Yuliya Gorb, National Science Foundation
Authors: Thuyen Dang, Yuliya Gorb, Silvia Jiménez Bolaños
2023 AWM Research Symposium
Recent Advancements in the Mathematics of Materials Science [Organized by Anna Zemlyanova and Silvia Jimenez Bolanos]

This talk discusses the rigorous periodic homogenization of a weakly coupled electroelastic system. This system comprises a nonlinear electrostatic equation and an elastic equation enriched with electrostriction, which finds application in describing materials like dielectric elastomers or deformable (elastic) dielectrics. This project reveals that the effective response of this system involves a homogeneous dielectric elastomer described by a nonlinear weakly coupled system of PDEs. The coefficients of these equations depend on the original heterogeneous material, composite geometry, and microstructure periodicity. Notably, this approach offers an explicit corrector result for homogenizing monotone operators, even under minimal regularity assumptions. Some additional facts including two Lp-gradient estimates applicable to elastic systems with discontinuous coefficients will be mentioned.

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