Optimized Phononic Crystals Exploiting Elastic-Plastic Response

Abstract In this paper we present an optimization approach for tailoring wave propagation and damage in phononic crystals along the longitudinal direction. We first adapt an optimization procedure, coupled to a semi-analytical treatment of elastic-plastic wave propagation, to assist in configuring phononic crystals of variable cross-section. Further optimization using a high-fidelity finite element model subsequently arrives at a final phononic crystal design. A scenario-specific objective function, coupled to elastic-plastic wave propagation predictions, serves as a performance metric for candidate phononic crystals consisting of a dogbone-like unit cell. As such, starting with an initial phononic crystal design, the dual-optimization approach yields phononic crystals exhibiting superior performance in comparison to a uniform rod. Notably, these optimized designs subtract material, producing lightweight and easily manufactured structures. We apply the approach to three idealized longitudinal problems involving elastic-plastic wave propagation: (i) vibration and damage mitigation, (ii) drop protection, and (iii) occupant protection. Through these scenarios we demonstrate the ability of optimized phononic crystals to mitigate damage by rejecting select elastic-plastic frequency content, moderate impulsive loading through engineered dispersion, and localize damage as a protective measure. Ultimately, the research results support the use of optimized structures as a means to extend the design space associated with elastic-plastic phononic systems.