Optimization of Nonlinear Constitutive Laws for Wave Manipulation
Brianna MacNider, University of California, San Diego
Microstructural features which exhibit nonlinear constitutive laws have shown promise in the context of novel applications and improved performance in wave tailoring in acoustic metamaterials, impact mitigation, and energy trapping materials. Experimental exploration of these applications, however, has been discrete and limited, due to the difficulty of designing desired constitutive laws into real-world structures. Topology optimization is a promising approach to address this type of inverse design problem, but to date has been under-explored due to challenges associated with non-uniqueness, high design space nonlinearity, and the presence of many local optima.
We explore a topology optimization approach which normalizes the structural stiffness out of the problem, instead purely targeting the desired shape of the nonlinearity. This simplifies traversal through this highly nonlinear local design space and enables the targeted optimization of structures for tailored nonlinear constitutive laws. We demonstrate the use of optimization to design geometrically nonlinear structures for multiple distinct classes of nonlinear constitutive laws, including softening, stiffening, negative stiffness, and stiffness switching type behaviors. In addition, we show the ability to fine tune a structure for a nearby nonlinear constitutive law, semi-continuously sweeping through a desired nonlinearity and designing structures for each degree of nonlinearity along the way. We further expand the approach to incorporate a nonlinear material model, show experimental validation of the optimized designs, and explore their use for wave tailoring and impact mitigation in quasi 1-D metamaterial chains.
Abstract Author(s): Brianna MacNider, H. Alicia Kim, Nicholas Boechler