A high efficiency k-space method solving wave propagation problems is proposed in this paper. The proposed method proves to provide high accuracy in wave propagation problems in damaged and undamaged materials. Numerical models using k-space method are verified with analytical solutions and FEM solution in both 2D and 3D case. The uniqueness of this paper is first, a novel wavenumber operator of anisotropic material is proposed and helps to relax the requirement on time step in Finite Difference scheme. Second, the inclusion of discontinuity such as cracks, delamination and material property change using k-space method is explicitly modelled, which will be helpful for inverse problems such as damage identification in the future. It's found that embedded crack has less impact on received signals compared to surface damage. The effect of crack density and crack length on the time of flight and waveform will be discussed later. The inverse formulation using the proposed method should be investigated and the high efficiency and accuracy of k-space method will greatly facilitate the efficiency of damage detection which will be discussed in the future.
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