Natali Arturo N, Carniel Emanuele L, Pavan Piero G, Sander Franz G, Dorow Christina, Geiger Martin
Centre of Mechanics of Biological Materials, University of Padova, Padova, Italy.
J Biomech Eng. 2008 Jun;130(3):031004. doi: 10.1115/1.2900415.
The periodontal ligament (PDL), as other soft biological tissues, shows a strongly non-linear and time-dependent mechanical response and can undergo large strains under physiological loads. Therefore, the characterization of the mechanical behavior of soft tissues entails the definition of constitutive models capable of accounting for geometric and material non-linearity. The microstructural arrangement determines specific anisotropic properties. A hyperelastic anisotropic formulation is adopted as the basis for the development of constitutive models for the PDL and properly arranged for investigating the viscous and damage phenomena as well to interpret significant aspects pertaining to ordinary and degenerative conditions. Visco-hyperelastic models are used to analyze the time-dependent mechanical response, while elasto-damage models account for the stiffness and strength decrease that can develop under significant loading or degenerative conditions. Experimental testing points out that damage response is affected by the strain rate associated with loading, showing a decrease in the damage limits as the strain rate increases. These phenomena can be investigated by means of a model capable of accounting for damage phenomena in relation to viscous effects. The visco-hyperelastic-damage model developed is defined on the basis of a Helmholtz free energy function depending on the strain-damage history. In particular, a specific damage criterion is formulated in order to evaluate the influence of the strain rate on damage. The model can be implemented in a general purpose finite element code. The accuracy of the formulation is evaluated by using results of experimental tests performed on animal model, accounting for different strain rates and for strain states capable of inducing damage phenomena. The comparison shows a good agreement between numerical results and experimental data.
牙周韧带（PDL）与其他软生物组织一样，表现出强烈的非线性和时间依赖性力学响应，并且在生理负荷下会经历大应变。因此，软组织力学行为的表征需要定义能够考虑几何和材料非线性的本构模型。微观结构排列决定了特定的各向异性特性。采用超弹性各向异性公式作为开发PDL本构模型的基础，并进行适当安排以研究粘性和损伤现象，以及解释与正常和退化条件相关的重要方面。粘弹性超弹性模型用于分析时间依赖性力学响应，而弹性损伤模型则考虑在显著加载或退化条件下可能出现的刚度和强度降低。实验测试指出，损伤响应受与加载相关的应变率影响，随着应变率增加，损伤极限降低。这些现象可以通过一个能够考虑与粘性效应相关的损伤现象的模型来研究。所开发的粘弹性超弹性损伤模型是基于一个依赖于应变损伤历史的亥姆霍兹自由能函数定义的。特别是，制定了一个特定的损伤准则来评估应变率对损伤的影响。该模型可以在通用有限元代码中实现。通过使用在动物模型上进行的实验测试结果来评估公式的准确性，考虑不同的应变率和能够引发损伤现象的应变状态。比较结果表明数值结果与实验数据之间具有良好的一致性。
