Strain Measurements of Shear Bands Based on Least-square Fitting of Local Displacements Based on the Digital Image Correlation Method
WANG Xue-bin1,2,HOU Wen-teng2,DONG Wei2,YANG Mei3,CAO Si-wen2
1. Institute of Computational Mechanics, Liaoning Technical University, Fuxin, Liaoning 123000, China
2. College of Mechanics and Engineering, Liaoning Technical University, Fuxin, Liaoning 123000, China
3. School of Mechanical Engineering, Liaoning Technical University, Fuxin, Liaoning 123000, China
Abstract：Strains in the fictitious shear band are measured by use of least-square fitting of local displacements of the digital image correlation method, and strains are compared with those obtained by use of the central difference method and the analytical solution. Effects of the size of the calculating window and the size of the subset are mainly demonstrated. It is found that when the calculating window is larger and the size of the subset is lower, strains are closer to the analytical solution. Strains during the failure process of the low liquid-limit clay specimen under uniaxial compression are measured by use of least-square fitting of local displacements method and the central difference method, and strains are measured by least-square fitting of local displacements method are more accurate, which is helpful for the accurate measurement of strains of shear bands.
王学滨,侯文腾,董伟,杨梅,曹思雯. 基于局部位移场最小二乘拟合数字图像相关方法的剪切带应变测量[J]. 计量学报, 2019, 40(4): 655-661.
WANG Xue-bin,HOU Wen-teng,DONG Wei,YANG Mei,CAO Si-wen. Strain Measurements of Shear Bands Based on Least-square Fitting of Local Displacements Based on the Digital Image Correlation Method. Acta Metrologica Sinica, 2019, 40(4): 655-661.
［1］Sutton M A, Turner J L, Bruck H A, et al. Full-representation of discretely sampled surface deformation for displacement and strain analysis［J］. Experimental Mechanics, 1991, 31(2): 168-177.
［2］Wang C C, Deng J M, Ateshian G A, et al. An automated approach for direct measurement of two-dimensional strain distributions within articular cartilage under unconfined compression［J］. Journal of Biomechanical Engineering, 2002, 124(5): 557-567.
［3］Meng L B, Jin G C, Yao X F. Application of iteration and finite element smoothing technique for displacement and strain measurement of digital speckle correlation［J］. Optics & Lasers in Engineering, 2007, 45(1): 57-63.
［4］潘兵, 谢惠民. 数字图像相关中基于位移场局部最小二乘拟合的全场应变测量［J］. 光学学报, 2007, 27(11): 1980-1986.
Pan B, Xie H M. Full-field strain measurement based on least-square fitting of local displacement for digital image correlation method［J］. Acta Optica Sinica, 2007, 27(11): 1980-1986.
［5］Schreier H W, Sutton M A. Systematic errors in digital image correlation due to undermatched subset shape functions［J］. Experimental Mechanics, 2002, 42(3): 303-310.
［6］范伟,林瑜阳,李钟慎. 基于BP神经网络的压电陶瓷蠕变预测［J］. 计量学报,2017,38(4):429-434.
Fan W,Lin Y Y,Li Z S. Prediction of the Creep of Piezoelectric Ceramic Based on BP Neural Network Optimized by Genetic Algorithm［J］. Acta Metrologica Sinica, 2017,38(4):429-434.
［7］Zhao J Q, Zeng P, Pan B, et al. Improved Hermite finite element smoothing method for full-field strain measurement over arbitrary region of interest in digital image correlation［J］. Optics & Lasers in Engineering, 2012, 50(11): 1662-1671.
［8］王学滨, 潘一山, 马瑾. 剪切带内部应变(率)分析及基于能量准则的失稳判据［J］. 工程力学, 2003, 20(2): 111-115.
Wang X B, Pan Y S, Ma J. Analysis of strain and strain rate in shear band and its instability based on energy criterion［J］. Engineering Mechanics, 2003, 20(2): 111-115.
［9］杜亚志. 基于粒子群优化与Newton-Raphson迭代的DIC方法的剪切带变形精细测量［D］. 阜新:辽宁工程技术大学, 2016.
Du Y Z. Fine measurements of shear bands using the DIC method based on the particle swarm optimization algorithm and Newton-Raphson method［D］. Fuxin: Liaoning Technical University, 2016.
［10］王学滨, 杜亚志, 潘一山. 考虑一阶和二阶位移梯度的数字图像相关方法在剪切带测量中的比较［J］. 工程力学, 2013, 30(7): 282-287.
Wang X B, Du Y Z, Pan Y S. A comparison of DIC methods considering the first-and second-order displacement gradients in shear band measurements［J］. Engineering Mechanics, 2013, 30(7): 282-287.
［11］杜亚志, 王学滨, 董伟. 基于一阶及二阶DIC方法的常应变剪切带的测量误差分析［J］. 计量学报, 2018, 39(1): 66-71.
Du Y Z, Wang X B, Dong W. Analyses of measurement errors of shear bands with constant strains based on the one-and two-order DIC methods［J］. Acta Metrologica Sinica, 2018, 39(1): 66-71.
［12］王学滨, 杜亚志, 潘一山, 等. 基于数字图像相关方法的等应变率下不同含水率砂样剪切带观测［J］. 岩土力学, 2015, 36(3): 625-632.
Wang X B, Du Y Z, Pan Y S, et al. Measurement of shear bands of sand specimens with different water contents under constant strain rate based on digital image correlation method［J］. Rock and Soil Mechanics, 2015, 36(3): 625-632.
［13］王学滨, 张楠, 潘一山, 等. 单轴压缩湿土样最大剪切应变场数字图像相关方法结果的统计分析［J］. 岩土工程学报, 2016, 38(6): 996-1003.
Wang X B, Zhang N, Pan Y S, et al. Statistial analyses of maximum shear strain fields for wet soil specimens in uniaxial compression using digital image correlation method［J］. Chinese Journal of Geotechnical Engineering, 2016, 38(6): 996-1003.
2019, Vol. 40 
