Variational-based finite element simulation of fiber-reinforced materials with fiber bending stiffness inmoving thermodynamical systems.

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In scientific research and material science, computational simulations are more and more used for reducing costly and time consuming experimental investigations. Especially in the case of composite materials, computational simulations provide the possibility to determine appropriate composites numerically first, before these composite materials are produced physically. In this way, many work hours and financial expense can be saved in the sample production, because the number of samples will be reduced. In order to determine appropriate composite materials by using the common finite element method, there is a need for an exact as possible modelling of the appearing stress states in the considered parts. In the case of the often appearing thin-walled composite structures, the exact description of the bending behaviour in a computational simulation is therefore necessary. Especially regarding dynamical loads, bending vibrations have to be predictable, in order to know the right surrounding space and the appropriate support of the composite parts. This requires to avoid locking effects in finite elements and the modelling of each material stiffness. Thus, in the case of fiber-reinforced polymers with a predominant portion of solid fibers, the computational modelling of a fiber bending stiffness is necessary. Especially for parts subject to dynamical loads, the modelling of an inertia influence by means of the fibers contributes to obtain meaningful computational results.The goal of the submitted research project is the modelling of fiber bending or finite fiber diameter, respectively, in the scope of thermodynamics, such that a dynamical simulation of the underlying material model is numerically exact, numerically stable and CPU-time efficient. This is provided by the energy-momentum consistent time integration algorithms to be developed in this research project, which are based on a locking-free space discretization and an automatic time-step size control.