Raz Einat, Lanir Yoram
J Biomech Eng. 2009 Nov;131(11):111008. doi: 10.1115/1.3212107.
There is still no agreement on the nature of tissues' viscoelasticity and on its reliable modeling. We speculate that disagreements between previous observations stem from difficulties of separating between viscoelastic and preconditioning effects, since both are manifested by similar response features. Here, this and related issues were studied in the tendon as a prototype for other soft tissues. Sheep digital tendons were preconditioned under strain that was higher by 1% than the one used in subsequent testing. Each specimen was then subjected to stress relaxation, and quick release or creep. A stochastic microstructural viscoelastic theory was developed based on the collagen fibers' properties and on their gradual recruitment with stretch. Model parameters were estimated from stress relaxation data and predictions were compared with the creep data. Following its validation, the new recruitment viscoelasticity (RVE) model was compared, both theoretically and experimentally, with the quasilinear viscoelastic (QLV) theory. The applied preconditioning protocol produced subsequent pure viscoelastic response. The proposed RVE model provided excellent fit to both stress relaxation and creep data. Both analytical and numerical comparisons showed that the new RVE theory and the popular QLV one are equivalent under deformation schemes at which no fibers buckle. Otherwise, the equivalence breaks down; QLV may predict negative stress, in contrast to data of the quick release tests, while RVE predicts no such negative stress. The results are consistent with the following conclusions: (1) fully preconditioned tendon exhibits pure viscoelastic response, (2) nonlinearity of the tendon viscoelasticity is induced by gradual recruitment of its fibers, (3) a new structure-based RVE theory is a reliable representation of the tendon viscoelastic properties under both stress relaxation and creep tests, and (4) the QLV theory is equivalent to the RVE one (and valid) only under deformations in which no fibers buckle. The results also suggest that the collagen fibers themselves are linear viscoelastic.
关于组织粘弹性的本质及其可靠建模仍未达成共识。我们推测，先前观察结果之间的分歧源于难以区分粘弹性和预处理效应，因为两者都表现出相似的响应特征。在此，以肌腱作为其他软组织的原型，对这一问题及相关问题进行了研究。绵羊趾腱在比后续测试中使用的应变高1%的应变下进行预处理。然后对每个标本进行应力松弛、快速释放或蠕变测试。基于胶原纤维的特性及其随拉伸逐渐募集的情况，建立了一种随机微观结构粘弹性理论。根据应力松弛数据估计模型参数，并将预测结果与蠕变数据进行比较。经过验证后，将新的募集粘弹性（RVE）模型与准线性粘弹性（QLV）理论进行了理论和实验比较。所应用的预处理方案产生了随后的纯粘弹性响应。所提出的RVE模型对应力松弛和蠕变数据均提供了出色的拟合。分析和数值比较均表明，在没有纤维屈曲的变形方案下，新的RVE理论与流行的QLV理论是等效的。否则，等效性就会失效；与快速释放测试数据相比，QLV可能会预测出负应力，而RVE则不会预测出这种负应力。结果与以下结论一致：（1）完全预处理的肌腱表现出纯粘弹性响应；（2）肌腱粘弹性的非线性是由其纤维的逐渐募集引起的；（3）一种新的基于结构的RVE理论是肌腱在应力松弛和蠕变测试下粘弹性特性的可靠表征；（4）QLV理论仅在没有纤维屈曲的变形下与RVE理论等效（且有效）。结果还表明，胶原纤维本身是线性粘弹性的。
