Nitsche's method enhanced isogeometric homogenization of unidirectional composites with cylindrically orthotropic carbon/graphite fibers

Abstract

An isogeometric homogenization (IGH) technique is constructed for the homogenization and localization of unidirectional composites with radially or circumferentially orthotropic carbon/graphite fibers. The proposed theory employs multiple non-conforming Non-Uniform Rational B-Splines (NURBS) patches to depict repeating unit cells (RUCs) representative of composite microstructures. Displacements are formulated using a two-scale expansion that integrates macroscopic and microscopic contributions, with the latter addressed through the isogeometric analysis technique. Nitsche’s method is utilized to apply the interfacial traction and displacement continuity and periodicity conditions. The capability and accuracy of the IGH theory were validated upon comparison with the elasticity solutions that take into account explicitly fiber morphologies, along with classical micromechanics solutions based on equivalent fiber moduli. A comparative analysis with conventional finite element techniques showcases the developed theory’s ability to accurately replicate the singular stress field at the fiber center and to capture smooth stress distributions where significant stress gradients are encountered.