Deformation gradient tensor decomposition for representing matrix cracks in fiber-reinforced materials

A new method is presented for the representation of matrix cracks in continuum damage mechanics (CDM) models for fiber-reinforced materials. The method is based on the additive decomposition of the deformation gradient tensor into 'crack' and 'bulk material' components, analogous to the additive strain decomposition of the smeared-crack approach. The potential improvements to the accuracy of CDM models that utilize the presented method are demonstrated for a single element subjected to simple shear deformation and for a unidirectional open-hole tension specimen. The presented method avoids load transfer across matrix cracks and eliminates the prediction of spurious secondary failure modes that occurs when conventional strain-based CDM models are used in geometrically nonlinear finite element analyses involving large shear deformations.