Finite Element Modeling of Shell Shape in the Freshwater Turtle Pseudemys concinna Reveals a Trade-Off between Mechanical Strength and Hydrodynamic Efficiency

Aquatic species can experience different selective pressures on morphology in different flow regimes. Species inhabiting lotic regimes often adapt to these conditions by evolving low-drag (i.e., streamlined) morphologies that reduce the likelihood of dislodgment or displacement. However, hydrodynamic factors are not the only selective pressures influencing organismal morphology and shapes well suited to flow conditions may compromise performance in other roles. We investigated the possibility of morphological trade-offs in the turtle Pseudemys concinna. Individuals living in lotic environments have flatter, more streamlined shells than those living in lentic environments; however, this flatter shape may also make the shells less capable of resisting predator-induced loads. We tested the idea that ‘‘lotic’’ shell shapes are weaker than ‘‘lentic’’ shell shapes, concomitantly examining effects of sex. Geometric morphometric data were used to transform an existing finite element shell model into a series of models corresponding to the shapes of individual turtles. Models were assigned identical material properties and loaded under identical conditions, and the stresses produced by a series of eight loads were extracted to describe the strength of the shells. ‘‘Lotic’’ shell shapes produced significantly higher stresses than ‘‘lentic’’ shell shapes, indicating that the former is weaker than the latter. Females had significantly stronger shell shapes than males, although these differences were less consistent than differences between flow regimes. We conclude that, despite the potential for many-to-one mapping of shell shape onto strength, P. concinna experiences a trade-off in shell shape between hydrodynamic and mechanical performance. This trade-off may be evident in many other turtle species or any other aquatic species that also depend on a shell for defense. However, evolution of body size may provide an avenue of escape from this trade-off in some cases, as changes in size can drastically affect mechanical performance while having little effect on hydrodynamic performance.

Anisotropy in plastic deformation of extruded magnesium alloy sheet during tensile straining at high temperature

Experimental measurements are used to characterize the anisotropy of flow stress in extruded magnesium alloy AZ31 sheet during uniaxial tension tests at temperatures between 350°C and 450°C, and strain rates ranging from 10-5 to 10-2 s-1. The sheet exhibits lower flow stress and higher tensile ductility when loaded with the tensile axis perpendicular to the extrusion direction compared to when it is loaded parallel to the extrusion direction. This anisotropy is found to be grain size, strain rate, and temperature dependent, but is only weakly dependent on texture. A microstructure based model (D. E. Cipoletti, A. F. Bower, P. E. Krajewski, Scr. Mater., 64 (2011) 931–934) is used to explain the origin of the anisotropic behavior. In contrast to room temperature behavior, where anisotropy is principally a consequence of the low resistance to slip on the basal slip system, elevated temperature anisotropy is found to be caused by the grain structure of extruded sheet. The grains are elongated parallel to the extrusion direction, leading to a lower effective grain size perpendicular to the extrusion direction. As a result, grain boundary sliding occurs more readily if the material is loaded perpendicular to the extrusion direction.