SUN Yue, FENG Xiang-chu, XIAO Jun, WANG Ying. MLS-Based Postprocessing Procedure for Discontinuous Deformation Analysis[J]. Applied Mathematics and Mechanics, 2017, 38(7): 743-754. doi: 10.21656/1000-0887.370259
 Citation: SUN Yue, FENG Xiang-chu, XIAO Jun, WANG Ying. MLS-Based Postprocessing Procedure for Discontinuous Deformation Analysis[J]. Applied Mathematics and Mechanics, 2017, 38(7): 743-754.

# MLS-Based Postprocessing Procedure for Discontinuous Deformation Analysis

##### doi: 10.21656/1000-0887.370259
Funds:  The National Natural Science Foundation of China(61271294;61471338)
• Rev Recd Date: 2016-11-18
• Publish Date: 2017-07-15
• The discontinuous deformation analysis (DDA) simulates fracture propagations by introducing fictitious joint meshes in blocks to generate sub-blocks. In order to obtain accurate stress distributions with this method, a stress recovery procedure was proposed based on the moving least squares (MLS) interpolation technique. With the MLS shape functions and their derivatives, the stress at any point within a block can be expressed by means of nodal displacements. Numerical examples were given to verify the accuracy and effectiveness of the proposed method. Comparison of the stress results between the analytical method, the averaging postprocessing method and the proposed MLS-based postprocessing procedure indicates that, the MLS-based stress recovery procedure is of high accuracy in providing more reliable block stress distributions.
•  [1] SHI Gen-hua. Discontinuous deformation analysis: a new numerical model for the statics and dynamics of block systems[D]. Berkeley, SF, USA: University of California, Berkeley, 1988. [2] JIAO Yu-yong, ZHANG Huan-qiang, ZHANG Xiu-li, et al. A two-dimensional coupled hydromechanical discontinuum model for simulating rock hydraulic fracturing[J]. International Journal for Numerical and Analytical Methods in Geomechanics,2015,39(5): 457-481. [3] Morgan W E, Aral M M. An implicitly coupled hydro-geomechanical model for hydraulic fracture simulation with the discontinuous deformation analysis[J]. International Journal of Rock Mechanics and Mining Sciences,2015,73: 82-94. [4] ZHENG Hong, LI Xiao-kai. Mixed linear complementarity formulation of discontinuous deformation analysis[J]. International Journal of Rock Mechanics and Mining Sciences,2015,75: 23-32. [5] 邬爱清, 刘晓莹, 张杨, 等. 基于DDA的弹性力学全高阶多项式位移逼近方法及其实例验证[J]. 固体力学学报, 2014,35(2): 142-149.(WU Ai-qing, LIU Xiao-ying, ZHANG Yang, et al. A DDA based complete and high order polynomial displacement approximation method in elastic mechanics and its cases verification[J]. Chinese Journal of Solid Mechanics,2014,35(2): 142-149.(in Chinese)) [6] Beyabanaki S A R, Jafari A, Biabanaki S O R. Nodal-based three-dimensional discontinuous deformation analysis (3-D DDA)[J]. Computers and Geotechnics,2009,36(3): 359-372. [7] CHOO Ling-qian, ZHAO Zhi-ye, CHEN Hui-mei, et al. Hydraulic fracturing modeling using the discontinuous deformation analysis (DDA) method[J]. Computers and Geotechnics,2016,76: 12-22. [8] 马永政, 郑宏, 李春光. 耦合无网格法的非连续变形分析法研究[J]. 岩石力学与工程学报, 2007,26(S2): 4195-4201.(MA Yong-zheng, ZHENG Hong, LI Chun-guang. Research on discontinuous deformation analysis coupled with meshfree methods[J]. Chinese Journal of Rock Mechanics and Engineering,2007,26(S2): 4195-4201.(in Chinese)) [9] 马永政, 郑宏, 李春光. 应用自然邻接点插值法的块体非连续变形分析[J]. 岩土力学, 2008,29(1): 119-124.(MA Yong-zheng, ZHENG Hong, LI Chun-guang. Applying natural neighbor interpolation to discontinuous deformation analysis of block system[J]. Rock and Soil Mechanics,2008,29(1): 119-124.(in Chinese)) [10] 马永政, 蔡可键, 郑宏. 混合多位移模式的非连续变形分析法研究[J]. 岩土力学, 2016,37(3): 867-874.(MA Yong-zheng, CAI Ke-jian, ZHENG Hong. An analysis of discontinuous deformation with mixed multiple deformation modes[J]. Rock and Soil Mechanics,2016,37(3): 867-874.(in Chinese)) [11] NING You-jun, YANG Jun, AN Xin-mei, et al. Modelling rock fracturing and blast-induced rock mass failure via advanced discretisation within the discontinuous deformation analysis framework[J]. Computers and Geotechnics,2011,38(1): 40-49. [12] JIAO Yu-yong, ZHANG Xiu-li, ZHAO Jian. Two-dimensional DDA contact constitutive model for simulating rock fragmentation[J]. Journal of Engineering Mechanics,2012,138(2): 199-209. [13] ZHAO Zhi-ye, GU Jiong. Stress recovery procedure for discontinuous deformation analysis[J]. Advances in Engineering Software,2009,40(1): 52-57. [14] 孙新志, 李小林. 复变量移动最小二乘近似在Sobolev空间中的误差估计[J]. 应用数学和力学, 2016,37(4): 416-425.(SUN Xin-zhi, LI Xiao-lin. Error estimates for the complex variable moving least square approximation in Sobolev spaces[J]. Applied Mathematics and Mechanics,2016,37(4): 416-425.(in Chinese)) [15] Tabbara M, Blacker T, Belytschko T. Finite element derivative recovery by moving least square interpolants[J]. Computer Methods in Applied Mechanics and Engineering,1994,117(1/2): 211-223. [16] Bordas S, Duflot M. Derivative recovery and a posteriori error estimate for extended finite elements[J]. Computer Methods in Applied Mechanics and Engineering,2007,96(35/36): 3381-3399. [17] Ródenas J J, González-Estrada O A, Fuenmayor F J, et al. Enhanced error estimator based on a nearly equilibrated moving least squares recovery technique for FEM and XFEM[J]. Computational Mechanics,2013,52(2): 321-344. [18] SUN Yue, CHEN Qian, FENG Xiang-chu, et al. Discontinuous deformation analysis enriched by the bonding block model[J]. Mathematical Problems in Engineering,2015,2015: 723263. doi: 10.1155/2015/723263. [19] 邬爱清, 冯细霞, 卢波. 非连续变形分析中时间步及弹簧刚度取值研究[J]. 岩土力学, 2015,36(3): 891-897.(WU Ai-qing， FENG Xi-xia， LU Bo. Parametric research on time step and spring stiffness in DDA[J]. Rock and Soil Mechancis,2015,36(3): 891-897.(in Chinese)) [20] Timoshenko S P, Goodier J N. Theory of Elasticity [M]. 3rd ed. New York: McGraw-Hill Companies Inc, 1970.

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