肌腱断裂的微观结构模型
A microstructural model of tendon failure
摘要：
胶原纤维是肌腱最重要的结构成分。当肌腱被拉伸时，它们的卷曲结构和肌腱内的平行排列会导致独特的非线性应力-应变曲线。微观结构模型可用于将微观胶原纤维力学与宏观肌腱力学相关联，从而使我们能够识别应力-应变曲线中存在的每个特征背后的机制。目前文献中的模型大多集中在钢筋束的弹性行为上，而很少有在不引入唯象参数的情况下建立弹性极限以上的模型。我们开发了一个模型，建立在胶原蛋白的招聘方法，只包含微观结构参数。我们分裂成弹性和塑性部分的原纤维中的应力，并假设原纤维屈服拉伸和断裂拉伸分别由一个分布函数，而不是单值描述。通过改变分布的形状及其重叠区域，我们可以生成宏观肌腱应力-应变曲线，这些曲线可以生成实验观察到的全部特征，包括使用现有模型无法解释的特征。这些功能包括第二个线性区域发生后，钢筋束已经屈服，和阶梯状故障行为后，应力达到峰值。当我们与现有的模型进行比较时，我们发现我们的模型将平均均方根误差从4.15MPa降低到1.61MPa，并且得到的参数值更接近于实验发现的值。由于我们的模型仅包含具有直接物理解释的参数，因此它可用于预测老化，疾病和损伤等过程如何影响肌腱的力学行为，前提是我们可以量化这些过程对微观结构的影响。
英文摘要：
Collagen fibrils are the most important structural component of tendons. Their crimped structure and parallel arrangement within the tendon lead to a distinctive non-linear stress-strain curve when a tendon is stretched. Microstructural models can be used to relate microscale collagen fibril mechanics to macroscale tendon mechanics, allowing us to identify the mechanisms behind each feature present in the stress-strain curve. Most models in the literature focus on the elastic behaviour of the tendon, and there are few which model beyond the elastic limit without introducing phenomenological parameters. We develop a model, built upon a collagen recruitment approach, that only contains microstructural parameters. We split the stress in the fibrils into elastic and plastic parts, and assume that the fibril yield stretch and rupture stretch are each described by a distribution function, rather than being single-valued. By changing the shapes of the distributions and their regions of overlap, we can produce macroscale tendon stress-strain curves that generate the full range of features observed experimentally, including those that could not be explained using existing models. These features include second linear regions occurring after the tendon has yielded, and step-like failure behaviour present after the stress has peaked. When we compare with an existing model, we find that our model reduces the average root mean squared error from 4.15MPa to 1.61MPa, and the resulting parameter values are closer to those found experimentally. Since our model contains only parameters that have a direct physical interpretation, it can be used to predict how processes such as ageing, disease, and injury affect the mechanical behaviour of tendons, provided we can quantify the effects of these processes on the microstructure.
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