Quantitative comparison between fast fourier transform and finite element method for micromechanical modeling of composite
Résumé
A variety of numerical methods can be applied for multi-scale simulation of composite materials in general and textile reinforced composites in particular. Among numerical methods, the Finite Element Method (FEM) is the main tool for modeling textile composites [1]. Recent developments have brought increased interest in the Fast Fourier Transform (FFT) based method for multi-scale material modeling. This method uses image-based techniques and also gives accurate results as FEM voxel-based models do [2]. Backing to 1994, the FFT method was proposed initially by P.Suquet and H.Moulinec [3], as a voxel-based methodology that does not need stiffness matrix assembling like FEM. It can thus be very efficient in the field of digital materials and easily parallelized. The main drawback of voxel-based models is the presence of strong oscillations due to the non-smooth interface [4]. From the best of our knowledge, the FFT and FEM are often compared in a general way. In this work, specific problems of the micromechanics of composite materials were addressed in order to compare quantitatively FFT and FEM solutions of the stress field at the interface, based on the direct output and with the introduction of a smoothing method. The open-source software AMITEX [5] is applied for all FFT calculations and ABAQUS is applied for all FEM calculations.
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