Kahler Bill, Kotousov Andrei, Borkowski Krzysztof
School of Dentistry, The University of Adelaide, SA 5005, Australia.
Dent Mater. 2006 Oct;22(10):942-7. doi: 10.1016/j.dental.2005.10.005. Epub 2005 Dec 19.
Numerous analyses for the shrinkage stress in the adhesive resin-based composite restorations mostly rely on numerical models. However, various finite element studies have inherent difficulties and inconsistencies associated with the use of different anatomy (tooth and restoration), boundary conditions (root and interfaces) and shrinkage models. As a consequence many numerical results remain inconclusive.
The objective of this paper is to develop a simplified analytical model of shrinkage stress and investigate effects of material properties of the restorative material, size of the restoration and volumetric shrinkage on the magnitude of the shrinkage stress in the vicinity of the dental-restoration interface.
The model is based on the following assumptions. The geometry is axisymmetric; all materials are linear-elastic; and the polymerization of the restoration material results in uniform volume shrinkage. An application of compatibility conditions leads to the system of five linear algebraic equations to five unknown variables, which can be easily resolved using standard techniques.
An explicit equation for the tensile stress at the interface was obtained. It was shown that higher Young's modulus, Poisson's ratio and volume shrinkage of the restorative material normally lead to larger tensile stress at the interface, which increases the risk of debonding. The results obtained based in this work, in general, are in a good agreement with published results of finite element studies.
The model allows comparison of different adhesive restorative materials with respect to the fracture risk of the interface induced by the development of the shrinkage stress at the restoration-dentine interface during polymerization. The model can be used to validate more sophisticated computational models as well as to conduct various optimization studies and preliminary assessments of fracture risk.
对基于树脂的复合粘结修复体收缩应力的众多分析大多依赖于数值模型。然而,各种有限元研究在使用不同的解剖结构(牙齿和修复体)、边界条件(牙根和界面)以及收缩模型时存在固有的困难和不一致性。因此,许多数值结果仍然没有定论。
本文的目的是建立一个简化的收缩应力分析模型,并研究修复材料的材料特性、修复体尺寸和体积收缩对牙修复体界面附近收缩应力大小的影响。
该模型基于以下假设。几何形状是轴对称的;所有材料都是线弹性的;修复材料的聚合导致均匀的体积收缩。应用相容性条件得到一个包含五个线性代数方程和五个未知变量的系统,使用标准技术可以很容易地求解。
得到了界面处拉应力的显式方程。结果表明,修复材料较高的杨氏模量、泊松比和体积收缩通常会导致界面处较大的拉应力,这增加了脱粘的风险。总体而言,基于这项工作获得的结果与已发表的有限元研究结果吻合良好。
该模型能够比较不同的粘结修复材料在聚合过程中修复体 - 牙本质界面处因收缩应力产生而导致的界面断裂风险。该模型可用于验证更复杂的计算模型,以及进行各种优化研究和断裂风险的初步评估。