Modelling negative linear compressibility in tetragonal beam structures

Abstract

Most materials compress axially in all directions when loaded hydrostatically. Contrary to this, some materials have been discovered that exhibit negative linear compressibility and, as such, expand along a specific axis or plane. This paper analyses a fundamental mechanism by using a combination of finite element simulations and analytical derivations to show that negative linear compressibility can be found in a body-centred or face-centred tetragonal network of nodes connected by a network of beams. The magnitude and direction of this behaviour depends on the cross geometry in the network.

Negative Compressibility of 3D Cellular Models Constructed by Hinging Hexagonal Truss Mechanism

“…And the expressions of Poisson's ratios of these two models are same due to the same framework structure so the euqation, β L (OX i ) (Model I) = 2 β L (OX i ) (Model III) , can be easily to understand. More than that, through the comparison of these two models, it can be indicated that in addition to the geometry features which have already been widely discussed , the arrangement of the framework structure can also have a great effect on the compressibility properties and arranging the framework in a dense way just like the Model III is not conductive to the enhancement of negative compressibility effect.…”

“…Some systems which are made up of two different materials with particular geometric features and connectivities can also exhibit NLC . By using a combination of finite element simulations and analytical derivations, it was shown that NLC can be exhibited in body‐ or face‐centered tetragonal structures . It has also been shown that some systems made from rotating rigid units which are usually associated with auxeticity can also exhibit negative linear compressibility for certain conditions .…”

Carbon allotropes exhibiting negative linear compressibility

“…In this case, negative compressibility generally arises due to very high positive Poisson's ratios and anisotropy. On the other hand negative compressibility can also be achieved in porous solid systems as a result of the fluid particles exerting a pressure both from within the pores of the material and on its surface, altering the relative orientation of the structural features in the system, which may result in NLC . At the nanoscale it is more common to have negative linear compressibility being manifested as a result of the former effect.…”

Metamaterials with negative compressibility — a novel concept with a long history

“…Three-dimensional compressibility was always an exception; the positivity of compressibility is per definitionem equal to the stability [7]. Materials which expand under pressure cannot be stable, they would explode, and therefore construction of this kind of system was always a great scientific challenge [8][9][10], although systems with low-dimensional negative * E-mail: imre.attila@energia.mta.hu compressibility (like 1D line-compressibility) can be found quite easily [11].…”