Abstract
We demonstrate the complexity that can exist in the modelling of auxetic lattices. By introducing pin-jointed members and large deformations to the analysis of a re-entrant structure, we create a material which has both auxetic and non-auxetic phases. Such lattices exhibit complex equilibrium behaviour during the highly nonlinear transition between these two states. The local response is seen to switch many times between stable and unstable states, exhibiting both positive and negative stiffnesses. However, there is shown to exist an underlying emergent modulus over the transitional phase, to describe the average axial stiffness of a system comprising a large number of cells.
| Original language | English |
|---|---|
| Article number | 20180720 |
| Pages (from-to) | 1-15 |
| Number of pages | 15 |
| Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |
| Volume | 475 |
| Issue number | 2224 |
| DOIs | |
| Publication status | Published - 3 Apr 2019 |
Funding
Data accessibility. This article has no additional data. Authors’ contributions. This piece of work represents an equal collaboration in all aspects of the paper. Competing interests. There are no competing interests. Funding. This work was supported by The Alan Turing Institute under the EPSRC grant EP/N510129/1. Acknowledgements. There are no acknowledgements in this paper.
Keywords
- Auxetic
- Bifurcation
- Complex system
- Emergence
- Phase transforming
ASJC Scopus subject areas
- General Mathematics
- General Engineering
- General Physics and Astronomy