Momentum conserving dynamic variational approach for the modeling of fiber-bending stiffness in fiber-reinforced composites

Abstract

Rotor-dynamical systems made of 3D-fiber-reinforced composites which are subjected to dynamical loads exhibit an increased fiber bending stiffness in numerical simulations. We propose a numerical modeling approach of fiber-reinforced composites that treats this behaviour accurately. Our model uses a multi-field mixed finite element formulation based on a dynamic variational approach, as demonstrated in [1], to perform long-term dynamic simulations that yield numerical solutions with increased accuracy in efficient CPU-time.We extend a Cauchy continuum with higher-order gradients of the deformation mapping as an independent field in the functional formulation, as suggested in [2], to model the bending stiffness of fibers accurately. This extended continuum also takes into account the higher-order energy contributions including the fiber curvature along with popular proven approaches that avoid the numerical locking effect of the fibers efficiently.We apply the proposed approach on Cook’s cantilever beam with a hyperelastic, transversely isotropic, polyconvex material behavior in a transient dynamic analysis. The beam is subjected to bending loads with a strong dependence of the overall stiffness on the fiber orientation. The spatial and temporal convergence as well as the conservation properties are analyzed. It is observed that the model needs an improved numerical treatment to conserve total momenta as well as total energy.REFERENCES M. Groß and J. Dietzsch, "Variational-based locking-free energy–momentum schemes of higher-order for thermo-viscoelastic fiber-reinforced continua", Computer Methods in Applied Mechanics and Engineering, (2019), 631-671, 343. T. Asmanoglo and A. Menzel, “A multi-field finite element approach for the modelling of fibre-reinforced composites with fibre-bending stiffness”, Computer Methods in Applied Mechanics and Engineering, (2017), 1037-1067, 317.