Empirical modelling using dummy atoms (EMUDA): an alternative approach for studying “auxetic” structures

Abstract

Auxetics (materials or structures) are systems with a negative Poisson's ratio, a property that arises from the way various geometric features in the structure (or internal structure in the case of materials) deform when subjected to uniaxial loads. Such systems are normally studied by examining the behaviour of idealised representations of structures, which deform in a controlled fashion (e.g. deforming solely through hinging or stretching). Methods used for the analysis typically involve construction of real physical macro-models and/or derivation of analytical expressions for the mechanical properties. This paper proposes an alternative method for analysing such structures whereby idealised “hinging” or “stretching” structures are constructed within a molecular modelling environment using dummy atoms and examined using standard molecular mechanics techniques. We will show that this methodology of “empirical modelling using dummy atoms” (EMUDA) successfully reproduces the known properties of 2D conventional and auxetic hexagonal honeycombs hence confirming the suitability of this technique for studying auxetic structures.

Keywords:

• Auxetic
• Negative Poisson's ratio
• Honeycomb
• Modelling
• EMUDA

Acknowledgements

The work of Pierre-Sandre Farrugia is gratefully acknowledged.

Notes

^† In reality, one would also expect that the “rod elements” will “flex” to some extent, but the flexure mode of deformation [29] is not being included in these simulations due to the difficulty to represent flexure through the EMUDA methodology.

^† It should be noted that the simplified labelling system using only two different “atom types” (A and B) as shown in figure 2b could be used since this simplified labelling system still permits the differentiation between the “bonds” of length l (i.e. bonds A–B) from the “bonds” of length h (i.e. bonds A–A and B–B) whilst all the A–B–B and A–A–B bond angles refer to θ-angles.