Echinoderms: Hierarchically Organized Light Weight Skeletons

Nebelsick, James H.; Dynowski, Janina F.; Grossmann, Jan Nils; Tötzke, Christian

doi:10.1007/978-94-017-9398-8_8

Cited by 21 publications

(23 citation statements)

References 77 publications

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“…The echinoid’s skeleton is a hierarchical multi-element construction ( Fig 1 ), consisting of numerous individual skeletal parts, including the plates from which the test (shell) is formed, spines, skeletal discs of the tube-feet, and skeletal elements of the pedicellariae [ 1 , 2 ] These minute skeletal elements are constructed of the stereom, which resembles a micro-beam system ( Fig 1D ). The stereom of the echinoid spines has been investigated for its structural design [ 3 – 6 ] and mechanical performance [ 6 – 8 ] using both 2-dimensional (2d) images and 3-dimensional (3d) models.…”

Section: Introductionmentioning

confidence: 99%

Structural design of the echinoid’s trabecular system

Grun

Nebelsick

2018

PLoS ONE

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The multi-plated skeleton of echinoids is made of the stereom, a light-weight construction which resembles a micro-beam framework. Although the two-dimensional design of the stereom has been studied, its spatial architecture is only little known. It is, however, imperative to understand the spatial architecture of the trabecular system in order to interpret its structural principles of this load-bearing construction. The echinoid’s trabecular system is thus analyzed in-depth with respect to eight topological descriptors. The echinoid’s plates are divided into two regions, the center of which consists of an unordered stereom, and the margin which consists of an ordered stereom. The eight trabecular descriptors indicate that the basal topology of the two plate regions are similar. The trabecular system predominantly consists of short and stocky trabeculae that show little tortuosity. The majority of trabeculae intersect in a 3N configuration, where three trabeculae intersect in one common node. Trabeculae in the 3N configuration intersect in an angle of around 120° resulting in a planar and triangular motif. These planar elements, when arranged in an angular off-set, can resist multi-dimensional loads. Results also show that the trabecular orientation perpendicular to the plate’s surface is at an angle of 60°. The trabecular orientation in the plate’s horizontal plane is directional. Both trabecular orientations reflect a construction which is capable of resisting applied loads and can distribute these loads over the entire skeleton. The spatial architecture of the echinoid’s trabecular system is thus considered to be a performative light-weight and load-bearing system.

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Section: Introductionmentioning

confidence: 99%

Structural design of the echinoid’s trabecular system

Grun

Nebelsick

2018

PLoS ONE

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“…For example, clypeasteroid echinoid tests include internal supports which connect oral and apical plates (Nebelsick et al . ), which would require representation by a non‐planar graph. The number of possible planar graphs is extremely large for even moderate numbers of plate vertices (Table ).…”

Section: Resultsmentioning

confidence: 99%

Fullerene‐like structures of Cretaceous crinoids reveal topologically limited skeletal possibilities

Cuthill

Hunter

2020

Palaeontology

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There are few cases where numbers or types of possible phenotypes are known, although vast state spaces have been postulated. Rarely applied in this context, graph theory and topology enable enumeration of possible phenotypes and evolutionary transitions. Here, we generate polyhedral calyx graphs for the Late Cretaceous, stemless crinoids Marsupites testudinarius and Uintacrinus socialis (Uintacrinoidea Zittel) revealing structural similarities to carbon fullerene and fulleroid molecules (respectively). The U. socialis calyx incorporates numerous plates (e.g. graph vertices |V| ≥ 197), which are small, light, low-density and have four to eight sides. Therefore, the corresponding number of possible plate arrangements (number of polyhedral graphs) is large (≫1 9 10 14 ). Graph vertices representing plates with sides >6 introduce negative Gaussian curvature (surface saddle points) and topological instability, increasing buckling risk. However, observed numbers of vertices for Uintacrinus do not allow more stable pentaradial configurations. In

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“…The echinoid skeleton typically represents a light-weight structure [ 18 ]. The overall test density and thus the amount of structural material in the test of E. pusillus are less than 50%.…”

Section: Discussionmentioning

confidence: 99%

Structural design of the minute clypeasteroid echinoidEchinocyamus pusillus

Grun

Nebelsick

2018

R. Soc. open sci.

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The clypeasteroid echinoid skeleton is a multi-plated, light-weight shell construction produced by biomineralization processes. In shell constructions, joints between individual elements are considered as weak points, yet these echinoid skeletons show an extensive preservation potential in both Recent and fossil environments. The remarkable strength of the test is achieved by skeletal reinforcement structures and their constructional layouts. Micro-computed tomography and scanning electron microscopy are used for microstructural and volumetric analyses of the echinoid's skeleton. It is shown that strengthening mechanisms act on different hierarchical levels from the overall shape of the skeleton to skeletal interlocking. The tight-fitting and interlocking plate joints lead to a shell considered to behave as a monolithic structure. The plate's architecture features distinct regions interpreted as a significant load-transferring system. The internal support system follows the segmentation of the remaining skeleton, where sutural layout and stereom distribution are designed for effective load transfer. The structural analysis of the multi-plated, yet monolithic skeleton of Echinocyamus pusillus reveals new aspects of the micro-morphology and its structural relevance for the load-bearing behaviour. The analysed structural principles allow E. pusillus to be considered as a role model for the development of multi-element, light-weight shell constructions.

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Echinoderms: Hierarchically Organized Light Weight Skeletons

Cited by 21 publications

References 77 publications

Structural design of the echinoid’s trabecular system

Structural design of the echinoid’s trabecular system

Fullerene‐like structures of Cretaceous crinoids reveal topologically limited skeletal possibilities

Structural design of the minute clypeasteroid echinoidEchinocyamus pusillus

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