Abstract
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.
Highlights
Polycrystalline materials at a microscopic level show clear heterogeneous deformation patterns
The first is on the effect of the length scale contrast method for the gradient damage model
Since the considered properties are uniform, we introduce a small imperfection by means of a 1% reduction of the critical stress σc for the grid points in the interval x ∈ [−l/20, l/20] within the interphase band, in order to trigger localisation
Summary
Polycrystalline materials at a microscopic level show clear heterogeneous deformation patterns. This heterogeneity arises from the locally fluctuating mechanical properties of different phases and differences in lattice orientations between different grains. An FEM perspective on an FFT based spectral formulation for small strain non-linear material behaviour was given in [6] and its extension to a finite strain setting was presented in [7]. Alongside such improvements, much effort has gone into making the method suitable for various applications. The computational efficiency of FFT methods makes them attractive to solve multi-field problems, for e.g. a nonlocal crystal plasticity formulation [8], ferroelectric switching [9], etc
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