Physically consistent simulation of thermodynamics of fiber-reinforced plastics

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During the mechanical manufacturing of axisymmetric bodies with fiber-reinforced polymers (FRP) as pipes or shafts by using a winding process, engineers use so-called rovings. A roving denotes a bundle of parallel arranged continuous filaments. The number of filaments lies in the range of multiple thousands. Therefore, the diameter of a roving lies in the range of millimeters. Moreover, rovings are used to produce woven composites.A further manufacture technology is the Tailored-Fiber-Placement, in which rovings are fixed by cords on a base material. In these manufacture procedures, only rovings are used. The anisotropic behaviour of the resulting metamaterials can be modelled as in the project (sign removed) by means of structural tensors. But, an important feature of rovings is their bending stiffness. The physical bending stiffness of rovings is not considered in the project (sign removed). The fibers in this project are implicity assumed as infinitely thin. The bending stiffness of the rovings leads to a large curvature under loading, but to a small curvature at loading free boundaries. Hence, a finite element mesh is simulated too flexible by means of the mixed finite element methods of project (sign removed).Goal of the project (sign removed) is to take into account the correct physical bending stiffness of FRP parts made of rovings. In this way, the energy-momentum schemes avoid artificial locking behaviour by using the mixed finite elements of project (sign removed), but exactly simulate each physical stiffness of the FRP part. Further, we aim at taking into account the material inhomogeneity, because we obtain by rovings a multiscale problem with a macroscopic scale (the FRP part), a mesoscopic scale and microscopic scale (the roving).