Abstract
In this paper, a new criterion is proposed for the modeling multiple discontinuities i.e. crack, hole and inclusion passing through an element by XIGA. The modeling of multiple discontinuities passing through an element is done by imposing the additional degrees of freedom at the control points lying inside the influence of elements intersected by the discontinuities. In XIGA, the crack faces are modeled by discontinuous Heaviside jump functions, whereas the singularity in stress field at the crack tip is modeled by crack tip enrichment functions. The modeling of holes and inclusions is performed by Heaviside jump function and distance function respectively. The value of stress intensity factor is computed using domain form of interaction integral approach. Few static plane edge crack problems are analyzed in the presence of holes and inclusions to validate the proposed criterion. The results obtained by XIGA are compared with XFEM.
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Indra Vir Singh is working as an Associate Professor in the Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, India. He has received his B.Tech Degree in Mechanical from AMU Aligarh, India in 1996, M.Tech in Applied Mechanics from IIT Delhi, India in 1998, and his Ph.D. in Meshfree Methods from BITS Pilani, India in 2004. He has more than 80 research articles in various Journals. His research interests include XFEM, Meshfree Methods, XIGA and Computational Fracture Mechanics.
Gagandeep Bhardwaj is presently pursuing his Ph.D. in Mechanical Engineering from Indian Institute of Technology, Roorkee, India since 2012. He has received his B. Tech in Mechanical Engineering from Punjab Technical University, Jalandhar, India in 2008 and his M. Tech in Applied Mechanics from MNNIT, Allahabad India in 2011. His research interests include computational fracture mechanics.
B. K. Mishra is presently working as a Professor in the Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee. He has received his B.Tech in Mechanical Engineering from BHU Vanarasi, India in 1982, M.Tech in Mechanical Engineering from IIT Kanpur, India in 1985 and his Ph.D. in Mechanical Engineering from BHU, Varanasi, India in 1990. He has more than 24 years of Teaching and Research Experience. He has about 100 research articles in various Journals and Conferences. His research interests include Computational Fracture Mechanics, Composites and Vibrations.
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Singh, I.V., Bhardwaj, G. & Mishra, B.K. A new criterion for modeling multiple discontinuities passing through an element using XIGA. J Mech Sci Technol 29, 1131–1143 (2015). https://doi.org/10.1007/s12206-015-0225-8
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DOI: https://doi.org/10.1007/s12206-015-0225-8