Yvonne Ou, University of Delaware
2022 AWM Research Symposium
Recent Advancements in the Mathematics of Materials
Some geological materials such as quartz and biological materials such as cortical bones and cancellous bones exhibit piezo-electric behaviors, for which a mechanical wave such as ultrasound can trigger electro-magnetic waves. In this talk, we consider the porous composite materials made of linear piezo-electric solid with pores saturated with linear conducting fluid, a model that mimics in vivo bones. A focus of this talk is on the time domain well-posedness of this system of equations. The goal is to take the two-scale homogenization limit of this system in order to understand how the microstructures affect the effective properties of such porous piezoelectric composites.