Grun TB et al. (2018), Structural stress response of segmented natural...

ECB-ART-46405

J R Soc Interface 2018 Jun 01;15143:. doi: 10.1098/rsif.2018.0164.

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Structural stress response of segmented natural shells: a numerical case study on the clypeasteroid echinoid Echinocyamus pusillus.

Grun TB , von Scheven M , Bischoff M , Nebelsick JH .

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The skeleton of Echinocyamus pusillus is considered as an exceptional model organism for structural strength and skeletal integrity within the echinoids as demonstrated by the absence of supportive collagenous fibres between single plates and the high preservation potential of their skeletons. The structural principles behind this remarkably stable, multi-plated, light-weight construction remain hardly explored. In this study, high-resolution X-ray micro-computed tomography, finite-element analysis and physical crushing tests are used to examine the structural mechanisms of this echinoid''s skeleton. The virtual model of E. pusillus shows that the material is heterogeneously distributed with high material accumulations in the internal buttress system and at the plate boundaries. Finite-element analysis indicates that the heterogeneous material distribution has no effect on the skeleton''s strength. This numerical approach also demonstrates that the internal buttress system is of high significance for the overall skeletal stability of this flattened echinoid. Results of the finite-element analyses with respect to the buttress importance were evaluated by physical crushing tests. These uniaxial compression experiments support the results of the simulation analysis. Additionally, the crushing tests demonstrate that organic tissues do not significantly contribute to the skeletal stability. The strength of the echinoid shell, hence, predominantly relies on the structural design.

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	Figure 1. Micro CT rendering of E. pusillus from Giglio island, Italy. (a) Skeleton in aboral view. The ambulacral system and microstructures such as the tubercles and glassy tubercles are visible. (b) Skeleton in oral view with the prominent peristome and periproct visible. (c) Top view of the oral side. The internal supports are visible, as well as the basicoronal ring around the peristome. (d) View on the inner part of the aboral side. Pores and the limits of the buttresses are visible. ap, ambulacral pore; bd, distal region of the buttress; bp, proximal area of the buttress; br, basicoronal ring; bs, buttress; gp, genital pore; gt, glassy tubercle; pl, petal; ps, peristome; pt, plate thickening; pp, periproct; su, suture; tr, transversal ridge; tu, tubercle. Scale bar, 500 µm.
	Figure 2. Colour-coded 3D rendering of E. pusillus. (a) Section showing the material distribution within the plates and the internal supports in horizontal and oblique view. Red indicates high material densities at the outer surface (tubercles and glassy tubercles), sutures and within the buttress system. (b) Frontal section of the skeleton. Plate centres are dominated by a low material density (green). (c) The lateral section shows that material densities are similarly distributed along the longitudinal axis. (d) A detailed section of a single buttress shows that the material density is highest (red) in direction to the peristome and along the suture areas. The average stereom of the buttress is dominated by intermediate dense (yellow) material. Scale bar, 500 µm.
	Figure 3. Voxel model of E. pusillus. (a) Original geometry including the buttresses and heterogeneous material distribution. (b) Modified geometry without the buttresses and heterogeneous material distribution.
	Figure 4. Undeformed (grey) and deformed (coloured) section of the voxel model of E. pusillus. Deformation is scaled by a factor of 25. The colours show the magnitude of the vertical displacement. (a) Original geometry including the buttresses with heterogeneous material distribution. (b) Original geometry including the buttresses with homogeneous material distribution. (c) Modified geometry without the buttresses with heterogeneous material distribution. (d) Modified geometry without the buttresses with homogeneous material distribution.
	Figure 5. Contour plot of the Cauchy stresses in z direction in a section of the voxel model of E. pusillus. (a) Original geometry including the buttresses with heterogeneous material distribution. (b) Original geometry including the buttresses with homogeneous material distribution. (c) Modified geometry without the buttresses with heterogeneous material distribution. (d) Modified geometry without the buttresses with homogeneous material distribution.
	Figure 6. Contour plot of the Cauchy stresses in y direction in a section of the voxel model of E. pusillus. (a) Original geometry including the buttresses with heterogeneous material distribution. (b) Original geometry including the buttresses with homogeneous material distribution. (c) Modified geometry without the buttresses with heterogeneous material distribution. (d) Modified geometry without the buttresses with homogeneous material distribution.
	Figure 7. Box plots of statistical analyses for the load-bearing capacity of the skeleton along three treatment groups. (a) Skeleton length comparison indicating that the analysed skeletons are of similar size classes along the treatment groups. (b) The comparison of force applied until structural failure occurs indicates that buttressing is a structurally importantly parameter.

References [+] :

Grun, Structural design of the minute clypeasteroid echinoid Echinocyamus pusillus. 2018, Pubmed, Echinobase