Sawtooth patterns in flexural force curves of structural biological materials are not signatures of toughness enhancement: Part II.

Stiff biological materials (SBMs), such as nacre and bone, are composites that display remarkable toughness enhancements over their primary constituents, which are brittle minerals. These enhancements are thought to be a consequence of different mechanisms made possible by the SBMs' internal lamellar architecture. One such mechanism is the Cook-Gordon (crack-arrest-and-reinitiation) mechanism, whose operation manifests in flexural tests as a sawtooth pattern in the force-displacement curves. The curves from flexural tests carried out on marine sponge spicules, which also possess a lamellar architecture, also display a sawtooth-pattern, suggesting the presence of the Cook-Gordon mechanism. Intriguingly, the spicules were recently found not to display any significant toughness enhancement. To resolve this apparent contradiction, in the preceding paper (Kochiyama et al., 2021), we put forward the hypothesis that the sawtooth pattern was due to the spicules slipping at the tests' supports. In this paper, we present a model for the spicule's flexural tests in which we allow for the possibility for the specimen to slip at the test's supports. We model contact between the specimen and the test's supports using the Coulomb's friction law. By choosing experimentally reasonable values for the friction coefficient, we were able to get the model's predictions to match experimental measurements remarkably well. Additionally, on incorporating the spicules' surface roughness into the model, which we did by varying the friction coefficient along the spicule's length, its predictions can also be made to match the measured sawtooth patterns. We find that the sawtooth patterns in the model are due to slip type instabilities, which further reinforces the hypothesis put forward in our preceding paper.