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Yu Ningyu, Li Qun. THE EXPLICIT RELATION BETWEEN THE M-INTEGRAL AND THE ELASTIC MODULI OF INCLUSION/DAMAGES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(1): 87-93. DOI: 10.6052/0459-1879-13-097
Citation: Yu Ningyu, Li Qun. THE EXPLICIT RELATION BETWEEN THE M-INTEGRAL AND THE ELASTIC MODULI OF INCLUSION/DAMAGES[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(1): 87-93. DOI: 10.6052/0459-1879-13-097

THE EXPLICIT RELATION BETWEEN THE M-INTEGRAL AND THE ELASTIC MODULI OF INCLUSION/DAMAGES

Funds: The project was supported by the National Natural Science Foundation of China (11202156, 10932007, 11021202).
  • Received Date: March 31, 2013
  • Revised Date: May 27, 2013
  • The M-integral represents the energy release rate due to the self-similar expansion of defects in material configurational mechanics while the reduction of effective elastic moduli is an inner damage parameter in traditional damage mechanics. This study will focus on the inherent relation between them in order to build the bridge of material configurational mechanics and damage mechanics. The explicit expression of M-integral is derived by using Muskhelishvili complex potential for the infinite plane with a circle inclusion. And the explicit expression of M-integral reveals the explicit relation between M-integral and the elastic moduli of the inclusion. A finite element method analysis is then performed to simulate the complex defects embedded in an elastic-plastic plane. The results reveal the inherent relation between the reduction of the effective elastic moduli for damaged area and the M-integral. In conclusion, the M-integral as an outer variable is believed to be capable of replacing the inner variable (reduction of the effective moduli) to describe the defects evolution in damaged material.
  • Chen YZ. A technique for evaluating the stress intensity factors by means of the M-integral. Engineering Fracture Mechanics, 1986, 23: 777-780
    Choi NY, Earmme YY. Evaluation of stress intensity factors in circular arc-shaped interfacial crack using L integral. Mechanics of Materials, 1992, 14: 141-153
    Chen YZ, Lee KY. Analysis of the M-integral in plane elasticity. Journal of Applied Mechanics, 2004, 71: 572-574
    李群,王芳文. 含微缺陷各向异性复合材料中的J_k积分和M积分. 西安交通大学学报, 2008, 42(1): 60-64 (Li Qun, Wang Fangwen. Jk-integral and M-integral in anisotropic composite material containing multiple defects. Journal of Xi'an Jiaotong University, 2008, 42(1): 60-64 (in Chinese))
    郭树祥, 许希武. 任意多椭圆孔多裂纹无限大板的应力强度因子与M积分. 固体力学学报, 2006, 27(1): 7-14 (Guo Shuxiang, Xu Xiwu. The SIFS and M-integral of the infinite plane with multiple elliptical holes and cracks. Acta Mechanica Solida Sinica, 2006, 27(1): 7-14 (in Chinese))
    王德法, 高小云, 师俊平. 三维固体问题中M积分与总势能变化关系的研究. 水利与建筑工程学报, 2009, 7(1): 36-38 (Wang Defa, Gao Xiaoyun, Shi Junping. Study on relation between M-integral and change of total potential energy in three-dimensional Solids. Journal of Water Resources and Architectural Engineering, 2009, 7(1): 36-38 (in Chinese))
    Chen YH, Hasebe N. A consistency check for strongly interacting multiple crack problems in isotropic, bimaterial and orthotropic bodies. International Journal of Fracture, 1998, 89: 333-353
    Chen YH. M-integral analysis for two-dimensional solids with strongly interacting cracks, Part I: In an infinite brittle solids. International Journal of Solids and Structures, 2001, 38: 3193-3212
    Chang JH, Chien AJ. Evaluation of M-integral for anisotropic elastic media with multiple defects. International Journal of Fracture, 2002, 114: 267-289
    Chang JH, Wu WH. Using M-integral for multi-cracked problems subjected to nonconservative and nonuniform crack surface tractions. International Journal of Solids and Structures, 2011, 48: 2605-2613
    Hu YF, Chen YH. M-integral description for a strip with two microcracks before and after coalescence. Journal of Applied Mechanics, 2009, 76: 061017
    Wang FW, Chen YH. Fatigue damage driving force based on the M-integral concept. Procedia Engineering, 2010, 2: 231-239
    Hui T, Chen YH. The M-integral analysis for a nano-inclusion in plane elastic materials under uni-axial or bi-axial loadings. Journal of Applied Mechanics, 2010, 77: 021019
    Hu YF, Li Q, Shi JP, et al. Surface/interface effect and size/configuration dependence on the energy release in nanoporous membrane. Journal of Applied Physics, 2012, 112: 034302
    Muskhelishvili NI, Some basic problems of the mathematical theory of elasticity. Leyden: Noordhoff, 1953
    Sendeckyj GP. Elastic Inclusion Problems in Plane Elastostatics. Int J Solids Struct, 1970, 6: 1535-1543
    Ru CQ. A new method for an inhomogeneity with stepwise graded interphase under thermomechanical loadings. J Elasticity, 1999, 56: 107-127
    Banerjee B, Adams DO. On predicting the effective elastic properties of polymer bonded explosives using the recursive cell method. International Journal of Solids and Structures, 2004, 41: 481-509
    Carka D, Landis CM. On the path-dependence of the J-integral near a stationary crack in an elastic-plastic material. Journal of Applied Mechanics, 2011, 78: 011006
    Li Q, Hu YF, Chen YH. On the physical interpretation of the M-integral in nonlinear elastic defect mechanics. International Journal of Damage Mechanics, 2012, doi: 10.1177/1056789512456860
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