Nonlinear Constitutive Law Optimization for Wave Tailoring in Architected Materials*

Nonlinearity is at the forefront of research that seeks to achieve novel wave properties in architected systems. Microstructural elements which display nonlinear constitutive laws have been extensively explored in the context of novel applications in acoustic metamaterials, impact mitigation, and energy trapping materials. To date, however, much experimental exploration of this space has been discrete and opportunistic, due to the difficulty of realizing desired constitutive laws in real-world structures. Topology optimization is a powerful tool to address such an inverse design problem, but has been underutilized in this space due to the high nonlinearity of the design space and the presence of many local optima.

We explore a topology optimization approach which simplifies and expands traversal through the local design space, enabling the successful optimization of microstructure elements for tailored nonlinear constitutive laws. Using a geometrically nonlinear, finite strain, displacement control level set topology optimization scheme, we optimize structures for multiple types of nonlinear constitutive laws, including softening, stiffening, and stiffness switching. We show experimental validation of the optimized designs, and explore their use in wave tailoring metamaterial chains. Expanded capabilities of this approach into the bistable regime and impact mitigation are also investigated.