A thermodynamically consistent viscoelastic with rate-dependent damage constitutive model

In this paper, a thermodynamically consistent viscoelastic and rate-dependent continuum damage constitutive model is proposed under small-deformation assumption. The model is consistent with quasi-static loading case that it is able to reproduce correct static strength when loading rate approaches to 0 by introducing a so-called pseudo damage state variable $. In addition, the model can present increasing strength and strain at failure with increasing strain rate. The evolution of the pseudo damage state variable is described as a rate form of power of effective stress, while the damage state variable is given by a viscosity-like rate form equation. The viscoelastic behavior is described by the classic PRONY series. Finally, the paper provides uniaxial tension, tension of plate-with-hole, and tension of particle-reinforced heterogeneous material as numerical examples to show viscoelastic behavior and damage development process.