Brown University, School of Engineering, 184 Hope Street, Providence, RI, USA.
Brown University, School of Engineering, 184 Hope Street, Providence, RI, USA.
J Mech Behav Biomed Mater. 2021 Dec;124:104787. doi: 10.1016/j.jmbbm.2021.104787. Epub 2021 Aug 29.
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.
刚性生物材料（SBMs），如珍珠层和骨骼，是复合材料，与脆性矿物相比，其具有显著的韧性增强。人们认为，这些增强是由 SBMs 的层状结构所带来的不同机制造成的。其中一种机制是 Cook-Gordon（裂纹止动和重新启动）机制，其在弯曲测试中的表现为力-位移曲线上的锯齿图案。对具有层状结构的海绵骨针进行弯曲测试得到的曲线也显示出锯齿图案，这表明存在 Cook-Gordon 机制。有趣的是，最近发现骨针并没有表现出任何显著的韧性增强。为了解决这一明显的矛盾，在前一篇论文中（Kochiyama 等人，2021 年），我们提出了一个假设，即锯齿图案是由于骨针在测试支架处滑动造成的。在本文中，我们提出了一个骨针弯曲测试的模型，其中我们允许在测试支架处发生骨针滑动的可能性。我们使用库仑摩擦定律来模拟标本与测试支架之间的接触。通过选择实验上合理的摩擦系数值，我们能够使模型的预测与实验测量非常吻合。此外，通过将骨针的表面粗糙度纳入模型中，我们沿着骨针的长度改变摩擦系数，其预测也可以与测量的锯齿图案相匹配。我们发现，模型中的锯齿图案是由于滑动类型的不稳定性造成的，这进一步证实了我们在前一篇论文中提出的假设。
