Mechanics of elliptical interlocking sutures in biological interfaces.

Biological materials, such as beetle elytra and bird beaks, exhibit complex interfaces with diverse morphologies that have evolved to enhance their mechanical properties. However, the relationships between their geometric forms and mechanical properties remain inadequately understood. Here, we develop a theoretical model, supported by finite element simulations and experiments, to explore the strengthening and toughening mechanisms of biological interfaces characterized by elliptical interlocking sutures. We examine how aspect ratio, interlocking angle, and friction influence the stiffness, strength, and toughness (defined as the area under the stress-strain curve) of these interfaces. A phase diagram is presented to analyze the typical failure modes of sutured interfaces. We discuss the mechanistic advantages of various elliptical suture designs and demonstrate that the optimal aspect ratio and interlocking angle predicted by our model correspond closely with those observed in beetle elytra. This study advances our understanding of the mechanical principles governing biological sutured interfaces and provides valuable insights for the design of engineering joints, interlocking structures, and protective systems. STATEMENT OF SIGNIFICANCE: Biological interfaces characterized by elliptical interlocking sutures exist widely in nature. They exhibit superior mechanical properties and efficient biological functions. Here, we develop a theoretical model to explore their strengthening and toughening mechanisms. We reveal the effects of aspect ratio, interlocking angle, and friction of the interfaces on their load-bearing capability, deformability, and failure mechanisms. The failure modes of the sutured interfaces are deciphered and their mechanistic advantages are uncovered. The mechanically optimal suture geometries predicted by our theoretical model align with those in beetle elytra. This work deepens our understanding of the structure-property interrelations of biological sutured interfaces. The obtained results hold a promise in the design of, e.g., engineering joints, interlocking structures, and protective systems.