Fig 1.
Sample orientation in the elephant tusk.
(a) System of reference of elephant tusk cross-sections considered in this paper with the longitudinal plane (L plane), the tangential plane (Ta plane) and the transverse plane (Tr plane) and the respective axial, tangential and radial direction, (b) optical image of a transverse section of the tusk showing the checkerboard Schreger pattern and (c) optical image of a longitudinal section showing the alternate parallel bright and dark bands of the Schreger pattern.
Fig 2.
(a) Cross-sections of the tusk cut at different angles (27°, 45° and 67°), (b-d) optical images of the surfaces of the 27°, 45° and 67° planes, (e) schematic variations of the shape of the Schreger pattern according to the cutting angle. The dark lines represent the Schreger lines and the gray forms represent the related Schreger rhomboid shapes.
Fig 3.
The Schreger pattern and the 2D tubular microstructure of the transverse plane.
(a) Schreger pattern of polished transverse section of the tusk, (b) and (c) higher magnifications of (a), (d) and (e) related microstructure observed by reflected light microscopy, (f) and (g) higher magnifications of (d) and (e). The yellow rectangles show the location of the different magnifications and the white dotted lines indicate the bright area of the Schreger pattern.
Fig 4.
Comparison between the gray values of regions of dots versus regions of lines in the transverse plane.
Histograms of the gray values of a region of dots and a region of lines (corresponding to dark and bright Schreger areas, respectively). Mean gray value and standard deviation of each selected area is indicated (0: black, 255: white).
Fig 5.
The Schreger pattern and the 2D tubular microstructure in the longitudinal plane.
(a) photography of a thin section with the visible Schreger bands indicated, (b) observation of this same section by transmitted light with the sinusoidal trend of tubules drawn, (c) magnified sinusoid trend observed by transmitted light of a thin section, (d) thick section observed by reflected light where the dark and bright bands were hardly visible, (e-g) magnifications of the insets indicated in (d).
Fig 6.
Relation between the orientation of tubules and the resulting shapes and average spacing of tubule cross-sections.
(a) Experimental observation under reflected light microscopy of a polished ivory section of the transverse plane, (b) Variation of the length of the cross-section of tubules depending on the cutting angle α, (c and d) 2D projections of the sectioned tubules with 0°< α < 90° of (c) the ordered cube where tubules are periodic and (d) the disordered cube where tubules are non-periodic. Average dot and line spacing are indicated in μm (line spacing = 120 μm/number of lines and dot spacing = √ (14400 μm2/number of dots) and (e) plot of the average dot spacing versus α.
Fig 7.
The 2D tubular microstructure of the tangential plane.
(a) Fractured section of the elephant tusk (1.6 cm away from the cement) with the impact of the fracture represented by the cross and the arrow, the transverse and tangential planes indicated and the Schreger lines and the Schreger line intersections of the transverse plane also displayed, (b) magnification of the tangential plane of (a), (c) area indicated in b between two Schreger line intersections and observed under SEM, and (d-g) magnification of the zones indicated in c.
Fig 8.
Representation of the 3D distorted helical model.
A set of helical tubules is represented. For the sake of the visualization of the model the diameter of the tubules and the spacing between them have been increased times 5 and 10 respectively. However, the dimension of the helices and the continuous phase shift of π after 1 mm are properly scaled. From the red tubule to the turquoise one the continuous phase shift of π after 1 mm is observed.
Fig 9.
2D sections of the transverse, the longitudinal and the tangential planes of (a) the experimental data, (b) the Miles and White model and (c) the Miles and White model with a phase shift (PS) of π/2 after 500 μm instead of π and (d) the Virág model.
The parameters used for Miles and White model were sinusoids with 250 sin(2π / 1000t) as equation with a diameter of 2 μm, 6 μm spaced and having one stepwise tubule PS of π after 500 μm; for Virág model: sinusoids with 300 sin(2π / 1000 t) as equation with a diameter of 2 μm, spaced by 13 μm and having one continuous PS of π after 1 mm and a stepwise one of π after 500 μm. Under every 2D section five magnified areas (34 x 34 μm2) are shown.
Fig 10.
2D sections of the transverse, the longitudinal and the tangential planes of the helical model.
(a) without phase shift (PS) of the tubules, (b) with continuous PS of π after 1 mm and (c) with both a continuous PS of π after 1 mm and a stepwise PS of π after 500 μm.
Table 1.
Summary table of the experimental parameters compared to the ones obtained with the different 3D models.