Finite element simulation of fracture in a restored premolar tooth using high aspect ratio elements

Abstract Introduction The term cracked tooth syndrome refers to an incomplete fracture of a vital posterior tooth that involves the dentin and occasionally extends into the pulp. There is a very limited number of publications trying to model dentin crack growth using numerical techniques. Therefore, it is essential to numerically model this phenomenon in order to improve the clinical procedures. Methods A 2D finite element model is proposed to simulate crack initiation and propagation in a restored premolar tooth. The geometric model was based on computed tomography data. A special finite element technique, named mesh fragmentation technique, is used to model and analyze the behavior of the tooth. This technique was used to model cracks in quasi-brittle materials based on the use of interface solid finite elements with high aspects ratio. A tension damage constitutive relation between stresses and strains consistent with the continuous strong discontinuity approach is used to describe crack formation and propagation. Results The main aspects of modeling technique and procedures are explained in detail as well as the whole results, including both elastic and fracture analyses of the restored tooth. Conclusion The results of the current fracture analysis show that, under various loading conditions, there is no crack initiation in the restored tooth under typical loading magnitude. However, in the case of tooth with a pre-existing crack, which can be aroused during the restoration process, a crack propagation was observed, while they did not reach a critical fracture state.

摘要 引言
牙隐裂综合征（cracked tooth syndrome）指累及牙本质（dentin）、偶尔延伸至牙髓（pulp）的活髓后牙不完全骨折。目前针对牙本质裂纹扩展开展数值建模的研究文献极少，因此通过数值建模对该现象进行研究以优化临床诊疗流程具有重要意义。
方法 本文提出一种二维有限元模型（2D finite element model），用于模拟修复后前磨牙的裂纹萌生与扩展过程。该几何模型基于计算机断层扫描（computed tomography）数据构建，采用一种名为网格破碎技术（mesh fragmentation technique）的特殊有限元方法对牙齿的力学行为进行建模与分析。该技术依托高长细比界面实体有限元，已被应用于准脆性材料的裂纹建模研究。同时采用与连续强间断法（continuous strong discontinuity approach）一致的应力-应变拉损伤本构关系，以描述裂纹的形成与扩展机制。
结果 本文详细阐释了建模技术与流程的核心要点，并完整呈现了全部分析结果，包括修复后牙齿的弹性力学与断裂力学分析结果。
结论 本次断裂分析结果显示，在典型载荷幅值作用下，修复后牙齿未出现裂纹萌生现象。但若牙齿存在修复过程中产生的预制裂纹，则可观察到裂纹扩展行为，不过裂纹并未达到临界断裂状态。