In this thesis, the Finite Cell Method (FCM) has been developed for the Lemaitre and a nonlocal integral damage problem. This method is a combination of a fictitious domain approach with higher-order finite elements, adaptive integration, and weak enforcement of the non-conforming essential boundary conditions. This alleviates the urge for boundary conforming meshes that are time-consuming to be generated free of error. For developing the FCM in the fields of damage mechanics, the formulation is implemented in a high-order finite element package tailored for the Finite Cell Method. The advantage of using this code is to access all subroutines and the possibility of changing them where it is necessary. Besides that the Gauss points are accessible and it facilates the implementation of an integral nonlocal model. The nonlocal ductile damage constitutive model used is a thermodynamically consistent theory of integral type in which the damage variable is integrated over the whole domain.Bench mark 2D and 3D examples are solved to validate the results of the Lemaitre model and a good agreement is obsereved between FCM results and previous researchers’. Experimental tests are performed on AA7075-T6 alloy to validate the result of 3D examples in the nonlocal model. A good agreement of the simulation and experiments has been achieved. Further, the non-local damage model compared to the local models performs better in terms of convergence and numerical stability Keywords: The Finite Cell Method, Damage Mechanics, High order finite elements, nonlocal Integral formulation
