Negative thermal expansion in transversely isotropic space frame trusses

Abstract

The negative thermal expansion (NTE) of a type of space frame structure is investigated herein. On the basis of a space frame structure consisting of tetrahedral representative volume elements, a volumetric thermal strain and a volumetric coefficient of thermal expansion (CTE) models are developed in this paper. The NTE trusses developed herein exhibit a special case of anisotropy known as transverse isotropy. This is achieved by using two types of rod materials, each for the three apex rods and the three base rods. From these models, the conditions for attaining negative volumetric strain and negative coefficients of volumetric expansion due to change in temperature are established. Two definitions of NTE are given herein: (a) overall NTE and (b) incremental NTE. Based on these two definitions of NTE, the conditions that lead to (i) definite NTE and (ii) selective NTE are established. Plotted results reveal a trend in which the extent of negative thermal expansion is increased for lower apex‐to‐base rod length and CTE ratios, and higher base rod CTE.

Structurally Efficient Three-dimensional Metamaterials with Controllable Thermal Expansion

“…The first mechanism results in stationary-nodes ( Fig. 1a ) 9 28 29 30 31 33 34 35 , and can be used in an Octet cell to generate thermal expansion isotropy. The second mechanism that we identify here for the first time resorts to stationary-lines that appear in a bi-material tetrahedron upon thermal expansion ( Fig.…”

“…Recent works on mechanical metamaterials have shown that the CTE of periodic materials can be tuned by purposefully designing the architecture of their repeating unit and proper selection of the constituent materials 2 3 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 . It has been shown that low CTE can be obtained through a purely mechanical, and thus temperature-independent, mechanism 3 , which can be in principle designed to make the material operate over a wide range of temperature.…”

“…Existing mechanical metamaterials, however, have their limitations. The majority are two dimensional and can accommodate only in-plane thermal deformation 2 3 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 28 29 30 34 35 . A handful are three-dimensional 9 25 26 27 28 29 30 31 32 33 .…”

“…A very small set of architectures, on the other hand, are stretch dominated with high specific stiffness, but these concepts can generate only a narrow range of CTE and cannot yield a vanishing CTE. The trade-off between CTE tunability and structural efficiency is currently unresolved with current concepts achieving high CTE tunability only at the expense of a dramatic loss in their specific stiffness and specific strength 25 32 , and vice versa 9 26 27 28 29 30 31 33 . The goal of this work is to create a structurally efficient 3D architected material with highly tunable CTE including zero.…”

Auxetic Materials and Related Systems

“…(To remind, NPR, usually denoted as ν αβ in a general case of an anisotropic material, means that when stretched in direction α the material becomes fatter ( not thinner) in direction β (transverse to α ) in which the response is measured.) The remaining six papers concern negative thermal expansion (NTE) , negative stiffness (NS) , ‘negative’ magnetic properties , and graphene .…”