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HW5 HW3 HW1 SW5 SW3 SW1
0.0 0.3 0.6 0.9
15
15
12
HW5R HW3R HW1R SW5R SW3R SW1R HW5R+ HW3R+ HW1R+ SW5R+ SW3R+ SW1R+
9
-1.8 -1.5 -1.2 -0.9 -0.6 -0.3
12
6
9
3
0
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6
-3
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0 1 2 3 4 5
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-3 -2 -1
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Axial strain (%)
Figure4. Thickness strain versus axial strain plots for all handsheets. Each datapoint represents the average thickness strain of fi ve specimens. Standard deviation in the thickness strain measurement appears shaded above and below the datapoint. (Left) plots for all samples with an inset for thickness strain below 0.8% strain. (Right) top fi gure shows plots for softwood handsheets and bottom fi gure shows plots for hardwood handsheets. Softwood samples are represented by yellow and hardwoods by blue. Larger squares indicate thicker samples. Open squares indicate unre fi ned handsheets, while lightly shaded and solid squares indicate re fi ned and heavily-re fi ned handsheets, respectively.
until θ = θ 0 and then increase while θ < θ 0 . See Figure 5(d2). 2) Free segments at fi ber ends or those resulting from shorter, breaking, or splitting of fi bers will, at least directly, not participate in the auxetic mechanism (Figure 5(d3)). 3) Any free space between local auxetic units will not help the load to propagate between units and through paper, mitigating the auxetic response (Figure 5(d4)). 4) Flatter or smaller fi bers (with lower d ) may simultaneously result in a lower fi ber spacing ( x 0 ), thereby not resulting in an enhanced auxetic response, as one would expect from a lower d alone (Figure 5(d5)). 5) Fiber segments between contacts may not be fully extended initially (length larger than l ) and will consume the initial strain on the sample to get to a fully extended state fi rst, before pushing the contacts, thereby also mitigating the auxetic response (Figure 5(d6)). Keeping these factors in mind, we are now able to look at our experimental fi ndings more closely.
straightened. In simple geometrical terms, a fi ber segment can be seen as hinged at one end, pushing the contact point at the other end, such that the locus of the other end is a circle of radius l . The model in Figure 5a could be seen as two auxetic units lying side by side along the x -axis. Given this model, the effects of vary- ing d and x 0 were calculated, and a few of those have been plotted in Figure 5c. It is evident that decreasing d or increasing x 0 enhances the auxetic response; however, there are more factors at play when considering a structure that departs from the ideal one shown in Figure 5a.
3.1.1. Mechanistic Factors
1) The starting fi ber arrangement could be such that θ is larger than θ 0 (tan θ 0 = d/x 0 ), and the locus of the contact point is still a circle of radius l . [5,9] In this case, the thickness will fi rst decrease
2400589 (6 of 10)
Phys. Status Solidi B 2025 , 2400589
© 2025 The Author(s). physica status solidi (b) basic solid state physics published by Wiley-VCH GmbH
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