This paper presents the modelling of tensile failure of composites using novel enriched elements defined
based on the floating node method. An enriched ply element is developed, such that a matrix crack can
be modelled explicitly within its domain. An enriched cohesive element is developed to incorporate the
boundaries of matrix cracks on the interface, such that the local stress concentrations on the interface can
be captured. The edge status variable approach allows the automatic propagation of a large number of
matrix cracks in the mesh. A laminate element is formed, such that a fixed, planar mesh can be used for
laminates of arbitrary layups. The application examples demonstrate that the proposed method is capable
of predicting several challenging scenarios of composites tensile failure, such as the large number matrix
cracks, grip-to-grip longitudinal splits, widespread delamination, explosive splitting and distributed fibre
breaking in the 0 plies, etc. The complete failure process of ply-blocked composite laminates, up to the final
breaking of the loosened 0° strips, are here firstly reproduced by modelling.