A Multiscale Finite Element Model for Damage Simulations in Fiber-Reinforced Composites

Fiber-reinforced plastics are of increasing relevance in a broad variety of engineering applications. Developments in E-Mobility and ever-increasing demands on materials guarantee that this trend will continue. The increasing use and importance of FRP will in turn increase demand for appropriate methodologies for describing the complex mechanical properties of these materials. This thesis contributes to this end to the theoretical development and implementation of damage models. These models build on the so called smeared crack approach, whereby the damage in the material is assumed to have a continuous distribution. With the help of damage models, maximum bearing load computations can be performed and the damage initiation and propagation can be precisely followed. A variety of approaches are used in this thesis: firstly, a macroscopic view of anisotropic damage models is presented. The model utilizes either Hashin's failure criterion or Cuntze's failure mode concept to determine damage initiation. At the onset of damage, a linear degradation model is used, the path of which is determined by the critical energy release rate. In conjunction with the characteristic element length, an accurate calculation of the dissipated energy in the finite element model is assured. A second approach is based on a coupled multi-scaled finite element model. The model presented here is a two-scale model consisting of a micro scale and a macro scale. The distortions in the macro scale are mapped onto the micro scale using appropriate boundary conditions. In the micro scale, the modeling of the damage is carried out separately on the individual fiber and polymer components. The nonlinear micro model is solved by means of Newton-Raphson method before the homogenized stresses and material tangents are delivered to the macro system. This process is repeated until global equilibrium is achieved. The micro scale model utilizes an exponential degradation law, which lacks an elastic initial region and has proven to be especially robust. The multi scale model affects damage at locations where it actually occurs, giving it a significant advantage over macroscopic models. The use of costly failure criterion is spared in this approach. Furthermore, use of the multi scale approach allows detailed observations of the failure in the material, and failure modes such as fiber-polymer separation can easily be implemented. The counter-argument to this approach is the significant computational cost, caused by the necessity of a complete iteration loop in the micro system for every integration point in the global system. However, the structure of the models makes them especially suitable for simultaneous parallel processing, so that it can be expected that they supersede macroscopic models in the mid term future