MATERIAL SHAPE OPTIMIZATION FOR FIBER REINFORCED COMPOSITES APPLYING A DAMAGE FORMULATION

Abstract

The present thesis proposes material optimization schemes for fiber reinforced composites, specifically for a new composite material, denoted as Fiber Reinforced Concrete (FRC) or Textile Reinforced Concrete (TRC); here a reinforcement mesh of long carbon or glass fibers is embedded in a fine grained concrete (mortar) matrix. Unlike conventional steel reinforcement, these textile fibers are corrosion free; this holds also for AR-glass due to its high alkali-proof. This favorable property allows to manufacture light-weight thinwalled composite structures. However the critical aspect of this composite is that the structural response of FRC may show brittle failure due to the material brittleness of both constituents concrete and fiber in addition to their complex interfacial behavior. This specific characteristic of FRC is an ideal target for material optimization applying the overall structural ductility as objective which ought to be maximized for a prescribed fiber volume. For this objective it is of course not sufficient to base the optimization process on a linear elastic material model, so that it is mandatory to consider material nonlinearities. In the present study a gradient enhanced isotropic damage model is applied for both matrix and fiber materials and a discrete bond model is used for their interface. The structural response of FRC depends on several parameters, e.g. fiber size, fiber length, fiber location/orientation, impregnation, surface roughness of fiber, and the kind of fiber material itself. From these the most influential parameters like fiber dimensions and locations are chosen as design variables for optimization. Conventional material optimization applying simply ‘smeared-type elements’ mostly concentrate on the fiber orientation defined at each finite element. This approach is not detailed enough when the influence of other important parameters mentioned above ought to be investigated. Considering the design requirements for the present objective, this thesis proposes three kinds of material optimization schemes, namely multiphase material optimization, material shape optimization, and multiphase layout optimization. Multiphase material optimization determines an optimal distribution of several materials over a prescribed design domain in a fixed finite element mesh. This methodology is related to topology optimization, especially to the Solid Isotropic Microstructure with Penalization (SIMP) approach. With this method optimal fiber size, fiber length, and combination of different fiber materials can be obtained. The task of material shape optimization is to improve the structural ductility of FRC with respect to ‘fiber geometry’ which is independent of the fixed finite element mesh. By applying a so-called embedded finite element formulation, the complexity of discretization for thin fibers in a conventional finite element formulation is diminished. Multiphase layout optimization provides not only optimal fiber geometry but also optimal fiber size or the kind of fiber materials simultaneously. This methodology is achieved by combining above multiphase material and material shape optimization. For the optimization problems a gradient-based optimization scheme is assumed. An optimality criteria method and a method of moving asymptotes are applied considering their numerical high efficiency and robustness. For the sensitivity analyses variational direct analytical/semi-analytical methods are utilized. The performance of the proposed methods is demonstrated by a series of numerical examples; it is verified that the ductility of FRC can be substantially improved. The proposed methods providing optimal designs are promising and methodically challenging. They are also applicable to other fiber reinforced composites, for example Fiber Reinforced Glass (FRG).