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5 The New Carissa was a freighter that ran aground on a beach near Coos Bay, Oregon, USA, during a storm on February 4, 1999, and subsequently broke apart. jpg) The hypothesis of confined plasticity, that is, the plasticity that is confined to the region near the crack tip, is important for prediction of the fatigue crack growth. The first implementation of the X-FEM for fatigue fracture analysis of cracks in homogeneous, isotropic, elastic–plastic two-dimensional solids subject to mixed mode in the case of confined plasticity was presented by Elguedj, Gravouil, and Combescure (2006), where the well-known Hutchinson–Rice–Rosengren (HRR) fields were used to present the singularities in elasto-plastic fracture mechanics.
6 Hydraulic fracturing is the process of drilling a bore hole into a geological formation that contains microscopic pockets of natural gas and oil, and then fracturing the formation so that the gas and oil can escape into the bore hole and be drawn to the surface. It is a technique in which typically water is mixed with sand and chemicals, and the mixture is injected at high pressure into a wellbore to create small fractures, along which fluids such as gas, petroleum, uranium-bearing solution, and brine water may migrate to the well Modeling of hydraulic fracture propagation has attracted considerable attention since the early 1950s because of its practical applications in a broad range of engineering areas.
2007, 2009) employed the sub-structured FE/X-FEM approach to compute the SIFs in large aircraft thin walled structures containing cracks. Bayesteh and Mohammadi (2011) studied the effect of crack tip enrichment functions in the X-FEM analysis of shells by evaluating fracture mechanics parameters such as the SIF, crack-tip opening displacement, and crack-tip opening angle. Larsson, Mediavilla, and Fagerström (2011) presented a formulation based on the cohesive zone concept applied to a kinematically consistent shell model enhanced with an X-FEM based discontinuous kinematical representation.