An energy‐momentum space‐time discretization of a constrained micropolar continuum for 3D fiber‐reinforced composites

Abstract

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.