Topology Optimization of Nonlinear Metamaterials

Optimal topology for periodic structures exhibiting nonlinearity is considered for two-dimensional plane stress systems. Optimal, in this context, refers to a design which maximizes the frequency shift (and thus bandgap shift) at the edge of the first Brillouin Zone for the acoustic branch. Parametric analyses and a genetic algorithm implementation identify topologies that produce large increases in complete bandgap width or group velocity variation. Analysis of Bloch wavemodes which produce large nonlinear frequency shifts reveals that the largest contributions to the frequency shift are primarily produced from localized strains in thin layers of compliant, nonlinear matrix material.