# 野猪牙齿在微小外力下的应力分析Stress Analysis of Wild Boar Teeth under Tiny External Forces

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In this paper, the displacement field and strain field of biomaterial-wild pig teeth are analyzed by MATLAB’s 2D digital image correlation program Ncorr. Through the high-definition camera, the digital image of the wild boar teeth before being subjected to external force and subjected to a small external force was obtained. The displacement of the center points of the two sets of digital images was determined by Newton-Rapshon algorithm, and the displacement changes and stress strains of the wild boar teeth under the action of tiny external forces were analyzed. Finally, through the analysis of the numerical calculation results, the displacement and stress changes at some specific positions are given, which provides a theoretical basis for the study of wild boar teeth.

1. 引言

2. 数字图像的基本原理

2.1. 形函数

Figure 1. Relation diagram of reference sub-region and deformation sub-region

$\left\{\begin{array}{l}{x}^{\prime }=x+u+\frac{\partial u}{\partial x}\Delta x+\frac{\partial u}{\partial y}\Delta y\\ {y}^{\prime }=y+v+\frac{\partial v}{\partial x}\Delta x+\frac{\partial v}{\partial y}\Delta y\end{array}$ (1)

$\left[\begin{array}{c}{x}^{\prime }\\ {y}^{\prime }\end{array}\right]=\left[\begin{array}{ccc}\begin{array}{c}1+{u}_{x}\\ {v}_{x}\end{array}& \begin{array}{c}{u}_{y}\\ 1+{v}_{y}\end{array}& \begin{array}{c}u\\ v\end{array}\end{array}\right]\left[\begin{array}{c}x\\ y\\ 1\end{array}\right]$ (2)

2.2. 相关准则

${C}_{f,g}\left(P\right)=\underset{x=-M}{\overset{M}{\sum }}\underset{y=-M}{\overset{M}{\sum }}{\left[\frac{f\left(x,y\right)}{\sqrt{\underset{x=-M}{\overset{M}{\sum }}\underset{y=-M}{\overset{M}{\sum }}\left[{f\left(x,y\right)\right]}^{2}}}-\frac{g\left({x}^{\prime },{y}^{\prime }\right)}{\sqrt{\underset{x=-M}{\overset{M}{\sum }}\underset{y=-M}{\overset{M}{\sum }}{\left[g\left({x}^{\prime },{y}^{\prime }\right)\right]}^{2}}}\right]}^{2}$ (3)

3. 试验测量与分析

3.1. 数字图像测量系统和试验材料介绍

Figure 2. Digital image experiment platform

3.2. 实验具体过程

1) 人工散斑：在实验开始前需要对样本喷洒人工散斑，具体做法为在试样表面喷上一薄层白色油漆作为底色，然后再喷上黑色油漆，从而得到黑白人工散斑。

2) 固定样本：实验中矩形框，即野猪牙齿，固定端四点固定在卷交机上，距离平台前端40 mm，并在矩形梁自由端施加1 kg的砝码，同时采集图像。

Figure 3. Schematic diagram of wild boar's fangs

3) 实验参数设置：利用Ncorr软件对位移场和应变场进行分析。利用Ncorr软件计算应变场时，从参考图像中选择一个子集，并在变形图像中跟踪其相应位置。

3.3. 测量结果与分析

Figure 6. Lateral displacement of material under external force

Figure 7. Longitudinal displacement of material under external forces

Figure 8. Transverse stress variation of material under external force

Figure 9. Longitudinal stress change of material under external force

4. 结论

Figure 10. Variation of lateral displacement in different regions

Figure 11. Variation of longitudinal displacement in different regions

Figure 12. Exx strain in different measuring areas

Figure 13. Eyy strain in different measuring areas

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