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Every year, fracture imposes high economic costs and casualties to all societies. Since the beginning of the twentieth century, scientific approach to this issue has lead to invention of a new branch in mechanics, called fracture mechanics. In general, fracture problems fall into two categories. Brittle fracture, like what happens in glass, in which, few plastic deformations and energy absorption occurs and ductile fracture, which is preceded by large plastic deformations and energy absorption. This kind of fracture is usual in ductile metals like low carbon steel. Finite Element which is considered as the most important numerical method in the mechanics of materials, is also, widely used in... 

In this thesis, based on the combination of Extended Finite Element Method (X-FEM) and appropriate material constitutive models, an efficient method is proposed to model ductile fracture under quasi-static, cyclic and dynamic conditions. X-FEM is a novel method in which with the use of appropriate enrichment functions, discontinuity geometry is separated from the computational mesh and hence the need for a remeshing step is alleviated. The non-linear material behavior in the crack tip process zone can best be modeled with methods based on continuum damage mechanics. These methods model the ductile fracture mechanisms, phenomenologically. In this thesis, in order to model the ductile... 

In the last decades, Hydraulic Fracturing has been found widespread applications. One of its main applications is fracture producing in hydrocarbon reservoirs and increasing the outflow of oil and gas. Thus, control and prediction of crack path is really necessary. One of the major parts in any model is an appropriate crack propagation criteria. Many criterion has been proposed in literature. These models often assume some simplifying assumptions. They often consider isotropic media. In fact, this assumption is not applicable in geo-mechanics. In other words, there are many inhomogenities such as micro-cracks and microdefects. These appear in the flow characteristics (e.g. permeability) and...