Topology Optimization for Manufacturable Thermoelastic Metamaterials

Abstract

Applications for thermoelastic metamaterials, in which extremely positive, zero or negative thermal expansion is desired, are plentiful. Nevertheless they are rarely applied, due to their poor manufacturability. To enhance their applicability, a topology optimization framework is proposed and verified, able to generate finite thermoelastic metamaterials with tailored unidirectional thermal expansion, manufacturable through automated multi-material additive manufacturing methods. The superelement method is utilized to optimize for finite thermoelastic unit cell arrays connected to solid strips allowing for easy mounting, instead of non-realizable infinite arrays which are optimized in existing frameworks that use the homogenization method. The robust formulation is combined with a filter domain extension approach, to obtain manufacturing tolerant, black and white solutions and minimum length scale control. Uniform material layers are enforced, to obtain layered designs manufacturable with multi-material additive manufacturing methods. Using the proposed framework, a finite thermoelastic unit cell array is optimized for near zero thermal expansion. It is validated that the superelement method is more suitable for the computation of the thermoelastic response of small unit cell arrays, compared to the commonly used homogenization method. A physical sample is manufactured and experimentally validated. Experimental validation confirms numerical predictions and shows that the proposed design approach is able to generate performant and realizable thermoelastic metamaterials.