Abstract

Unidirectionally reinforced composite materials often employ a stiff but brittle reinforcement embedded in a comparably compliant but ductile matrix. Although the material micro-structure is normally at a significantly lower length scale compared to the component dimensions, the separation of scales assumption is not always a valid one. This is for example the case when studying the formation of kink-bands inside a larger component. In such cases, in order to avoid a computationally prohibitive explicit discretization of the micro-structure, appropriate high fidelity computational homogenization methods have to be developed.

Most of the available homogenization methods aim at representing materials with a micro-structure exclusively relying on a displacement field valid at the macro-scale. A different approach is to use additional kinematic variables for capturing more accurately the kinematic behavior of the micro-structure. In the past, a micro-rotation variable corresponding to the Cosserat continuum theory was used in addition to the homogenized displacements field in order to account for the bending stiffness of the reinforcing fibers in UD composites. Pushing this concept further, in the present work we employ a number of additionally kinematic variables in order to obtain an even richer representation of deformations in the micro-structure. In its most advanced variant the model can capture the occurrence of quasi-brittle fracture in the fibers due to bending. The level of fidelity of the method is demonstrated by comparing its results to simulations with an explicit discretization of the micro-structure.