A cubic spline implementation of non-linear shear behaviour in three-dimensional progressive damage models for composite laminates

An experimental study was carried out to characterise the constitutive response of carbon fibre-reinforced epoxy laminates. While maintaining essentially linear behaviour in the fibre and transverse directions, this material displays significant non-linear shear stress–strain behaviour to rupture. It is shown that the well known Hahn-Tsai non-linear shear model does not provide an acceptable fit for the strain range examined and so a novel approach was derived where a cubic spline interpolation method was used to capture the non-linear shear behaviour. The well known ply discount model, based on Hashin’s failure criteria, was also used to predict fibre and transverse matrix damage in the laminates. The spline approach is coupled with maximum strain failure criteria to predict the response in the in-plane and out-of-plane shear directions. The material Jacobian matrix is fully defined, thus allowing a full implicit material model to be implemented. Hence, the model is suitable for both implicit and explicit finite element codes. It is shown that the model accurately predicts the response of the material for load cases in which shear stresses dominate. The performance of the model is demonstrated by considering a number of laminate configurations and failure of an open-hole tension specimen.