Anisotropic elasticity by Ting T.C.T.

By Ting T.C.T.

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2013) presented an edge-based smoothing technique combined with the X-FEM method for fracture analysis of composite materials that took the advantages of the X-FEM and ES-FEM methods. Zhao, Bordas, and Qu (2013) presented a hybrid smoothed X-FEM–LSM for modeling nanoscale inhomogeneities with interfacial energy effect, in which the Gurtin–Murdoch surface elasticity model was 16 Extended Finite Element Method used to account for the interface stress effect and the Wachspress interpolants were employed to construct the shape functions in the smoothed X-FEM method.

Holl et al. (2014) presented a multi-scale technique to investigate advancing cracks in three-dimensional spaces with a reference to gas turbine blades, which was able to capture crack growth taking localization effects from the fine scale into account. 3 Cohesive Fracture Mechanics LEFM is only applicable when the size of the fracture process zone (FPZ) at the crack tip is small compared to the size of the crack and the size of the specimen (Bazant and Planas, 1998). Hence, alternative models must be chosen to take into account the FPZ.

2012b) performed a non-Newtonian viscous flow analysis in complex geometries with internal moving parts and narrow gaps based on a non-conforming mesh refinement approach and the X-FEM method. Court, Fournié, and Lozinski (2014) proposed a fictitious domain approach inspired by the X-FEM for the Stokes problem, in which the interface between the fluid and the structure was localized by a level-set function, and the Dirichlet boundary conditions were taken into account using the Lagrange multiplier.

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