid wedge projectile shot into a bed of grains (2x slow-motion). Bottom: A solid wheel is driven over continuum granular media in the general 3D setting (and is stopped by a wall on the left). Colors indicate accumulated plastic strain here.