A viscoelastic–viscoplastic constitutive model considering damage evolution for time dependent materials: Application to asphalt mixes

In this paper, employing the definition of an effective configuration in the continuum damage mechanics, mechanical response of a compressible viscoelastic–viscoplastic material is investigated. We present a phenomenological viscoelastic–viscoplastic–viscodamage constitutive model, developed within the framework of irreversible thermodynamics. The formulation is based on the additive decomposition of the total strain into elastic, viscoelastic, and viscoplastic parts in the effective configuration. Thus, the Helmholtz energy is partitioned into elastic, elastic–viscoelastic, and viscoplastic parts. Then, each one is divided into deviatoric and volumetric energies. Considering the Clausius–Duhem inequality and Drucker–Prager potential function, the effective stress and effective viscoelastic and viscoplastic strain evolution equations are achieved. A damage evolution equation is proposed in the form of a prescribed function. Then, utilizing the semi-implicit discretization method, all the internal variables are found in each increment. The material parameters are calibrated using the creep and creep-recovery tests in the literature. Finally, capability of the proposed model is demonstrated using the model prediction of creep-recovery and repeated creep-recovery tests compared with the experimental data available in the literature for asphalt mixes, where a good agreement is revealed.