The present work aims to address open issues hindering the development of nonlinear wave modulation SHM/NDE methods for the detection of delaminations in composite laminates. Specifically, the mechanisms generating the nonlinear indices are clarified and the relationship of the latter with damage and wave parameters is investigated. A robust and computationally fast, time domain spectral finite element, containing high-order layerwise laminate mechanics is further extended to model delaminated composite strips. Contact mechanisms enabling impacts between the delaminated interfaces are included in the formulation. Simulations of high-frequency antisymmetric and symmetric ultrasonic wave propagation in Carbon/Epoxy strips with various delaminations sizes are presented. The simulations reveal complex nonlinear phenomena involving interactions between wave conversion and contacts in the delaminated region, which subsequently result in frequency harmonics in the dynamic response, manifesting the presence of delamination. The dependence of the generated harmonics and their modulation factor, to the type of assumed contact, the size of damage and the frequency/wavelength of the excited wave are further studied. Finally experimental measurements are used to validate the analytical conclusions.