The skeletal plates of echinoids consist of a peculiar lightweight structure, called stereom, which is organized in a porous three-dimensional lattice-like meshwork. The stereom is characterized by an extremely complex and diverse microarchitecture, largely varying not only from species to species but also among different test plates. It consists of different basic types combined in extremely different ways according to specific functional needs, creating species-specific structural patterns. These patterns can lead to specific mechanical behaviours, which can inspire biomimetic technology and design development. In this framework, the present study aimed to characterize the species-specific pattern of the Paracentrotus lividus interambulacral plate and the main microstructural features regarding its geometrical variability and mechanical responses. The results achieved quantitatively highlighted the differences between the analysed stereom types providing new insights regarding their topological configuration and isotropic and anisotropic behaviour. Interestingly, data also revealed that the galleried stereom present at the tubercle is significantly different from the one located at the suture. These analyses and findings are encouraging and provide a starting point for future research to unravel the wide range of mechanical strategies evolved in the echinoid skeletal structure.

Creases are purposely introduced to thin structures for designing deployable origami, artistic geometries, and functional structures with tunable nonlinear mechanics. Modeling the mechanics of creased structures is challenging because creases introduce geometric discontinuity and often have complex mechanical responses due to local material damage. In this work, we propose a continuous description of the sharp geometry of creases and apply it to the study of creased annuli, made by introducing radial creases to annular strips with the creases annealed to behave elastically. We find that creased annuli have generic bistability and can be folded into various compact shapes, depending on the crease pattern and the overcurvature of the flat annulus. We use a regularized Dirac delta function (RDDF) to describe the geometry of a crease, with the finite spike of the RDDF capturing the localized curvature. Together with anisotropic rod theory, we solve the nonlinear mechanics of creased annuli, with its stability determined by the standard conjugate point test. We find excellent agreement between precision tabletop models, numerical predictions from our analytical framework, and modeling results from finite element simulations. We further show that by varying the rest curvature of the thin strip, dynamic switches between different states of creased annuli can be achieved, which could inspire the design of deployable and morphable structures. We believe that our smooth description of discontinuous geometries will benefit the mechanical modeling and design of a wide spectrum of engineering structures that embrace geometric and material discontinuities.

No abstract

No abstract