Flexible sutures reduce bending moments in shells: from the echinoid test to tessellated shell structures

Abstract

In the field of structural engineering, lightweight and resistant shell structures can be designed by efficiently integrating and optimizing form, structure and function to achieve the capability to sustain a variety of loading conditions with a reduced use of resources. Interestingly, a limitless variety of high-performance shell structures can be found in nature. Their study can lead to the acquisition of new functional solutions that can be employed to design innovative bioinspired constructions. In this framework, the present study aimed to illustrate the main results obtained in the mechanical analysis of the echinoid test in the common sea urchin Paracentrotus lividus (Lamarck, 1816) and to employ its principles to design lightweight shell structures. For this purpose, visual survey, photogrammetry, three-dimensional modelling, three-point bending tests and finite-element modelling were used to interpret the mechanical behaviour of the tessellated structure that characterize the echinoid test. The results achieved demonstrated that this structural topology, consisting of rigid plates joined by flexible sutures, allows for a significant reduction of bending moments. This strategy was generalized and applied to design both free-form and form-found shell structures for architecture exhibiting improved structural efficiency.

Constructional design of echinoid endoskeleton: main structural components and their potential for biomimetic applications

“…μCT and photogrammetry), digital modelling and simulation, e.g. FEA are recently being adopted, providing novel answers to questions about test morphology, functional performance and mechanical behaviour (figure 5) [46,55,57,60,138,141,164,165]. As pioneers in this field, Philippi and Nachtigall (1996) conducted FEA-analysis describing the behaviour of the regular echinoid test (Echinus esculentus) under diverse loads [60].…”

“…A general bottom-up is here simplified in five key steps [74]; in addition, a case study on Paracentrotus lividus's test is used as an example [141,165]. (1) Identification of a biological model, usually identifiable on the basis of an analogy of function and of problem solving related to the final application: P. lividus test model as a shell structure enduring environmental mechanical stress.…”

Programming quadric metasurfaces via infinitesimal origami maps of monohedral hexagonal tessellations: Part I

“…The echinoid shell constitutes one of those examples. In [16], it was shown that the sutured hexagonal shell tessellation of the echinoid is a more efficient load-carrying structure with respect to a continuum doubly curved shell of same constitution. Interestingly, the difference between the principal curvatures in echinoid shells is qualitatively reproduced by the tessellated plates studied in [15] made of similarly elongated hexagonal tiles.…”

“…In other studies evaluated the mechanical response of tessellations appearing in the carapace of boxfishes [17], plant seedcoats [18] and in the cartilage of stingrays [19]. It is worth recalling that 3-valent tessellated geometries emerge also in the pattern of yield lines in the failure mechanisms of simply supported plates subjected to transverse loads [20], a fact which, in light of the findings in [15,16], surmises that 3-valent sutured tessellations in biological structures could have originated as a response to structural cracking to improve their strength, or/and to better conform to doubly curved surfaces. In this line of thought, Fratzl et al [21] reviewed several cases of structural tessellations combining stiffness, strength and flexibility.…”

Echinoid skeleton: an insight on the species-specific pattern of the Paracentrotus lividus plate and its microstructural variability

“…The particular domeshaped and tessellated test of the regular echinoids has attracted the attention of researchers from different fields of science [1,[4][5][6][7]. The test has a mesodermal origin and, with the exception of the imbricate-plated tests of the Palaeozoic species, diadematoids and echinothurioids, it is composed of a series of calcitic skeletal plates joined by skeletal interlocks and collagenous sutures (sutural collagen fibres) [8][9][10]. These plates are arranged in ten double vertical columns, representing alternating five ambulacral zones and five interambulacral zones [11].…”