New strain energy-based thermo-elastoviscoplastic isotropic damage–self-healing model for bituminous composites—Part I: Formulations

New initial strain energy-based thermo-elastoviscoplastic isotropic damage–self-healing formulations for bituminous materials are developed and implemented for numerical predictions of experimental measurements. A class of elastoviscoplastic constitutive damage–self-healing model, based on a continuum thermodynamic framework, is proposed within an initial elastic strain energy-based formulation. An Arrhenius-type temperature term is uncoupled with Helmholtz free energy potential to account for the effect of temperature. In particular, the governing incremental damage and healing evolutions are coupled and characterized through the net stress concept in conjunction with the hypothesis of strain equivalence. The viscoplastic flow is introduced by means of an additive split of the stress tensor. The (undamaged) energy norm of strain tensor is redefined and employed as equivalent strain. A rate-dependent (viscous) damage model with a structure analogous to viscoplasticity of the Perzyna type is used for rate sensitivity of bituminous materials. In net space, Drucker–Prager yield function and Perzyna viscoplastic model are employed. Completely new computational algorithms are systematically developed in Part II of this sequel, based on the two-step operator splitting methodology. Comparisons with experimental results and numerical simulations are undertaken in Part II of this work.