Lieou Charles K C, Elbanna Ahmed E, Carlson Jean M
Department of Physics, University of California, Santa Barbara, Santa Barbara, California 93106, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jul;88(1):012703. doi: 10.1103/PhysRevE.88.012703. Epub 2013 Jul 3.
Sacrificial bonds and hidden length in structural molecules account for the greatly increased fracture toughness of biological materials compared to synthetic materials without such structural features by providing a molecular-scale mechanism for energy dissipation. One example is in the polymeric glue connection between collagen fibrils in animal bone. In this paper we propose a simple kinetic model that describes the breakage of sacrificial bonds and the release of hidden length, based on Bell's theory. We postulate a master equation governing the rates of bond breakage and formation. This enables us to predict the mechanical behavior of a quasi-one-dimensional ensemble of polymers at different stretching rates. We find that both the rupture peak heights and maximum stretching distance increase with the stretching rate. In addition, our theory naturally permits the possibility of self-healing in such biological structures.
结构分子中的牺牲键和隐藏长度通过提供一种分子尺度的能量耗散机制，使得生物材料相比于没有此类结构特征的合成材料，其断裂韧性大幅提高。一个例子是动物骨骼中胶原纤维之间的聚合胶连接。在本文中，我们基于贝尔理论提出了一个简单的动力学模型，该模型描述了牺牲键的断裂和隐藏长度的释放。我们假设了一个控制键断裂和形成速率的主方程。这使我们能够预测聚合物准一维集合体在不同拉伸速率下的力学行为。我们发现，断裂峰值高度和最大拉伸距离均随拉伸速率的增加而增大。此外，我们的理论自然地允许此类生物结构中存在自我修复的可能性。
