A Nonlinear Triaxial Damage Creep Model for Granite Based on Atangana–Baleanu Fractional Derivative

Abstract

Finding a fractional derivative that can more accurately describe the characteristics of a dynamic process is one of the objectives for fractional derivative modeling. In this paper, Atangana–Baleanu (AB) fractional order dashpots with constant and variable coefficients are constructed by using AB fractional derivatives with nonlocal and nonsingular kernel characteristics. Compared with Riemann–Liouville (RL) and conformable (KA) fractional order dashpot, AB fractional order dashpot can describe the viscoelastic properties of materials in full time. A new damage AB fractional derivative (DABFD) creep model is proposed by improving the Nishihara model with the help of the variable coefficient AB fractional dashpot. The parameters for the DABFD creep model are determined by fitting creep experimental data of Beishan granite. Compared with the Nishihara, damage RL fractional derivative (DRLFD) and damage KA fractional derivative (DKAFD) creep models, DABFD creep model has a better fitting and prediction accuracy. The parameter sensitivity for the DABFD creep model shows that different creep curves can be demonstrated with different DABFD creep model parameters. The model can better represent the viscoelastic properties and three stages of the creep process for rock.