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

在科学研究和材料科学中，计算模拟越来越多地用于减少昂贵和耗时的实验研究。特别是在复合材料的情况下，计算模拟提供了在物理生产这些复合材料之前首先通过数值确定合适的复合材料的可能性。通过这种方式，可以在样品生产中节省许多工时和财务费用，因为样品的数量将减少。为了确定适当的复合材料，通过使用普通的有限元方法，有必要为一个精确的尽可能出现在所考虑的部分的应力状态建模。在经常出现的薄壁复合材料结构的情况下，弯曲行为的准确描述，在计算模拟是必要的。特别是在动态载荷方面，弯曲振动必须是可预测的，以便了解正确的周围空间和复合材料部件的适当支撑。这需要避免有限元中的锁定效应和每种材料刚度的建模。因此，在纤维增强聚合物的固体纤维的主要部分的情况下，纤维弯曲刚度的计算建模是必要的。特别是对于承受动态载荷的部件，通过纤维对惯性影响的建模有助于获得有意义的计算结果。提交的研究项目的目标是在热力学范围内分别对纤维弯曲或有限纤维直径进行建模，以便对底层材料模型进行动态模拟，从而实现数值精确、数值稳定和CPU时间效率。这是由能量-动量一致的时间积分算法在本研究项目中开发，这是基于锁定自由空间离散化和自动时间步长控制。

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.