Lightweight Mechanical Metamaterials with Tunable Negative Thermal Expansion

Ice floating on water is a great manifestation of negative thermal expansion (NTE) in nature. The limited examples of natural materials possessing NTE have stimulated research on engineered structures. Previous studies on NTE structures were mostly focused on theoretical design with limited experimental demonstration in two-dimensional planar geometries. In this work, aided with multimaterial projection microstereolithography, we experimentally fabricate lightweight multimaterial lattices that exhibit significant negative thermal expansion in three directions and over a temperature range of 170 degrees. Such NTE is induced by the structural interaction of material components with distinct thermal expansion coefficients. The NTE can be tuned over a large range by varying the thermal expansion coefficient difference between constituent beams and geometrical arrangements. Our experimental results match qualitatively with a simple scaling law and quantitatively with computational models.

Figure 1

(a) Schematic of the multimaterial projection microstereolithography system. [(b) and (e)] Computer-aided designs and fabricated samples in [(c) and (f)] three-dimensional and [(d) and (g)] two-dimensional views of the fabricated unit cell and 2 by 2 lattice, respectively.

Figure 2

(a) Experimental and (d) finite element simulation sequences of a unit cell with increasing temperature. The red arrows indicate the inward bending of the reinforced PEGDA beams. [(c)–(d)] Experimentally observed and computationally calculated effective expansion ratios varied with increasing temperatures, (c) with varied volume concentrations of reinforced copper nanoparticles and (d) with varied lengths of beam $BC$ [indicated in the inset of (d)]. The shadow areas in (c) and (d) show the snap-through temperature range. The FEA-simulated negative-thermal-expansion coefficients are $-1.57\times {10}^{-5}$, $2.91\times {10}^{-5}$, and $-4.06\times {10}^{-5}{\mathrm{K}}^{-1}$ in (c), and $-1.71\times {10}^{-5}$, $2.91\times {10}^{-5}$, and $-3.93\times {10}^{-5}{\mathrm{K}}^{-1}$ in (d), respectively.

Figure 3

(a) A unit cell model to illustrate the key nodes. (b) Two bifurcation deformation paths of the simplest model with key nodes illustrated in (a). In path 1, node $B$ moves inward with increasing temperature. In path 2, node $B$ first moves outward, then snaps through inward, and smoothly moves inward with increasing temperature. (c) The thermal-induced strain in reinforced PEGDA beams with various copper reinforcement fractions in functions of temperature increase.

Figure 4

(a) A CAD model of a composite lattice by layering a number of unit cells. The inset of (a) shows the deformation mechanism between unit cells within the composite lattice. (b) Experimentally observed and computationally calculated effective expansion ratios and (c) experimental sequences of a 2 by 2 composite lattice under raising temperature. The arrows indicate the deformation.