The present study investigates the effect of inclusions on the shape and size of crack tip plastic zones in engineering materials subjected to static loads by employing the element free Galerkin method (EFGM). The modeling of the discontinuities produced by cracks and inclusions becomes independent of the grid chosen for analysis. The standard displacement approximation is modified by adding additional enrichment functions, which introduce the effects of different discontinuities into the formulation. The level set method has been used to represent different discontinuities present in the domain. The effect of inclusions on the extent of crack tip plastic zones is investigated by solving some numerical problems by the EFGM.<\/p>\r\n","references":"[1]\tCheung, S. and Luxmoore A. R. (2003) A finite element analysis of stable crack growth in an aluminium alloy. Eng. Fract. Mech., 70, 1153\u20131169.\r\n[2]\tSingh, I. V., Mishra, B. K., Bhattacharya, S. and Patil, R. U. (2012) The numerical simulation of fatigue crack growth using extended finite element method. Int. J. Fatigue, 36, 109\u2013119.\r\n[3]\tJameel, A. and Harmain, G. A. (2016) Modeling and numerical simulation of fatigue crack growth in cracked specimens containing material discontinuities. Strength of Materials, 48, 294\u2013306.\r\n[4]\tYan, A. M. and Nguyen-Dang, H. (1995) Multiple-cracked fatigue crack growth by BEM. Comput. Mech., 16, 273\u2013280.\r\n[5]\tPant, M., Singh, I. V. and Mishra, B. K. (2010) Numerical simulation of thermo-elastic fracture problems using element free Galerkin method. Int. J. Mech. Sci., 52, 1745\u20131755.\r\n[6]\tBelytschko, T., Lu, Y. Y. and Gu, L. (1995) Crack propagation by element-free Galerkin methods. Eng. Fract. Mech., 51, 295\u2013315.\r\n[7]\tMarc Duflot and Hung Nguyen-Dang. (2004) A meshless method with enriched weight functions for fatigue crack growth. Int. J. Numer. Methods Eng., 59, 1945\u20131961.\r\n[8]\tMarc Duflot and Hung Nguyen-Dang. (2004) Fatigue crack growth analysis by an enriched meshless method. J. Comput. Appl. Math., 168, 155\u2013164.\r\n[9]\tLancaster, P. and Salkauskas, K. (1981) Surfaces generated by moving least square methods. Math. Comput., 37, 141\u2013158.\r\n[10]\tBelytschko, T., Gu, L. and Lu, Y. Y. (1994) Fracture and crack growth by element-free Galerkin methods. Modell. Simul. Mater. Sci. Eng., 2, 519\u2013534.\r\n[11]\tLu, Y. Y., Belytschko, T. and Gu, L. (1994) A new implementation of the element free Galerkin method. Comput. Methods Appl. Mech. Eng., 113, 397\u2013414.\r\n[12]\tKrongauz, Y. and Belytschko, T. (1996) Enforcement of essential boundary conditions in meshless approximations using finite elements. Comput. Methods Appl. Mech. Eng., 131, 133\u2013145.\r\n[13]\tMukherjee, Y. X. and Mukherjee S. (1997) On boundary conditions in the element-free Galerkin method. Comput. Mech., 19, 264-270.\r\n[14]\tXu, Y. and Saigal, S. (1998) An element free Galerkin formulation for stable crack growth in an elastic solid. Comput. Methods Appl. Mech. Eng., 154, 331\u2013343.\r\n[15]\tLi, G. Y. and Belytschko, T. (2001) Element-free Galerkin method for contact problems in metal forming analysis. Eng. Comput., 18 (1), 62\u201378.\r\n[16]\tYanjin, G., Xin, W., Zhao, G. and Ping, L. (2009) A nonlinear numerical analysis for metal forming process using the rigid-(visco) plastic element free Galerkin method. Int. J. Adv. Manuf. Technol., 42, 83\u201392.\r\n[17]\tJameel, A. and Singh T. (2014) Modeling and Simulation of Large Deformation Bi-material Problems Using EFGM. Inroads, 3 (1), 48\u201353.\r\n[18]\tSukumar, N., Moran, B., Black, T. and Belytschko, T. (1997) An element-free Galerkin method for the three-dimensional fracture mechanics. Comput. Mech., 20, 170\u2013175.\r\n[19]\tJameel, A. and Harmain, G. A. (2015) Fatigue crack growth in presence of material discontinuities by EFGM. Int. J. Fatigue, 81, 105-116.\r\n[20]\tBelytschko, T., Krongauz, Y., Organ, D., Fleming, M. and Krysl, P. (1996) Meshless methods: An overview and recent developments. Comput. Methods Appl. Mech. Eng., 139, 3-47.\r\n[21]\tYazid, A., Abdelkader N. and Abdelmadjid H. (2009) A state-of-the-art review of the X-FEM for computational fracture mechanics. Appl. Math. Modelling., 33, 4269\u20134282.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 123, 2017"}