Chapter 4

Fundamental Concept and Formula of X-FEM


The fundamental concept and formula of the extended finite element method (X-FEM) are introduced in this chapter, like partition of unity and the level set method, as well as the technical process of program implementation. The expressions for enriched shape functions of the element are provided, which include the displacement discontinuity crack, called “strong discontinuity”, and strain discontinuity interface, called “weak discontinuity”, such as inclusions and interfaces of bimaterials. The essential theory and formula of fracture mechanics are used to establish the enriched shape functions at the crack tip, which are described in Chapter 2 for steady-state cracks and in Chapter 3

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