Evaluation Method of Wave Dispersive Effect in Heterogeneous Media Using a Non-convex and Multimodal Optimization Method

Abstract

The aim of this work is to estimate upper bounds of the Burnett coefficients in the high order homogenized wave equation, along with optimal microgeometries using a non-convex and mutimodal optimization method. We assumed that the two-dimensional unit cell is consist of a two-phase composite material with an 8-fold symmetry assumption. Under this geometrical assumption in the unit cell, the Burnett tensor is characterized by two scalar parameters. In order to estimate the upper bounds of the wave dispersion, we numerically compute Pareto fronts in the plane of the two scalar parameters under two equality constraints for the the phase proportions and for the homogenized tensor. The optimization problem is formulated considering a non-concave bound and solved using a shape optimization method.