Physically based constitutive model for damage in composites under dynamic loads

Abstract

The complex nature of fibre reinforced composites, their non-homogeneity and anisotropy make their modelling a very challenging task. Although the linear – elastic behaviour of composites is well understood, there is still a significant uncertainty regarding prediction of the damage initiation, damage evolution and material failure especially for the tri-axial state of stress or strain. Therefore, simplifying assumptions are inevitable in the constitutive modelling. This work shows development of a new composite damage constitutive model. The model is based on the concept of spectral decomposition of the stiffness tensor of a material. Spectral decomposition leads to identification of the number of the strain energy modes. They are used to define the material strain energy limits. Present material model is thermodynamically consistent and was developed in the framework of irreversible thermodynamics with internal state variables. The development process was supported by the mesoscale model analysis. The purpose of mesoscale models was twofold. Firstly, it allowed to understand of the mesoscale damage effects on the continuum (macroscopic) material behaviour. Secondly, it provided invaluable insight into the stress and strain state of the composite loaded in different deformation eigenmodes. The mesoscale modelling resulted in postulating a simplifying assumption that principal stiffnesses of the material are invariant for the composite subjected to damage in the applicability range. Moreover, the mesoscale model analysis was used to determine the strain energy limits in the material. The model is capable of predicting dynamic material response by coupling with equation of state. The form of the equation of state used in this work is applicable to anisotropic materials. The model was implemented in Dyna3D and was validated against the experimental data showing good agreement of damage extent shock wave propagation.