Topology optimization for metamaterials with negative thermal expansion coefficients using energy-based homogenization

Since the existing topology designs of negative thermal expansion metamaterials are primarily based on the asymptotic homogenization theory, this paper conducts a topology optimization method of negative thermal expansion metamaterials based on the computationally efficient energy-based homogenization for the first time. In this research, (1) a new effective thermal stress coefficient equation is pioneeringly proposed using energy-based homogenization frame, where its theoretical derivation process is presented as well as its effectiveness and computational efficiency are verified by comparative cases. Additionally, the matlab code is open-sourced for public learning. (2) A topology optimization design of both 2D and 3D metamaterials with negative thermal expansion properties is established innovatively with Discrete Material Optimization (DMO). Its advantages are illustrated compared with the convectional method and its results are validated by Finite Element Method simulations. The new methods have promising applications in the evaluation and optimization of thermal expansion properties of composites.