FFT-based interface decohesion modelling by a nonlocal interphase

In this paper, two nonlocal approaches to incorporate interface damage in fast Fourier transform (FFT) based spectral methods are analysed. In FFT based methods, the discretisation is generally non-conforming to the interfaces and hence interface elements cannot be used. This limitation is remedied using the interfacial band concept, i.e., an interphase region of a finite thickness is used to capture the response of a physical sharp interface. Mesh dependency due to localisation in the softening interphase is avoided by applying established regularisation strategies, integral based nonlocal averaging or gradient based nonlocal damage, which render the interphase nonlocal. Application of these regularisation techniques within the interphase sub-domain in a one dimensional FFT framework is explored. The effectiveness of both approaches in terms of capturing the physical fracture energy, computational aspects and ease of implementation is evaluated. The integral model is found to give more regularised solutions and thus a better approximation of the fracture energy.