Physically consistent simulation of thermodynamics of fiber-reinforced plastics

在用纤维增强聚合物（FRP）作为管道或轴通过缠绕工艺机械制造轴对称体期间，工程师使用所谓的粗纱。粗纱表示一束平行排列的连续长丝。细丝的数量在数千根的范围内。因此，粗纱的直径在毫米范围内。此外，粗纱还用于生产机织复合材料。另一种制造技术是定制纤维铺放技术，其中粗纱通过绳索固定在基材上。在这些制造过程中，仅使用粗纱。由此产生的超材料的各向异性行为可以通过结构张量来模拟，就像在项目中一样（去除符号）。但是，粗纱的一个重要特征是它们的弯曲刚度。本项目未考虑粗纱的物理弯曲刚度（标志已删除）。在这个项目中的纤维是隐含假设为无限薄。粗纱的弯曲刚度导致在负载下的大曲率，但在无负载边界处的小曲率。因此，通过项目的混合有限元方法（去除符号）模拟有限元网格过于灵活。项目的目标（去除符号）是考虑由粗纱制成的FRP部件的正确物理弯曲刚度。通过这种方式，能量-动量方案通过使用项目的混合有限元（符号被移除）避免了人为锁定行为，但准确地模拟了FRP部件的每个物理刚度。此外，我们的目标是考虑到材料的不均匀性，因为我们通过粗纱获得一个多尺度问题，宏观尺度（FRP部分），介观尺度和微观尺度（粗纱）。

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).