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CSE Seminar Announcement

A WENO finite-difference sheme for a new class of Hamilton-Jacobi equations in nonlinear mechanics


Thursday, March 30, 2017
1030 National Center for Supercomputing Applications (NCSA)
Noon - 1pm
Lunch Provided


Dr. Oscar Lopez-Pamies
Associate Professor
Civil and Environmental Engineering



Over the past two decades, advances in materials science have made it possible to process materials with highly controllable nanostructures. This has been especially true for soft organic materials with particulate nanostructures which, more often than not, have proved to possess drastically superior physical properties when compared to the properties of the plain materials without the nanoparticles. An impressive example is that of dielectric elastomer composites (DECs) — comprised of a dielectric elastomer matrix filled with a small amount of (semi)-conducting nanoparticles — which have shown potential to enable a broad range of high-end technologies, essentially as the next generation of sensor and actuators.
Aimed at directly relating the nanoscopic behavior of DECs to their remarkable macroscopic behavior, we have recently derived an exact homogenization solution for the macroscopic coupled electromechanical response of a general class of DECs under finite deformations and finite electric fields. The solution is implicitly given in terms of a new class of Hamilton-Jacobi (HJ) equations, surprisingly different from known HJ equations that have stemmed from a broad range of physical phenomena over the years. In this talk, I will briefly discuss the derivation of such a class of HJ equations and present at length a WENO finite-difference scheme of high order in “space” and “time” to construct their viscosity solutions. By way of a practical example, I will also present sample numerical solutions aimed at scrutinizing recent experimental findings.  



Oscar Lopez-Pamies received his B.S. degree in Mathematics and B.S. and M.S. degrees in Mechanical Engineering from the University of Maryland Baltimore County in 2001 and 2002, and his Ph.D. degrees in Applied Mechanics from the University of Pennsylvania and Ecole Polytechnique (France) in 2006. He served on the Mechanical Engineering faculty of SUNY Stony Brook between 2007 and 2011 before joining the Department of Civil and Environmental Engineering at the University of Illinois Urbana-Champaign, where he is currently Associate Professor and CEE Excellence Faculty Fellow. Oscar’s research focuses on the development of mathematical theories to describe, explain, and predict the macroscopic behavior, stability, and failure of highly deformable heterogeneous solids directly in terms of their microscopic behavior. He is the recipient of a number of academic honors, including the NSF CAREER award in 2011, the Journal of Applied Mechanics award in 2014, and the Young Investigator Medal from the Society of Engineering Science in 2017.

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