A material model for fibre-reinforced composites

The goal of this diploma thesis is the implementation of a theoretical non-linear material model for fibre-reinforced plastic (FRP) in a finite element program. Fibre-reinforced plastic is rather a composite than a material, consisting of the two components fibre and matrix. These two components are characterized by the large difference in material stiffness. Hence, the total stiffness of fibre-reinforced plastic depends on the alignment of the fibre. Consequently, the FRP exhibits anisotropic material behaviour. Moreover, the material behaviour of fibre-reinforced plastic is non-linear. These material non-linearities with simultaneous consideration of anisotropy can be described only with highly complex material models, which require questionable assumptions and simplications. To make the calculation process as simple and clear as possible, the fibre and the matrix are treated separately in the material model used in this diploma thesis. Thereby, the stiffness matrices of the two components are calculated separately and assembled to a single matrix of material stiffness volumetrically. For the polymer matrix isotropic material behavior is assumed. The fibre is treated as a one-dimensional continuum, which transfers forces only in its longitudinal axis. Multiple layers of fibres with different orientations in the composite are possible. With the help of these assumptions the material non-linearities can be described with relatively simple constitutive relations. For the fibre-reinforced plastic component matrix elasto-plastic material behaviour is considered. Yielding is determinated by the yield hypothesis of von Mises. The numerical implementation is based on the return mapping algorithm and an isotropic hardening law. For the fibre-reinforced plastic component fibre a damage model describes the degradation of the material properties. Cracking under tensile loading and microbuckling under compressive loading is predicted with the fraction hypothesis of Rankine. To prevent the spreading of damage under load redistribution from the tensile to the compressive regime, the theory of compressivestiffness-recovery is applied. Convergence with respect to the discretization within the framework of the finite element method is achieved by adjusting the stress-strain relation by means of a consistent characteristic length and the specfic fracture energy. To obtain consistency, furthermore linear softening is expected. A comparison of the received results with the results of test runs assuming exponential softening and a non-consistent characteristic length respectively, justify this approach. The underlying mathematical formulations are described and a function test in terms of example problems is conducted. The developed source codes are listed in the appendix.



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