<Abstrate>

Faced with a comparatively limited palette of minerals and organic

polymers as building materials, evolution has arrived repeatedly on

structural solutions that rely on clever geometric arrangements to

avoid mechanical trade-offs in stiffness, strength and flexibility. In

this tutorial review, we highlight the concept of tessellation, a

structural motif that involves periodic soft and hard elements arranged

in series and that appears in a vast array of invertebrate and vertebrate

animal biomaterials. We start from basic mechanics principles on the

effects of material heterogeneities in hypothetical structures, to derive

common concepts from a diversity of natural examples of one-, two- and

three-dimensional tilings/layerings. We show that the tessellation of a

hard, continuous surface – its atomization into discrete elements connected

by a softer phase – can theoretically result in maximization of material

toughness, with little expense to stiffness or strength. Moreover,

the arrangement of soft/flexible and hard/stiff elements into particular

geometries can permit surprising functions, such as signal filtering or

‘stretch and catch’ responses, where the constrained flexibility of systems

allows a built-in safety mechanism for ensuring that both compressive and

tensile loads are managed well. Our analysis unites examples ranging from

exoskeletal materials (fish scales, arthropod cuticle, turtle shell) to endoskeletal

materials (bone, shark cartilage, sponge spicules) to attachment devices

(mussel byssal threads), from both invertebrate and vertebrate animals,

while spotlighting success and potential for bio-inspired manmade applications.

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