Isogeometric homogenization of unidirectional nanocomposites with energetic surfaces

Abstract

The present work aims to propose an interface-enriched isogeometric analysis strategy for predicting the size-dependent effective moduli and local stress field of periodic arrays of nanosize inhomogeneity. The proposed framework allows for an exact representation of the curved boundary of inhomogeneity inside the matrix due to the representation of the geometry of repeating unit cells for microstructured materials with nonuniform rational B-splines. The energetic surface was characterized by the Gurtin-Murdoch model, and it was incorporated into the proposed framework by introducing additional surface energies linked to the bulk elements neighbouring the interface. The surface-enhanced isogeometric homogenization method was verified through comparisons with existing solutions found in the literature. It is demonstrated that the proposed framework enables the satisfaction of higher-order continuity of the displacement fields, leading to smooth and accurate predictions of the stress fields and homogenized moduli of nanocomposites, without encountering the convergence problems associated with conventional finite-element methods in the literature.