Mechanical and Civil Engineering Seminar
Mechanical and Civil Engineering Seminar Series
Title: Simulating solids like fluids: A fully Eulerian approach to fluid-structure interaction.
Fluids and solids tend to be addressed using distinct computational approaches. Solid deformation is most commonly simulated with Lagrangian finite-element methods, whereas fluid flow is amenable to Eulerian-frame approaches such as finite difference and finite volume methods. Problems that mix fluid and solid behaviors simultaneously present interesting numerical challenges. This is true when fluids and solids occupy different regions of space --- i.e. fluid-structure interaction (FSI) --- or in cases where materials behave like a solid but can undergo enormous levels of plastic flow more common of fluids --- i.e. granular materials and yield stress fluids. Here we focus on FSI, and discuss the development of a method called the Reference Map Technique, which allows us to simulate deformable solids on a fixed Eulerian grid. The key is to store and update the reference map field on the grid, which tracks the inverse motion. Using this technique to represent the solid phase, we can solve FSI problems on a single fixed grid using fast update procedures very similar to those used in two-phase Navier-Stokes fluid simulations. Various solid constitutive behaviors can be used, including nonlinear elasticity and plasticity. Systems of many submerged and interacting solids can be simulated, and, by activating the solids internally, we can simulate systems of soft active media. Incompressibility and/or rigidity constraints can also be applied by adopting Eulerian projection approaches commonly used in CFD. The addition of the reference map field to the grid also presents certain benefits when computing level-set interface advection, including a procedure to guarantee mass conservation.
Ken Kamrin received a BS in Engineering Physics and a minor in Mathematics at UC Berkeley in 2003, and a PhD in Applied Mathematics at MIT in 2008. Kamrin was an NSF Postdoctoral Research Fellow at Harvard University in the School of Engineering and Applied Sciences before joining the Mechanical Engineering faculty at MIT in 2011, where he was appointed the Class of 1956 Career Development Chair. He is currently a professor of Mechanical Engineering and Applied Mathematics at MIT. Kamrin's research focuses on constitutive modeling and computational mechanics for large deformation processes, with interests spanning elastic and plastic solid modeling, granular mechanics, amorphous solid mechanics, and fluid-structure interaction. Kamrin has been awarded fellowships from the Hertz foundation, US Defense Department, and National Science Foundation. Kamrin's honors include the 2010 Nicholas Metropolis Award from APS, the NSF CAREER Award in 2012, the 2015 Eshelby Mechanics Award for Young Faculty, the 2016 ASME Journal of Applied Mechanics Award, and the 2022 MacVicar Faculty Fellowship from MIT.
NOTE: At this time, in-person Mechanical and Civil Engineering Lectures are open to all Caltech students/staff/faculty/visitors.