Fig. 2
From: Mathematical modeling of auxetic systems: bridging the gap between analytical models and observation
The system being modelled which in general could have non-equal lengths and non-equal angles, but in this case, it shall be assumed that the system will have l1 = l2 = l and l3 = h (kept constant), and θ1 = θ2 = θ (a variable). For the purpose of this study, the system will only be uniaxially loaded in the vertical Ox2 direction and the ligaments will not be allowed to stretch, flex or move out of plane, i.e. θ is the only variable. Note that the parameters are defined in (a) whilst (b) shows various representations with the possible unit cells identified where (b-i) shows a re-entrant system, (b-ii) shows a non-re-entrant conventional honeycomb and (b-iii) shows a sheared system (or an irregular non-symmetric honeycomb). All of these conformations can be represented by the unit cells. Note that the convention being used to label θ is not the same as that used in previous work by (Abd El-Sayed et al., 1979; Evans et al., 1995; Gibson et al., 1982; Masters & Evans, 1996)