基于超-黏弹性的牙周膜本构模型构建及模拟

Construction and Simulation of Constitutive Model of Periodontal Ligament Based on Hyperelasticity-Viscoelasticity

为了准确描述牙周膜的生物力学行为,基于大变形连续介质力学理论及不可压缩各向同性假设,以人体牙周膜平面剪切和应力松弛实验数据为基础,利用有限元软件ABAQUS的数据拟合功能,构建牙周膜的超-黏弹性本构模型及参数。随后,通过对5组牙周膜平面剪切实验过程的模拟,验证牙周膜超-黏弹性模型的正确性。最后,通过有限元计算对比分析牙周膜线弹性模型与超-黏弹性模型对载荷的力学响应。结果表明在牙根位移量为0~0.06 mm时,牙周膜可近似用线弹性模型表示;当位移量大于0.06 mm,两种模型的差异显著,超-黏弹性模型更加符合牙周膜的材料特性。研究结果为牙周膜提供一种实用性强的超-黏弹性模型,为牙齿正畸的生物力学研究和治疗方案的精确设计提供理论依据。

In order to describe the biomechanical behaviors of PDL（ periodontal ligament） accurately,based on the theory of continuum mechanics in large deformation and the hypothesis of incompressible isotropy,a hyperelastic-viscoelastic model of PDL and parameters were constructed by data fitting function in finite element software ABAQUS based on experimental data of plane shear and stress relaxation of human PDL. Then,the PDL hyperelastic-viscoelastic model was evaluated on the accuracy through simulations to the plane shear experiments of five PDL specimens. Finally,the mechanical responses to loads of PDL linear elastic model and hyperelastic-viscoelastic model were compared and analyzed by finite element simulations. The results indicated PDL was approximately expressed by linear elastic model when the displacements of root were within 0 ～ 0. 06 mm,while hyperelastic-viscoelastic model was more accurate to describe the material characteristics of PDL when the displacements exceed 0. 06 mm,meanwhile a significant difference between two models could be observed. Based on this study,a practical PDL hyperelastic-viscoelastic model was acquired and a strong theoretical foundation was constructed for orthodontic biomechanical investigating and accurate treatment planning.