Optimization of fiber geometry for fiber reinforced composites considering damage

The present contribution deals with an optimization strategy of fiber reinforced composites. Although the methodical concept is very general we concentrate on Fiber Reinforced Concrete with a complex failure mechanism resulting from material brittleness of both constituents matrix and fibers. Because of these unfavorable characteristics the interface between fiber and matrix plays a particularly important role in the structural response. A prominent objective for this kind of composite is the improvement of ductility. The influential factors on the entire structural response of this composite are (i) material parameters involved in the interface, (ii) the material layout at the small scale level, and (iii) the fiber geometry on the macroscopic structural level. The purpose of the present paper is to improve the structural ductility of the fiber reinforced composites applying an optimization method with respect to the geometrical layout of continuous long textile fibers. The method proposed is achieved by applying a so-called embedded reinforcement formulation. This methodology is extended to a damage formulation in order to represent a realistic structural behavior. For the optimization problem a gradient-based optimization scheme is assumed. An optimality criteria method is applied because of its numerically high efficiency and robustness. The performance of the method is demonstrated by a series of numerical examples; it is verified that the ductility can be substantially improved.