Computational homogenization of sheet molding compound composites based on high fidelity representative volume elements

Sheet molding compound (SMC) composites combine high lightweight potential with excellent formability and are frequently used in industrial applications. To reduce safety factors in dimensioning SMC parts, the influence of processing parameters and stochastic variation of microstructural and physical properties needs to be quantified accurately. Taking into account the inherent three-scale structure of SMC, we improve the microstructure generator of Chen et al. [Compos. Struct. 188, pp. 25-38, 2018] in various respects. Firstly, we consistently rely upon state-of-the-art closure approximations for the fourth order fiber orientation tensor. More precisely, we show that for a planar fiber orientation state, there is an explicit formula for the fast exact closure approximation of Montgomery-Smith et al. [J. Fluid Mech. 680, pp. 321-335, 2011]. Secondly, we exploit the use of quasi-random numbers in sampling the fiber orientation distribution, leading to dramatic improvements in accuracy compared to pseudo-random Monte Carlo sampling. Last but not least, we rely upon fast Fourier transform based methods for rapid computational homogenization. With these methodological improvements at hand, we thoroughly investigate the influence of the mechanical and microstructural parameters on the effective elastic properties of SMC composites, and compare the results to direct numerical simulations on large scale digital volume images and mean-field estimates.