The nonlinear finite element method is a computational method in the variational simulation of material models for materials with and without microstructures . Taking into account microstructures of engineering materials in their computational models is often worthwhile to improve numerical predictions . An example is the modelling of fiber-reinforced materials, which are manufactured on the microscale by filaments or on the mesoscale by rovings, respectively. A macroscopic finite element simulation of both materials provides an anisotropic continuum model. However, fiber-reinforced materials based on rovings demand for continua with extended kinematics. A computational modelling of extended continua is possible by a mixed finite element method. In this contribution, we show the introduction of internal rotational degrees of freedom to model also a stiffness with respect to roving flexure and twist. Furthermore, a corresponding structure-preserving time integration is obtained. Numerical examples also demonstrate the additional continuum stiffness owing to the consideration of roving flexure and twist.
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