A thermodynamically consistent viscoelastic–viscoplastic constitutive model for self-healing materials

Self-healing materials, as a class of intelligent materials, are capable to recover a part of the weakened mechanical properties induced by damage. In this article, based on the thermodynamics of irreversible processes, employing the effective configuration in the continuum damage-healing mechanics, a viscoelastic–viscoplastic constitutive model is presented. In the constitutive model development, we adopt an additive decomposition of the total strain into elastic, viscoelastic, and viscoplastic parts. In this regard, defining the damage and healing variables and employing the strain energy equivalence hypothesis, stress and strain tensors in the effective configuration are obtained. Satisfying the Clausius–Duhem inequality, the evolution equations are introduced for viscoelastic and viscoplastic strains. The damage and healing variables also evolve according to two different evolutions. To employ the proposed model in different loading conditions, the time-discrete form of the model in the semi-implicit form is presented. Material parameters of the model are identified with creep, creep-recovery, and repeated creep-recovery tests on asphalt concrete materials in the literature. Finally, the capability of the proposed model is demonstrated applying the model prediction for creep-recovery and repeated creep-recovery case studies and comparing the results with the experimental data available in the literature.