Multifunctional design of lattice metamaterial with desired thermal expansion behaviors using topology optimization

Designing metamaterials with unprecedented coefficients of thermal expansion (CTEs) is an urgent demand for the majority engineering structures suffering from ambient temperature variation. Current studies on such artificial materials are mainly focused on achieving CTE tunnability through the purposeful design of material microstructure using an intuition based mechanism. In this study, the mechanical properties including maximum bulk modulus, specific stiffness and high thermal conductivity are combined with desired CTEs for designing multifunctional lattice metamaterials through the application of a non-intuitive topology optimization method. Toward this end, the continuous variable of member cross-sectional area is adopted to optimize lattice topology, section sizes of lattice members and material distributions, simultaneously. To meet the manufacturing requirements, an improved member intersection constraint that can cooperate with the present continuous design variable is introduced. A self-programmed routine that can be coupled with any commercial FEA software is developed to implement the present optimization method for the design of lattice metamaterials. Four typical optimization cases corresponding to different practical engineering issues are completed. Compared with the previously reported representative lattice metamaterials that are devised from the intuition or experience of designers, the optimization results obtained in this work demonstrate an obvious superiority in bulk modulus and specific stiffness. Additionally, a bimetallic specimen, fabricated using mechanical processing technology and composed of the metallic constituents Invar and Aluminum alloy, is presented to demonstrate the manufacturability of the optimized lattice microstructures.