Multilevel hierarchy in bi-material lattices with high specific stiffness and unbounded thermal expansion

Abstract

Dual-material concepts that expand or contract as desired upon changes in temperature exist but have their limitations. One upon which we focus here is the trade-off caused by the inherent thermo-elastic coupling that they feature, a condition that makes desired changes in thermal expansion penalize elastic stiffness, and vice versa. In this paper, we present hierarchical bi-material lattices that are stiff and can be designed to attain a theoretically unbounded range of thermal expansion without (i) impact onto elastic moduli and (ii) severe penalty in specific stiffness. Through a combination of theory, numerical simulations and experiments, we demonstrate the thermomechanical performance of eight hierarchical lattices, including two fractal-like hierarchical lattices with self-repeating units that are built from dual-material diamond shapes with low and high coefficients of thermal expansion (CTE). Results show that the achievable range of CTE can be enlarged by 66% through the addition of one order of hierarchy only, and that for a given CTE range the specific stiffness can be at least 1.4 times larger than that of existing stretch-dominated concepts. The concepts here introduced can open up new avenues towards multifunctional devices and structurally efficient materials with simultaneously customized thermal expansion and mechanical properties.