EMUDA modelling of 2D and 3D auxetic systems

Abstract

Some materials exhibit the unusual and unexpected property of expanding when stretched and getting narrow when compressed. These unusual materials are known as 'auxetic materials' and differ from conventional materials by having a negative Poisson's ratio (conventional materials have a positive Poisson's ratios). The empirical modelling technique termed EMUDA (an acronym for Empirical Modelling Using Dummy Atoms) has been proven to be a very reliable and efficient way of simulating various types of 2D structures. In this dissertation, this method is applied to a class of systems termed as 'Chiral structures' which have been shown to exhibit auxetic behaviour. In particular this work has concentrated on the trichiral, tetrachiral, hexachiral, anti-trichiral and anti-tetrachiral geometries. These structures were modelled using different sizes of interconnecting ligaments whilst keeping the sizes of the central nodes fixed. This work has shown that the stiffness of such systems, when subjected to uniaxial loads in tension, compression or shear, is highly dependent on the type of system, length of ligaments and the direction of loading. This dissertation also shows that, auxetic behaviour can be obtained by loading these structures from particular directions or by having a specific ligament to node ratio for the exception of the trichrial system. This work also explores a number of zeolite frameworks which were converted to their siliceous equivalents. These structures were modelled using the 'rigid rotating tetrahedra' approach which assumes that these frameworks are composed of highly rigid near perfect tetrahedra which deform through hinging I rotation. This is done through the use of a modified Burchart force field and by fixing the internal tetrahedral bonds and angles and by leaving out non-bond interactions from the energy expression. A number of siliceous frameworks are found to exhibit negative Poisson's ratios in particular the framework AHT which was shown to deform through the type II 'rotating rectangles' mechanism. Further work on a number of siliceous zeolite frameworks, focusing mainly on the effect of increasing rigidity of the tetrahedra, have yielded very interesting results where it is observed that an increase in rigidity is translated in an increase in auxetic character.