Suture interfaces with a triangular wave form commonly found in nature have recently been shown to exhibit exceptional mechanical behavior, where geometric parameters such as amplitude, frequency, and hierarchy can be used to nonlinearly tailor and amplify mechanical properties In this study, using the principle of complementary virtual work, we formulate a generalized, composite mechanical model for arbitrarily-shaped interdigitating suture interfaces in order to more broadly investigate the influence of wave-form geometry on load transmission, deformation mechanisms, anisotropy, and stiffness, strength, and toughness of the suture interface for tensile and shear loading conditions The application of this suture interface model is exemplified for the case of the general trapezoidal wave-form Expressions for the in-plane stiffness, strength and fracture toughness and failure mechanisms are derived as nonlinear functions of shape factor β (which characterizes the general trapezoidal shape as triangular, trapezoidal, rectangular or anti-trapezoidal), the wavelength/amplitude ratio, the interface width/wavelength ratio, and the stiffness and strength ratios of the skeletal/interfacial phases These results provide guidelines for choosing and tailoring interface geometry to optimize the mechanical performance in resisting different loads The presented model provides insights into the relation between the mechanical function and the morphological diversity of suture interface geometries observed in natural systems

http://web.mit.edu/cortiz/www/YaningJMPS2013.pdf

A generalized mechanical model for suture interfaces of arbitrary geometry

A major goal in evolutionary biology is to understand the processes that shape the evolutionary trajectory of clades. The repeated and similar large-scale morphological evolutionary trends of distinct lineages suggest that adaptation by means of natural selection (functional constraints) is the major cause of parallel evolution, a very common phenomenon in extinct and extant lineages. However, parallel evolution can result from other processes, which are usually ignored or difficult to identify, such as developmental constraints. Hence, understanding the underlying processes of parallel evolution still requires further research. Herein, we present a possible case of parallel evolution between two ammonoid lineages (Auguritidae and Pinacitidae) of Early-Middle Devonian age (405-395 Ma), which are extinct cephalopods with an external, chambered shell. In time and through phylogenetic order of appearance, both lineages display a morphological shift toward more involute coiling (i.e. more tightly coiled whorls), larger adult body size, more complex suture line (the folded walls separating the gas-filled buoyancy-chambers), and the development of an umbilical lid (a very peculiar extension of the lateral shell wall covering the umbilicus) in the most derived taxa. Increased involution toward shells with closed umbilicus has been demonstrated to reflect improved hydrodynamic properties of the shell and thus likely results from similar natural selection pressures. The peculiar umbilical lid might have also added to the improvement of the hydrodynamic properties of the shell. Finally, increasing complexity of suture lines likely results from covariation induced by trends of increasing adult size and whorl overlap given the morphogenetic properties of the suture. The morphological evolution of these two Devonian ammonoid lineages follows a near parallel evolutionary path for some important shell characters during several million years and through their phylogeny. Evolution of some traits (involution, umbilical lid) appears to be mainly driven by adaptation to improve the hydrodynamic properties of the shell, whereas other characters (sutural complexity) evolved due to covariation with features that play a central role in the morphogenesis of mollusc shells. This example provides evidence that parallel evolution can be driven simultaneously by different factors such as covariation (constructional constraints) and adaptation (natural selection).

/pdf/parallel-evolution-controlled-by-adaptation-and-covariation-42rym633kd.pdf

Parallel evolution controlled by adaptation and covariation in ammonoid cephalopods

The evolution of complexly folded septa in ammonoids has long been a controversial topic. Explanations of the function of these folded septa can be divided into physiological and mechanical hypotheses with the mechanical functions tending to find widespread support. The complexity of the cephalopod shell has made it difficult to directly test the mechanical properties of these structures without oversimplification of the septal morphology or extraction of a small sub-domain. However, the power of modern finite element analysis now permits direct testing of mechanical hypothesis on complete, empirical models of the shells taken from computed tomographic data. Here we compare, for the first time using empirical models, the capability of the shells of extant Nautilus pompilius, Spirula spirula, and the extinct ammonite Cadoceras sp. to withstand hydrostatic pressure and point loads. Results show hydrostatic pressure imparts highest stress on the final septum with the rest of the shell showing minimal compression. S. spirula shows the lowest stress under hydrostatic pressure while N. pompilius shows the highest stress. Cadoceras sp. shows the development of high stress along the attachment of the septal saddles with the shell wall. Stress due to point loads decreases when the point force is directed along the suture as opposed to the unsupported chamber wall. Cadoceras sp. shows the greatest decrease in stress between the point loads compared to all other models. Greater amplitude of septal flutes corresponds with greater stress due to hydrostatic pressure; however, greater amplitude decreases the stress magnitude of point loads directed along the suture. In our models, sutural complexity does not predict greater resistance to hydrostatic pressure but it does seem to increase resistance to point loads, such as would be from predators. This result permits discussion of palaeoecological reconstructions on the basis of septal morphology. We further suggest that the ratio used to characterize septal morphology in the septal strength index and in calculations of tensile strength of nacre are likely insufficient. A better understanding of the material properties of cephalopod nacre may allow the estimation of maximum depth limits of shelled cephalopods through finite element analysis.

Comparative cephalopod shell strength and the role of septum morphology on stress distribution

A major goal in evolutionary biology is to characterize and understand the patterns and processes that shape the evolutionary trajectory of clades through time and space. One common pattern in extinct and extant lineages is the pervasive occurrence of persistent phenotypic evolutionary trends. These trends of evolutionary lineages suggest that adaptation by means of natural selection is a major cause of homoplastic patterns such as convergence and parallel evolution. Such patterns can result from other processes, which are usually ignored or difficult to identify, such as chance, environmental changes, constructional or developmental constraints. How the evolution of organisms follows preferentially specific phenotypic trajectories remains poorly known. The ammonoids are well-known to display persistent phenotypic shifts through time. Commonly described trends in ammonoid lineages are increase in adult size, changes in coiling and increase in suture frilling. Some new methods for the study of ammonoid evolution are here exemplified by recent case studies.

Evolutionary Patterns of Ammonoids: Phenotypic Trends, Convergence, and Parallel Evolution

Most planispirally and regularly coiled ammonoid species show to varying degrees continuous morphological intraspecific variation of their shell. In many species, individuals range from slender, involute, compressed, and weakly ornamented forms to “robust” forms, which are more evolute, more depressed, and with coarser ornamentation. Additionally, more compressed shells tend to have more complex sutures. Within a species from a single sample, the frequency of these variants is represented by a continuous unimodal distribution (often normal). These covariation patterns of intraspecific variation have been abundantly documented and were coined “Buckman’s Laws of Covariation”. These rules help to delineate ammonoid morphospecies. This interdependent morphological variation suggests that shell morphogenesis may not be random but constrained either by adaptive constraints or simple constructional scaling rules. The cause(s) remain debated. Hence, although Buckman’s rules of covariation are now widely documented and acknowledged, several aspects of their scope and limits still remain to be investigated.

Buckman’s Rules of Covariation

Several hypotheses have been put forward to explain the sinuosity and complexity of suture lines in Ammonoidea. At present, the two principal opponent views maintain either that high complexity was a requisite to reinforce the shell in response to hydrostatic pressure, or that complexity augmented the attachment area for muscles. By using finite element calculations and analytical estimates of simplified ammonoid shell geometries, it is shown that complex suture lines reduced dramatically the strain and the stress in the phragmocone. The calculations lend support to the hypothesis that high sinuosity is an evolutionary response to external pressure. Additionally, it is found that without complex septa, the inward deformation of an ammonoid with thin shell would cause it to shrink in response to pressure and to lose buoyancy by a non-negligible amount.

Fabio Vittorio De Blasio

Papers

The role of suture complexity in diminishing strain and stress in ammonoid phragmocones