The periodontal ligament (PDL) exhibits different material mechanical properties along the long axis of the teeth. To explore the creep and the relaxation effects of dissimilar layers of PDL, this paper took the central incisors of porcine mandibular as experimental subjects and divided them perpendicular to the teeth axis into five layers. Creep experiments and relaxation experiments on five layers were conducted to obtain the creep compliance and relaxation modulus at different layers. Linear elastic model, generalized Kelvin model, and generalized Maxwell model were used to describe the major characteristics of the PDL: Instantaneous elasticity, creep and relaxation. Fitting accuracy of three-parameter, five-parameter, and seven-parameter of the model was compared, and the constitutive equations of different layers were established by the least square method. The results presented that the creep strain and the relaxation stress of PDL were exponentially correlated with time under different loading conditions. Different layers showed a significant effect on the creep strain and relaxation stress of PDL. Along the long axis of the teeth, the changing rule of the creep compliance and relaxation modulus of each layer showed quite the contrary, and the instantaneous elastic modulus first decreased to the minimum, then increased to the maximum. Higher instantaneous elastic modulus led to lower creep compliance and higher relaxation modulus. The generalized Kelvin model and the generalized Maxwell model well characterized the creep and relaxation properties of PDL. Fitting accuracy increased with the number of model parameters. The relaxation time of PDL was about one order of magnitude shorter than the creep retardation time, which indicated that the relaxation effect lasted shorter than the creep effect.

中文翻译：

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不同层牙周韧带受压黏弹性特性的实验研究

牙周韧带 (PDL) 沿牙齿长轴表现出不同的材料力学性能。为探索不同层PDL的蠕变和松弛效应，本文以猪下颌中切牙为实验对象，将其垂直于牙轴分为5层。进行了五层的蠕变实验和松弛实验，以获得不同层的蠕变柔量和松弛模量。线性弹性模型、广义开尔文模型和广义麦克斯韦模型用于描述PDL的主要特征：瞬时弹性、蠕变和松弛。比较了模型的三参数、五参数、七参数的拟合精度，并通过最小二乘法建立了不同层的本构方程。结果表明，在不同加载条件下，PDL的蠕变应变和松弛应力与时间呈指数相关。不同层对PDL的蠕变应变和松弛应力有显着影响。沿齿长轴方向，各层的蠕变柔量和松弛模量的变化规律完全相反，瞬时弹性模量先减小到最小值，然后增大到最大值。较高的瞬时弹性模量导致较低的蠕变柔量和较高的松弛模量。广义 Kelvin 模型和广义 Maxwell 模型很好地表征了 PDL 的蠕变和松弛特性。拟合精度随着模型参数数量的增加而增加。PDL的弛豫时间比蠕变延迟时间短约一个数量级，这表明弛豫效应比蠕变效应持续的时间短。