Linear and non-linear in-plane behaviour of a modified re-entrant core cell

In this paper, a work to improve to the auxetic re-entrant cell is reported. This work aims to conserve the negative or zero Poisson?s ratio feature of the classical re-entrant cell with no degradation while amplifying the in-plane elastic moduli. To develop and control the stiffness of the cell a new cell was created using a circular wall element in the middle of the classical re-entrant cell. The analytical expressions of the new re-entrant cell were derived and validated by finite element models. Derived analytical expressions of this work can be used to model the classical cell. Using this feature, validation of analytical and numerical models of this work is also provided with a classical cell?s experimental works reported in the literature. In the linear region, both the analytical and the finite element models match very closely with the literature experiments. Because of the highly non-linearity of the re-entrant structures, after the linear examination, this work was expanded to model the non-linear behaviour of both the classical and new cells numerically. Literature experiments also verify the non-linear finite element models of this work in means of the classical re-entrant cell?s results. Detailed design graphs are given for tuning the rigidity and negative Poisson?s ratios. The presented new design in this paper grants an extra rigidity while providing the same negative Poisson?s ratios with those of the classical cells.

Automated summary

This paper presents a method to improve the auxetic re-entrant cell by conserving negative or zero Poisson's ratio feature while enhancing stiffness. A new design element was introduced to achieve this improvement, with analytical expressions and finite element models used for validation. The results show that the new design provides additional rigidity while maintaining negative Poisson's ratios.