Initial strain energy-based thermo-elastoviscoplastic two-parameter damage–self-healing models for bituminous composites—Part I: Formulations

The initial strain energy-based thermo-elastoviscoplastic two-parameter damage–self-healing formulations for asphalt concrete materials are proposed and implemented for numerical simulations of experimental data. A class of elastoviscoplastic two-parameter constitutive damage–self-healing models, based on a continuum thermodynamic framework, is developed within an initial-elastic strain energy-based formulation. The Helmholtz free energy potential is employed and uncoupled with an Arrhenius-type temperature term in order to account for the effect of temperature. In particular, the governing incremental damage and healing evolutions are coupled in volumetric and deviatoric parts and characterized through the net stress concept in conjunction with the hypothesis of strain equivalence. The conceptual illustration is shown for the proposed governing incremental damage and healing evolutions. The (undamaged) energy norms of the volumetric and deviatoric strain tensors as the equivalent volumetric and deviatoric strains are redefined and employed for the two-parameter damage and healing criteria. A rate-dependent (viscous) volumetric and deviatoric damage model with a structure analogous to viscoplasticity of the Perzyna type is used for rate sensitivity of bituminous composites. Completely new computational algorithms are systematically proposed in Part II of this sequel, based on the two-step operator splitting methodology. Comparisons with experimental measurements and model predictions are demonstrated in Part II of this sequel as well.