The energy release rate for linear viscoelastic materials

For viscoelastic materials, the energy release rate is a fairly important parameter for determining whether the crack extends, but so far its meaning for viscoelastic materials is not yet clear enough. In this paper, the thermodynamic mechanical theory is used to derive the local and global energy release rate of viscoelastic materials when constitutive equations are given. Moreover, the method of deriving the viscoelastic energy release rate is discussed. The relation between the energy release rate and internal energy, Helmholz free energy is described. The equivalence between the local and global energy release rates is also proved after some doubts in previous papers are dispelled, although the upshot is not original. Furthermore, the concrete forms of the energy release rate for anisotropic, orthotropic and isotropic viscoelastic media are presented. The forms of the local and global energy release rates in the failure zone are discussed and the difference between the equation presented here and the one given in previous papers is pointed out.