Lakes R S, Vanderby R
Department of Engineering Physics, University of Wisconsin, Madison 53706-1687, USA.
J Biomech Eng. 1999 Dec;121(6):612-5. doi: 10.1115/1.2800861.
Experimental data (Thornton et al., 1997) show that relaxation proceeds more rapidly (a greater slope on a log-log scale) than creep in ligament, a fact not explained by linear viscoelasticity. An interrelation between creep and relaxation is therefore developed for ligaments based on a single-integral nonlinear superposition model. This interrelation differs from the convolution relation obtained by Laplace transforms for linear materials. We demonstrate via continuum concepts of nonlinear viscoelasticity that such a difference in rate between creep and relaxation phenomenologically occurs when the nonlinearity is of a strain-stiffening type, i.e., the stress-strain curve is concave up as observed in ligament. We also show that it is inconsistent to assume a Fung-type constitutive law (Fung, 1972) for both creep and relaxation. Using the published data of Thornton et al. (1997), the nonlinear interrelation developed herein predicts creep behavior from relaxation data well (R > or = 0.998). Although data are limited and the causal mechanisms associated with viscoelastic tissue behavior are complex, continuum concepts demonstrated here appear capable of interrelating creep and relaxation with fidelity.
实验数据（桑顿等人，1997年）表明，在韧带中，松弛比蠕变进行得更快（在对数-对数尺度上斜率更大），这一事实无法用线性粘弹性来解释。因此，基于单积分非线性叠加模型建立了韧带蠕变与松弛之间的相互关系。这种相互关系不同于通过拉普拉斯变换得到的线性材料的卷积关系。我们通过非线性粘弹性的连续介质概念证明，当非线性为应变强化类型时，即如在韧带中观察到的应力-应变曲线向上凹时，蠕变和松弛之间在速率上会出现这种差异。我们还表明，对蠕变和松弛都假设冯氏本构定律（冯，1972年）是不一致的。利用桑顿等人（1997年）发表的数据，本文建立的非线性相互关系能很好地从松弛数据预测蠕变行为（R≥0.998）。尽管数据有限且与粘弹性组织行为相关的因果机制很复杂，但这里展示的连续介质概念似乎能够如实地将蠕变和松弛联系起来。
