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In this paper gradient based topology optimization (TO) is used to discover3-D phononic structures that exhibit ultra-wide normalized all-angle all-modeband gaps. The challenging computational task of repeated 3-D phononicband-structure evaluations is accomplished by a combination of a fast mixedvariational eigenvalue solver and distributed Graphic Processing Unit (GPU)parallel computations. The TO algorithm utilizes the materialdistribution-based approach and a gradient-based optimizer. The designsensitivity for the mixed variational eigenvalue problem is derived using theadjoint method and is implemented through highly efficient vectorizationtechniques. We present optimized results for two-material simple cubic (SC),body centered cubic (BCC), and face centered cubic (FCC) crystal structures andshow that in each of these cases different initial designs converge to singleinclusion network topologies within their corresponding primitive cells. Theoptimized results show that large phononic stop bands for bulk wave propagationcan be achieved at lower than close packed spherical configurations leading tolighter unit cells. For tungsten carbide - epoxy crystals we identify all angleall mode normalized stop bands exceeding 100%, which is larger than what ispossible with only spherical inclusions.

3-D phononic crystals with ultra-wide band gaps