Cylindrical microplane model for compressive kink band failures and combined friction/inelasticity in fiber composites I: Formulation

This two-part paper presents a novel 3D cylindrical microplane model for the longitudinal compressive failure of fiber reinforced composites by kink band formation. The formulation details are presented in part-I, while the implementation, calibration, and validation, in part-II. The primary novelty is the first adaptation of the semi-multiscale microplane modeling approach to compressive kink band failures in composites. The salient novel feature of this adaptation is a cylindrical system of microplanes, introduced to capture the transversely isotropic behavior of the unidirectional lamina. The model implicitly resolves the macro–micro compatibility to calculate the local fiber rotation in the kink band, thus defining the orientation of the cylindrical microplane system. This allows an intuitive formulation of the kink band triggering mechanism involving axial inter-fiber microcracks at the microplane level. As another new advance, the internal friction is formulated at the microplane level, via a thermodynamically consistent combined damage/friction scheme, which is integral to compressive failures. The model formulation is general enough to allow application to both brittle and ductile matrix materials, and to in-plane and out-of-plane kinking. The macro–micro elastic correlations are established via strain energy density equivalence, and the calculation of the stiffness tensor of one microplane system is demonstrated.