## 4 Conclusions  
1. An accurate outer contour model of wheat grain was established, and the various tissue models could be obtained by separating the embryo, endosperm, and other tissues in the model.
2. A discrete-element simulation model of wheat grains was constructed by filling the tissue models of various parts of wheat grains with particles of different radii.
3. In the uniaxial compression test, the critical load of wheat crushing was 118.821 N. Through the single-factor test and the Plackett-Burman test, the significant factors affecting the relative error between the critical load test value and the simulation value was identified: critical tangential stress. The influence of critical normal stress and unit area normal stiffness on both was relatively small.
4. The steepest-climbing test was used to reduce the horizontal range of significant factors, followed by the Box-Behnken response surface test. Through the analysis of the test results, a quadratic polynomial regression equation was obtained. An ANOVA showed that the regression equations have a highly significant and a high fit. The regression equation was optimized and solved to obtain the optimal parameters as follows: the normal stiffness per unit area was 7.392 \(\times\) 10\({}^{10}\) N/m\({}^{3}\), the critical normal stress was 5.293 \(\times\) 10\({}^{6}\) Pa, and the critical tangential stress was 5.001 \(\times\) 10\({}^{6}\) Pa. The critical load of 122.392 N in the verification test and the physical error of 118.821 N was 3%, which verified the reliability of the simulation parameters of the wheat-grain crushing model.  
In our article, two important contents have been addressed: (1) establishing the precise wheat grain outer contour model and its embryo can be separated from other tissues; and (2) calibrating the bonding parameters of the discrete-element simulation model of the wheat grain. In terms of model reconstruction, a large number of references have been to compare the accuracy of the proposed model, and the modeling method could also be applied to other grain grains, such as corn, soybean, etc. In terms of bonding parameter calibration, most of them are in corn straw and alfalfa bud stalks. We used this research method to calibrate the wheat grains, which can study the breaking situation of wheat grains, such as the generating the site of the crushing crack and how the crack expands, providing the basis for this study.  
Conceptualization, Y.Z. ([PERSON]), W.S. and Y.H; methodology, Y.Z. ([PERSON]), W.S., Y.H., C.S. and K.Z.; software, W.S.; validation, W.S., J.G., Y.Z. ([PERSON]), J.L. and D.C.; writing--original draft, W.S.; writing--review and editing, W.S. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Open Fund Project of Key Laboratory of Grain Information Processing & Control, Ministry of Education, Henan University of Technology (Grant No. KFJ)2022007).  
Not applicable.  
The data presented in this study are available in the article.  
The authors thank the members of the Key Laboratory of Grain Information Processing and Control (Henan University of Technology), for their contributions to this project. In addition, thanks to [PERSON], COFCO Engineering & Technology (Zhengzhou) Co., Ltd. for the software help.  
The research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.