A Comparative Study on the Microstructures, Mineral Content, and Mechanical Properties of Non-Avian Reptilian Eggshells.

We analyze 214 freshly laid eggs belonging to 16 species across three orders of Class Reptilia. Using mechanical compression tests, we measure each egg's absolute stiffness (K, unit: N m-1) and relative stiffness (C number). The effective Young's modulus, E, was obtained by combining experimental and numerical methods. The mineral (CaCO3) content was measured by acid-base titration, the microstructures by scanning electron microscopy (SEM), and the crystallography by electron backscatter diffraction (EBSD). We find that the C number of reptilian eggs is, on average, higher than that of bird eggs, indicating that reptilian eggs are stiffer with respect to the egg mass than birds. However, Young's moduli of the reptilian eggshells (32.85 ± 3.48 GPa) are similar to those of avian eggshells (32.07 ± 5.95 GPa), even though those eggshells have different crystal forms, microstructures, and crystallography. Titration measurement shows that the reptilian eggshells are highly mineralized (>89% for nine Testudines species and 96% for Caiman crocodilus). Comparing the species with aragonite and calcite crystals, we find that calcite shells, including those of the Kwangsi gecko (inner part) and spectacled caiman (outer part), generally have larger grains than the aragonite ones. However, the grain size is not correlated to the effective Young's modulus. Also, as measured by the C number, the aragonite shells are, on average, stiffer than the calcite ones (except for the Kwangsi gecko), primarily due to their thicker shells.

Functional connections between bird eggshell stiffness and nest characteristics through risk of egg collision in nests.

Eggs and nests are two critical traits for the ecological success of birds. Their functional interactions, however, remain unclear. Here, we examined the functional connections between egg stiffness and nest attachment, site and structure for 1350 avian species. We revealed high eggshell stiffness for eggs in nests with a pensile attachment, located on non-tree vegetation or having a domed shape, suggesting that birds produce stiffer eggs in response to higher egg-collision risk in unstable or enclosed nests. Interdependence models suggested that the evolution of eggshell stiffness was more likely to be driven by than drive that of nest characters. Our results implied a trade-off between investment in competing for established nesting niches and producing stiff eggs to explore novel niches with high collision risk, possibly mediated by predation or thermoregulation. This study highlights an overlooked connection between nests and eggshells that may have broadened the ecological niches of birds.

Elastic Moduli of Avian Eggshell.

We analyze 700 freshly-laid eggs from 58 species (22 families and 13 orders) across three orders of magnitude in egg mass. We study the elastic moduli using three metrics: (i) effective Young's modulus, EFEM, by a combined experimental and numerical method; (ii) elastic modulus, Enano, by nanoindentation, and (iii) theoretical Young's modulus, Etheory. We measure the mineral content by acid-base titration, and crystallographic characteristics by electron backscatter diffraction (EBSD), on representative species. We find that the mineral content ranges between 83.1% (Zebra finch) and 96.5% (ostrich) and is positively correlated with EFEM-23.28 GPa (Zebra finch) and 47.76 GPa (ostrich). The EBSD shows that eggshell is anisotropic and non-homogeneous, and different species have different degrees of crystal orientation and texture. Ostrich eggshell exhibits strong texture in the thickness direction, whereas chicken eggshell has little. Such anisotropy and inhomogeneity are consistent with the nanoindentation tests. However, the crystal characteristics do not appear to correlate with EFEM, as EFEM represents an overall "average" elasticity of the entire shell. The experimental results are consistent with the theoretical prediction of linear elasticity. Our comprehensive investigation into the elastic moduli of avian eggshell over broad taxonomic scales provides a useful dataset for those who work on avian reproduction.

Correction to 'Cracking failure of curved hollow tree trunks'.

[This corrects the article DOI: 10.1098/rsos.200203.].

Cracking failure of curved hollow tree trunks.

Understanding the failure modes of curved hollow tree trunks is essential from both safety and conservation perspectives. Despite extensive research, the underlying mechanism that determines the cracking failure of curved hollow tree trunks remains unclear due to the lack of theoretical analysis that considers both the initial curvature and orthotropic material properties. Here we derive new mathematical expressions for predicting the bending moment, M crack, at which the cracking failure occurs. The failure mode of a tree species is then determined, as a function of t/R and cR, by comparing M crack with M bend, where t, R and c are, respectively, the trunk wall thickness, outer radius and initial curvature; M bend is the bending moment for conventional bending failure. Our equation shows that M crack is proportional to the tangential tensile strength of wood σT , increases with t/R, and decreases with the final cR. We analyse 11 tree species and find that hardwoods are more likely to fail in conventional bending, whereas softwoods tend to break due to cracking. This is due to the softwoods' much smaller tangential tensile strength, as observed from the data of 66 hardwoods and 43 softwoods. For larger cR, cracking failure is easier to occur in curvature-decreasing bending than curvature-increasing due to additional normal tensile force F acting on the neutral cross-section; on the other hand, for smaller cR, bending failure is easier to occur due to decreased final curvature. Our formulae are applicable to other natural and man-made curved hollow beams with orthotropic material properties. Our findings provide insights for those managing trees in urban situations and those managing for conservation of hollow-dependent fauna in both urban and rural settings.