Fig. 5
From: Locally-curved geometry generates bending cracks in the African elephant skin
The physical model captures qualitative and quantitative features of the cracked skin pattern. a, b Crack junctions on the elephant skin (arrows in a) and in simulations (b) typically display an angular profile with a small (<90°) and two large (>135°) angles. Propagating cracks tend to avoid the centre of trough junctions (black dot in b) because of the heterogeneous strain distribution at the intersection (Supplementary Fig. 9). c There is a good fit between the probability density functions (PDFs) of the angular distribution of real skin (red line, N = 2997) and simulated (green line, N = 966) cracks, whereas they differ markedly from that of trough angles (black line, N = 3645). Shaded regions represent 95% confidence intervals. Inset: probability of finding an angle between 100° and 140°; mean (error bars = s.d.) among 7 PDFs of observed cracks (red, Supplementary Tables 3 and 4), 5 PDFs of simulated cracks (green, average of 193 angles per PDF) and 6 PDFs of observed troughs (grey, Supplementary Tables 2 and 4). d Angular scatter plot (shaded regions represent 50% confidence regions, see Methods) showing the 2D average and angular spreading of the first two angles of skin crack junctions (red point, N = 999), simulated crack junctions (green square, N = 322) and trough junctions (black star, N = 1215). The similarly oriented and dispersed angular profiles of skin and simulated crack junctions contrast with the ‘triple-120°’ trough profile. Inset: angular spreadings of crack and trough junctions; mean (error bars = s.d.) among 7 angular scatter plots of observed cracks (red, Supplementary Tables 3 and 4), 5 plots of simulated cracks (green, average of 64 vertices per plot) and 6 plots of observed troughs (grey, Supplementary Tables 2 and 4). e, f Rare cases of cracks propagating outside the troughs (arrowheads) in elephant’s skin (e) and simulations (f). g, h Our physical model reproduces in silico the observed sheet alignment; yellow and dark blue lines represent the simulation surface, while the remaining sheets (red and light blue) form the thickness of the stratum corneum. The innermost uncracked sheets of stratum corneum are accounted for in the simulations (see supplementary text). i Top view of a crack (the dashed line indicates where the ‘virtual section’ (g, h) was cut)
