Accounting for Fiber Bending Effects in Homogenization of Long Fiber Reinforced Composites

The present work deals with homogenized finite-element models of long fiber reinforced composite materials in the context of studying compressive failure modes such as the formation of kink bands and fiber micro-buckling. Compared to finite-element models with an explicit discretization of the material micro-structure including individual fibers, homogenized models are computationally more efficient and hence more suitable for modeling of larger and complex structure. Nevertheless, the formulation of homogenized models is more complicated, especially if the bending stiffness of the reinforcing fibers is to be taken into account. In that case, so-called higher order strain terms need to be considered. In this paper, important relevant works from the literature are discussed and numerical results from a new homogenization model are presented. The new model accounts for two independent constitutive laws for the fiber and the matrix materials, respectively expressed in the frameworks of hyper-elasticity and hyper-elasto-plasticity. The presented numerical results include comparisons between the homogenized model and an explicit discretization of the composite microstructure. Both models are in good agreement. In cases where the fiber bending stiffness is significant,the homogenized finite-element model exhibits size-scale dependent material behavior, as predicted by the model with explicitly discretized individual fibers.