Multi-displacement microstructure modeling of two-dimensional elastic metamaterials

In this paper, an elastic metamaterial made of lead cylinders coated with elliptical rubbers in an epoxy matrix is considered, and a new multi-displacement microstructure model is proposed to capture the dipolar resonant motion. In the formulation, additional displacement and kinematic variables are introduced to describe global and local deformations, respectively. For the chiral metamaterial, one more rotation variable is needed. The macroscopic governing equations of the two-dimensional elastic metamaterial are explicitly derived. To verify the multi-displacement model, the wave dispersion curves from the current model are compared with those from the finite element simulation for wave propagation. The good agreement is observed in both the longitudinal and transverse wave modes.