Shrinkage stress and cuspal deflection in MOD restorations: analytical solutions and design guidelines
Shrinkage stress and cuspal deflection in MOD restorations: analytical solutions and design guidelines
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DOI：
10.1016/j.dental.2021.02.003
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发表时间：
2021-04-17
期刊：
影响因子：
5
通讯作者：
Fok, Alex S. L.
中科院分区：
文献类型：
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作者：
Aregawi, Wondwosen A.;Fok, Alex S. L.
Objective.本文旨在推导II类近中-咬合-远中（MOD）树脂复合材料模型中收缩应力和牙尖偏转的解析解，以更好地了解其对几何和材料参数的依赖性。基于应力解，它示出了如何设计曲线可以获得指导选择的尺寸和材料的准备和修复这类洞。空腔墙被视为悬臂梁，而树脂复合材料被模拟为Winkler的弹性基础与密集的线性弹簧。此外，一个数学模型，考虑到材料性能，样品的几何形状和周围的约束的合规性的综合影响，涉及到的收缩应力在“牙齿复合材料”接口的腔壁的局部顺应性。通过求解所得微分方程，得到了洞壁尖部挠度和收缩应力沿着方向的精确解析解，其形式与弹性地基梁在均布荷载作用下的形式相同。为了量化空腔底板处的收缩应力，树脂复合材料被假定为梁，在两端固定，并且加载有近似收缩应力的均匀分布的载荷。将所得解析解与有限元分析结果进行了比较。牙尖偏转的解析解包含无量纲参数y，其表示腔壁相对于固化树脂复合材料的刚度。对于相同的收缩应变，牙尖挠度随着y的减小而增大，即腔壁刚度减小或复合材料刚度增大。对于相同的y，瓣尖偏转与收缩应变成比例地增加。收缩应力沿着洞壁方向在洞角处最大，向咬合面方向减小，其最大值仅取决于树脂复合材料的弹性模量和收缩应变。对于低y值，咬合面处的界面应力可以变为压缩应力。空腔底部的界面应力远大于空腔壁面沿着的界面应力，并随复合材料厚度的增加呈指数增长。解析解与有限元预测吻合良好。经验证，本研究中提出的解析解和设计曲线可以提供有用的指导原则，以选择适当的洞制备和树脂复合材料的尺寸与适当的机械性能的II类MOD牙列，以帮助避免牙折和界面剥离所造成的聚合收缩。(c)2021年牙科材料学院。爱思唯尔公司出版All rights reserved.
Objective. This paper aimed to derive analytical solutions for the shrinkage stress and cuspal deflection in model Class-II mesial-occlusal-distal (MOD) resin-composite restorations to better understand their dependence on geometrical and material parameters. Based on the stress solutions, it was shown how design curves could be obtained to guide the selection of dimensions and materials for the preparation and restoration of this class of cavities.Methods. The cavity wall was considered as a cantilevered beam while the resin composite was modeled as Winkler's elastic foundation with closely-spaced linear springs. Further, a mathematical model that took into account the combined effect of material properties, sample geometry and compliance of the surrounding constraint was employed to relate the shrinkage stress at the "tooth-composite" interface to the local compliance of the cavity wall. Exact analytical solutions were obtained for cuspal deflection and shrinkage stress along the cavity wall by solving the resulting differential equation, which had the same form as that for a beam on elastic foundation with a distributed load. To quantify the shrinkage stress at the cavity floor, the resin composite was assumed to be a beam, fixed at both ends and loaded with a uniformly distributed load that approximated the shrinkage stress. The analytical solutions thus obtained were compared with results from finite element analysis (FEA).Results. The analytical solution for cuspal deflection contains a dimensionless parameter, y, which represents the stiffness of the cavity wall relative to that of the cured resin composite. For the same shrinkage strain, cuspal deflection increases with reducing y, i.e. reducing stiffness of the cavity wall or increasing stiffness of the composite. For the same y, cuspal deflection increases proportionally with shrinkage strain. Shrinkage stress along the cavity wall is maximum at the cavity corner and reduces towards the occlusal surface; the maximum value depends only on Young's modulus and the shrinkage strain of the resin composite. For low values of y, the interfacial stress at the occlusal surface can become compressive. The interfacial stress at the cavity floor can be much higher than that along the cavity wall, increasing exponentially with the resin composite's thickness. The analytical solutions agree well with FEA predictions.Significance. When validated, the analytical solutions and design curves presented in this study can provide useful guidelines for choosing appropriate dimensions of cavity preparations and resin composite materials with suitable mechanical properties for Class-II MOD restorations to help avoid tooth fracture and interfacial debonding caused by polymerization shrinkage.(c) 2021 The Academy of Dental Materials. Published by Elsevier Inc. All rights reserved.