On the dependence of orientation averaging mean field homogenization on planar fourth-order fiber orientation tensors

A comprehensive study on the influence of planar fourth-order fiber orientation tensors effective linear elastic stiffnesses predicted by averaging mean field homogenization is given. Fiber states sheet molding compound (SMC) are identified to be in most cases approximately planar. In case, all possible given a minimal invariant set structurally differing tensors. This defines three-dimensional body and forms basis for distribution terms tensor homogenized stiffnesses. The methodology this main contribution work can adopted analyze dependence any quantity which function tensor. At specific points inside tensors, calculated with selected schemes. These schemes based transversely isotropic elasticity following Advani Tucker (1987), explicitly recast as composition second fourth order Kanatani third kind. maximum entropy reconstruction leading enables new numerical formulation average special case. Polar plots Young’s modulus generalized bulk obtained arranged two-dimensional slices within admissible visualizing stiffness orientation-dependence differs significantly between homogenizations. Restrictions anisotropic material response caused orthotropy closure approximations discussed.