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

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. (C) 2017 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.