咬颌力作用下牙周膜应力应变分布

Stress Distribution of Periodontal Ligament Under the Biting Force

通过对咬颌力载荷作用下牙周膜的应力应变分析,为临床修复设计提供理论依据。将牙根近似为抛物线形柱体模型,对模型加载、求解,对近似模型牙周膜应力大小、分布结果进行分析;分析了剪力、轴力以及弯矩分别作用下牙周膜应力应变分布,并将计算结果应用到咬颌力载荷作用下牙周膜应力应变分析;选取从牙颈部截面到牙根尖截面等距划分的5个截面为研究对象,分析了各截面最大Von misses应力。理论分析结果与数值分析结果牙周膜的应力分布极为相似。牙周膜的高应力区出现在牙颈部与牙根中部之间,牙根中部至根尖应力水平很低,说明牙周膜对应力具有明显的缓冲作用,表明在咀嚼过程中,牙周膜不仅仅是简单地传递颌力,同时还有缓冲、储存颌力传导至周围牙槽骨的作用。

Through the stress-strain analysis of periodontal ligament under the biting force,it provides theoretical basis for the prosthesis design.Closed-form analytical formulas for a tooth of paraboloidal shape in pure translation are presented.These formulas are based on both the approximation of normal and tangential strains in terms of the transnational displacement of the tooth and the tooth equilibrium of the thin surrounding periodontal membrane.The tooth is considered to be a rigid body while the surrounding membrane is assumed to be an elastic foundation of uniform thickness.The proposed formulas are capable of determining the most important quantities involved the distribution of strain and stress tensors in the membrane,the maximum value of hydrostatic stress.In this paper,the results of theoretical analysis and numerical results of stress distribution in periodontal ligament are very similar.The high stress of the periodontal ligament is near the cervical region.From the central to apical root,the stress level of the periodontal ligament is very low.These show that the periodontal ligament has obvious cushioning action to the stress,and the process of chewing is not only passing the stress,but also buffering and passing the stress to the surrounding alveolar bone.