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

Abstract

AbstractIn 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.