Theoretical Bases of A Thermo-Mechanical Damage and DMT-Healing Model for Rock
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A theoretical framework is proposed to model thermo-mechanical (TM) crack opening, closure, and healing in rock. The model is based on Continuum Damage Mechanics and thermodynamics. The postulated free energy is a polynomial of deformation, temperature, damage and healing. The damage-driving force captures damage evolution due to mechanical or TM tensile stresses, as well as the decrease of material toughness at elevated temperature. Crack closure is modeled by adopting the concept of unilateral effect on rock stiffness. A mixed variable is introduced to account for anisotropic TM damage and rate -dependent healing. Crack rebonding is assumed to result from Diffusive Mass Transfer (DMT) processes, and accordingly, the healing evolution law is governed by the diffusion equation. Contrary to other models for rock, the healing deformation is not a creep volumetric deformation, but the difference between the deformation before and after DMT. A parametric study illustrates the model capabilities: the simulation of TM stress paths with higher degree of mechanical recovery for longer healing time or higher healing temperature. The proposed model is expected to better predict the long-term behavior of self-healing rock materials – containing clay of halite minerals for instance.