3-D phononic crystals with ultra-wide band gaps

TL;DR

This paper uses gradient-based topology optimization with GPU acceleration to design 3-D phononic crystals that achieve ultra-wide band gaps, enabling improved control of wave propagation in materials.

Contribution

It introduces a novel combination of topology optimization, a mixed variational eigenvalue solver, and GPU computing to discover 3-D phononic structures with unprecedented band gap widths.

Findings

Achieved normalized stop bands exceeding 100% in tungsten carbide-epoxy crystals.

Optimized structures converge to simple inclusion network topologies.

Large phononic stop bands are possible with lower density configurations.

Abstract

In this paper gradient based topology optimization (TO) is used to discover 3-D phononic structures that exhibit ultra-wide normalized all-angle all-mode band gaps. The challenging computational task of repeated 3-D phononic band-structure evaluations is accomplished by a combination of a fast mixed variational eigenvalue solver and distributed Graphic Processing Unit (GPU) parallel computations. The TO algorithm utilizes the material distribution-based approach and a gradient-based optimizer. The design sensitivity for the mixed variational eigenvalue problem is derived using the adjoint method and is implemented through highly efficient vectorization techniques. We present optimized results for two-material simple cubic (SC), body centered cubic (BCC), and face centered cubic (FCC) crystal structures and show that in each of these cases different initial designs converge to single inclusion network topologies within their corresponding primitive cells. The optimized results show that large phononic stop bands for bulk wave propagation can be achieved at lower than close packed spherical configurations leading to lighter unit cells. For tungsten carbide - epoxy crystals we identify all angle all mode normalized stop bands exceeding 100%, which is larger than what is possible with only spherical inclusions.