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 ϖ. 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. •A viscoelastic and rate-dependent continuum damage constitutive model is introduced.•The model is able to represent static strength when loading rate goes to 0.•Various numerical simulations are introduced to verify the material model.