Modeling of fiber‐bending stiffness in fiber‐reinforced composites with a dynamic mixed finite element method based on the principle of virtual power

Abstract

AbstractInvestigating the bending stiffness of fibers in fiber‐reinforced composites for rotor‐dynamical systems which are subjected to dynamical loads are essential in the development of system design. The proposed numerical modeling approach of fiber‐reinforced composites uses a multi‐field mixed finite element formulation based on a dynamic variational approach to perform long‐term dynamic simulations with CPU‐time efficient and increased accurate numerical solutions. To model the bending stiffness of fibers accurately, we extend a Cauchy continuum with higher‐order gradients of the deformation mapping as an independent field in the functional formulation. This extended continuum also takes into account the higher‐order energy contributions including the fiber curvature along with popular proven approaches that efficiently avoid the numerical locking effect of the fibers. The effect of the proposed approach is demonstrated through transient dynamic analysis on a cantilever beam with a hyperelastic, transversely isotropic, polyconvex material behavior. The beam is subjected to bending load with a strong dependence of the overall stiffness on the fiber orientation. The material and conservation properties are analyzed.