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Three-dimensional woven carbon-fiber reinforced polymers (3D-CFRP) are being increasingly used for blades in rotordynamical systems as turbine fans, shafts as well as disc brake rotors. By using dynamic mixed finite-element methods, these materials can be simulated as anisotropic continua with non-isothermal behaviour in the matrix as well as the fiber material. Therefore, we present a novel dynamic mixed finite-element method which is variational-based and capable to simulate these materials. This dynamic mixed finite-element method preserves each basic balance law emanating from the variational principle exact in a discrete setting. We demonstrate this physically-consistent simulation behaviour by using dynamic simulations of a disc brake rotor and a rotating pipe subject to thermal and mechanical loads.

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In 2D fiber-reinforced composites, single fibers with a diameter in the range of micrometers are embedded in a matrix material. 3D fiber-reinforced composites consist of fiber bundles (rovings) with diameters of millimeters. Therefore, 3D fiber-reinforced composites require an extended material modelling, because a fiber bundle has to be considered as a beam-like structure with curvature-twist (twisting and bending) stiffness. By means of an extended continuum formulation, we modell a micro inertia and a curvature-twist stiffness. We introduce these secondary effects by means of independent drilling degrees of freedom. The resulting constrained micropolar continuum is derived by a mixed principle of virtual power. In the discrete setting, this variational principle generates a mixed B-bar method and an energy-momentum scheme. We show transient numerical examples, which demonstrate the effect of micro inertia as well as the twisting and bending stiffness of the fiber bundles.