A semi-homogenized extended isogeometric analysis approach for fracture in functionally graded materials containing discontinuities

In this paper, we present a semi-homogenized extended isogeometric analysis approach for assessment of stress intensity factor of center cracked functionally graded domain containing discontinuities such as holes and inclusions. In the semi-homogenized approach, the presence of discontinuities is considered in the 30% region in the vicinity of crack, and the remaining part of the domain is modeled using equivalent homogenous material properties. The Heaviside and singular crack tip enrichment functions are employed to model the center crack, whereas crack topology is tracked using level set functions. The domain form of interaction integral approach is employed to estimate the stress intensity factors at the tips of the center crack. Several problems containing discontinuities in 30% portion of the domain are investigated using the semi-homogenized approach. The efficiency and accuracy of the developed method are examined by comparing the computed results with those attained by modeling discontinuities in the entire domain. The advantages of the semi-homogenized extended isogeometric analysis approach are highlighted in terms of higher computational efficiency.