Constitutive model for fibre reinforced composites with progressive damage based on the spectral decomposition of material stiffness tensor

Complex nature of the fibre reinforced composites, their non-homogeneity and anisotropy make their modelling a challenging task. Although the linear – elastic behaviour of the composites is well understood, there is still a significant uncertainty regarding prediction of damage initiation, damage evolution and material failure especially for a general loading case characterised with triaxial state of stress or strain. Consequently, simplifying assumptions are often unavoidable in development of constitutive models capable of accurately predicting damage. The approach used in this work uses decomposition of the strain energy based on spectral decomposition of the material stiffness tensor and an assumption that each strain energy component represent free energy for a characteristic deformation mode. The criteria for damage initiation are based on an assumption that the damage corresponding to a deformation mode is triggered when the strain energy for that mode exceeds a specified critical limit. In the proposed model the deformation modes are not interacting at continuum scale due to orthogonality of the eigenvectors, i.e. the stiffness tensor symmetry. Damage and its evolution are modelled by reduction of the principal material stiffness based on the effective stress concept and the hypothesis of strain energy equivalence. The constitutive model was implemented into Lawrence Livermore National Laboratory (LLNL) Dyna3d explicit hydrocode and coupled with a vector shock Equation of State. The modelling approach was verified and validated in a series of single element tests, plate impact test and high velocity impact of hard projectile impact on an aerospace grade carbon fibre reinforced plastic. The model accurately predicted material response to impact loading including the test cases characterised by presence of shock waves, e.g. the plate impact test. It was also demonstrated that the model was capable of predicting damage and delamination development in the simulation of the high velocity impact tests, where the numerical results were within 5% of the post impact experimental measurements.