Multiphase layout optimization for fiber reinforced composites considering a damage model

The present study addresses an optimization strategy for fiber reinforced composites, specifically Fiber Reinforced Concrete (FRC) with a complex failure mechanism resulting from material brittleness of both matrix and fibers and also from the nonlinear interfacial behavior between those constituents. A prominent objective for this kind of composite is the improvement of ductility. The entire structural response of this material strongly depends on three factors, (i) material layout of fiber on a small scale, (ii) fiber geometry on the macroscopic structural level, and (iii) material parameters of interface between matrix and fiber.The purpose of the present study is to improve the structural ductility of FRC by applying optimization; in the formulation not only the optimal material layout of fibers on the small scale but also the global fiber geometry are determined simultaneously. The proposed method is achieved by combining multiphase material optimization and material shape optimization, separately introduced by Kato et al. [11] and Kato and Ramm [12], respectively.For the optimization problem a gradient-based optimization scheme is assumed. A method of moving asymptotes (MMA) is applied because of its numerically high efficiency and robustness. The performance of the proposed method is demonstrated by a series of numerical examples and compared with pure material shape optimization. It is verified that the proposed method gives more efficient results than the individual material shape optimization and that the structural ductility can be substantially improved.