Professor Chris Rycroft

The reference map technique for simulating complex materials and multi-body interactions

Professor at the Department of Mathematics, University of Wisconsin-Madison

Chris Rycroft is an applied mathematician and has been at UW-Madison since summer 2022. Prior to starting at UW-Madison, he was the John L. Loeb Associate Professor at Harvard School of Engineering and Applied Sciences. He is interested in mathematical modeling and scientific computation for interdisciplinary applications, and he has collaborated with researchers in a variety of fields, such as materials science, biology, and mechanical engineering. In 2021 he received the Everett Mendelsohn Award, a Harvard-wide award for excellence in graduate mentoring.

Prior to his appointment at Harvard, Rycroft was a Morrey Assistant Professor in the Department of Mathematics at the University of California, Berkeley. Rycroft is a visiting faculty scientist at the Lawrence Berkeley Laboratory, where he has worked on several projects relating to energy production and efficiency. He obtained his Ph.D. in Mathematics in 2007 from the Massachusetts Institute of Technology.

Abstract

The reference map technique for simulating complex materials and multi-body interactions

Conventional computational methods often create a dilemma for fluid–structure interaction problems. Typically, solids are simulated using a Lagrangian approach with grid that moves with the material, whereas fluids are simulated using an Eulerian approach with a fixed spatial grid, requiring some type of interfacial coupling between the two different perspectives. Here, a fully Eulerian method for simulating structures immersed in a fluid will be presented [1]. By introducing a reference map variable to model finite-deformation constitutive relations in the structures on the same grid as the fluid, the interfacial coupling problem is highly simplified. The method is particularly well suited for simulating soft, highly-deformable materials and many-body contact problems [2], and several examples in two and three dimensions [3] will be presented.[1] K. Kamrin, C. H. Rycroft, and J.-C. Nave, J. Mech. Phys. Solids 60, 1952–1969 (2012).[2] C. H. Rycroft et al., J. Fluid Mech. 898, A9 (2020).[3] Y. L. Lin, N. J. Derr, and C. H. Rycroft, Proc. Natl. Acad. Sci. 119, e2105338118 (2022).

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