基于超弹性模型的牙周膜力学行为数值模拟

为了准确预测牙周膜的力学行为,采用指数超弹性模型对牙周膜剪切实验及临床口腔正畸进行模拟分析,基于连续介质力学理论推导了模型的本构方程和弹性张量,开发了模型的ABAQUS UMAT子程序,并通过指数超弹性模型的本构方程与4组剪切实验数据的拟合获得模型参数.拟合结果表明,指数超弹性模型能够准确描述牙周膜的非线性力学行为.同时,通过有限元分析所获计算结果分别与4组牙周膜剪切实验结果的对比,验证了所开发的牙周膜指数超弹性模型UMAT子程序的正确性.经临床口腔正畸模拟结果显示,在正畸载荷作用下,牙周膜的应力主要集中在牙颈和根尖处.

Numerical Simulation of Mechanical Behaviors of Periodontal Ligament Based on Hyperelastic Model

To accurately predict the mechanical behavior of the periodontal ligament, an exponential hyperelastic model was used to simulate and analyze the shear experiments and orthodontic treatment. The constitutive equation and elasticity tensor for the hyperelastic model were obtained based on the large deformation of continuum mechanics, and the ABAQUS UMAT subroutine for the model was developed. The parameters of the model were obtained by means of the fittings between the model and four shear experimental data. The results demonstrate that the exponential hyperelastic model can well describe the nonlinear mechanical behavior of the periodontal ligament. Meanwhile, comparisons of numerical results and four periodontal ligament shear experimental data prove the validity of the UMAT subroutine developed for the model. The simulation result of the orthodontic treatment show that the stresses within the periodontal ligament under orthodontic load are concentrated in the areas near the cervical positions and the root apex.