Homogenization of Elastic Dielectric Composites Containing Space Charges: A Pathway Towards Materials with Extreme Properties (and related topics)
16 November, 2018 @ 2:30 pm - 3:30 pm
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. His research focuses on the development of mathematical theories and associated numerical methods to describe, explain, and predict the behavior, stability, and failure of highly deformable heterogeneous solids. He is the recipient of a number of academic honors, including the Young Scientist Prize from the European Mechanics Society in 2009, 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.
In the first part of this talk, I will present the derivation of the homogenized equations for the macroscopic response of elastic dielectric composites containing space charges (i.e., electric source terms) that oscillate rapidly at the length scale of the microstructure. The derivation will be carried out first in the setting of small deformations and moderate electric fields by means of a two-scale asymptotic analysis and then in finite deformations. Two types of rapidly oscillating space charges will be considered: passive and active. The latter type corresponds to space charges that appear within the composite in response to externally applied electrical stimuli, while the former corresponds to space charges that are present within the composite from the outset. The obtained homogenized equations will reveal that the presence of (passive or active) space charges within elastic dielectric composites can have a significant and even dominant effect on their macroscopic response, possibly leading to extreme behaviors ranging from unusually large permittivities and electrostriction coefficients to metamaterial-type properties featuring negative permittivities. These results suggest a promising strategy to design highly deformable dielectric composites — such as electrets and dielectric elastomer composites — with exceptional electromechanical properties.
In the second part of the talk, I will turn the focus on how elastic dielectric composites can fail. In particular, I will present a new theory of nucleation and propagation of fracture and healing in elastomers. The theory rests on two central ideas. The first one is to view elastomers as solids capable to undergo finite deformations and capable also to phase transition to another solid of vanishingly small stiffness — whereas the forward phase transition serves to characterize the nucleation and propagation of fracture, the reverse phase transition characterizes the healing. The second central idea is to take the phase transition to be driven by the competition between a combination of strain energy and hydrostatic stress concentration in the bulk and surface energy on the created/healed new surfaces in the elastomer. After outlining a numerical implementation of the theory capable of efficiently dealing with large deformations and the typical near incompressibility of elastomers, I will close by confronting its predictions with a number of recent experiments.