Objectives

To investigate the elastic properties of human enamel using resonant ultrasound spectroscopy (RUS).

Methods

Six rectangular parallelepiped specimens were prepared from six human third molars. For all specimens, the theoretical resonant frequencies were calculated using the Rayleigh-Ritz method, knowing the specimen mass density and dimensions, and using a priori stiffness constants. The experimental resonant frequencies were measured and extracted by RUS. Then, the optimal stiffness constants were retrieved by adjustment of the theoretical resonant frequencies to the measured ones based on the Levenberg-Marquardt method. The engineering elastic moduli, including Young’s moduli, shear moduli, and Poisson’s ratios, were also calculated based on the optimal stiffness constants.

Results

The five independent stiffness constants C₁₁, C₁₂, C₁₃, C₃₃, and C₄₄ were 90.2 ± 6.65 GPa, 34.7 ± 6.90 GPa, 29.5 ± 4.82 GPa, 83.5 ± 8.93 GPa, and 37.0 ± 10.9 GPa, respectively. Young’s moduli E₁₁ and E₃₃, shear moduli G₁₃ and G₁₂, and Poisson’s ratios υ₁₂ and υ₁₃ were 71.7 ± 7.34 GPa, 69.2 ± 7.32 GPa, 37.0 ± 10.9 GPa, 28.1 ± 4.35 GPa, 0.303 ± 0.098, and 0.248 ± 0.060, respectively.

Significance

Elastic properties are critical for developing dental materials and designing dental prostheses. The RUS method may provide more precise measurement of elastic properties of dental materials.

中文翻译：

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基于共振超声光谱法的人类牙釉质弹性性能测量。

目标

为了研究使用共振超声光谱法（RUS）的人类牙釉质的弹性特性。

方法

从六个人类第三颗臼齿制备了六个长方体标本。对于所有样品，使用Rayleigh-Ritz方法计算出理论共振频率，知道样品的质量密度和尺寸，并使用先验刚度常数。通过RUS测量并提取了实验谐振频率。然后，根据Levenberg-Marquardt方法，通过将理论共振频率调整为被测频率，从而获得最佳刚度常数。还基于最佳刚度常数计算了工程弹性模量，包括杨氏模量，剪切模量和泊松比。

结果

五个独立的刚度常数C ₁₁，C ₁₂，C ₁₃，C ₃₃和C ₄₄分别为90.2±6.65 GPa，34.7±6.90 GPa，29.5±4.82 GPa，83.5±8.93 GPa和37.0±10.9 GPa。杨氏模量Ë ₁₁和ë ₃₃，剪切模量G ^ ₁₃和G ^ ₁₂，和泊松比υ ₁₂和υ ₁₃分别为71.7±7.34 GPA，69.2±7.32 GPA，37.0±10.9 GPA，28.1±4.35 GPA，0.303±0.098，和分别为0.248±0.060。

意义

弹性特性对于开发牙科材料和设计假牙至关重要。RUS方法可以提供更精确的牙科材料弹性性能测量。