Dr. Oscar Lopez-Pamies is an Associate Professor and CEE Excellence Faculty Fellow in the Department of Civil and Environmental Engineering at the University of Illinois.
His 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.
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.