A Thermodynamic Consistent Elastoplastic Fractional Time-Dependent Damage Model For Rock-Like Materials

This paper aims at presenting a thermodynamically consistent elastoplastic fractional time-dependent damage model for describing short- and long-term behaviors of rock-like materials. The model utilizes generalized potential theory with a yield criterion, a non-associated flow rule and an isotropic plastic hardening function for describing the evolution of plasticity. A time-dependent Lemaitre-type damage is introduced through fractional derivative considering the short- and long-term evolution of microstructure, which leads to progressive degradation of elastic modulus and failure strength of material. In this context, both instantaneous and delayed deformations shall be well described within the unique constitutive model. For practical application, an efficient and convergent semi-implicit return mapping (SRM) algorithm involving a plasticity-damage decoupling corrector is developed. The proposed model is finally adopted to predict the mechanical and deformation behavior of several types of rocks under different loading conditions in conventional or quasi-static (different loading strain rate) triaxial compression tests, creep tests and relaxation tests. Comparisons between model predictions and experimental data demonstrate that the proposed model has the capability to reproduce main features of short and long-term behaviors of rock-like materials.