A scalable framework for large-scale 3D multimaterial topology optimization with octree-based mesh adaptation

Advancements in multimaterial additive manufacturing have the potential to enable the creation of topology optimized structures with both shape and material tailoring. However, multimaterial topology optimization methods that use Discrete Material Optimization (DMO) face three technical challenges for large-scale high-resolution problems: 1) the large-scale design space, since selection variables must be added for each additional candidate material; 2) the treatment of numerous sparse partition of unity constraints required in some DMO parametrizations; and 3) the multimaterial design space that has more local minima than an equivalent single material design space. This paper addresses these issues by presenting a parallel, scalable analysis and design optimization framework for multimaterial topology optimization that optionally uses local mesh refinement using semi-structured octree meshes. The advantages of this framework are demonstrated by showcasing its solution and design scalability and by efficiently solving large 3D multimaterial compliance-minimization problems with both isotropic and orthotropic material options on meshes with up to 329 million elements. For the largest case, the adaptive strategy is shown to achieve a compliance objective within 1.86% with roughly 1/4 the mesh size.