Variable-Order Time-Fractional Kelvin Peridynamics for Rock Steady Creep

A variable-order time-fractional Kelvin peridynamics model is proposed, where the variable order is utilized to reflect the changes of viscosity in viscoelastic materials to effectively capture the damage and deformation of rock steady creep. The corresponding constitutive model is established by coupling a spring and an Abel dashpot. Through the Caputo definition of fractional-order derivatives, finite increment formulations for the constitutive model are derived to facilitate numerical implementation by an explicit time integration scheme. We accordingly introduce a model parameter evaluation method for practical applications. To verify the validity and correctness of the model, constant-order time-fractional peridynamics is used to compare with the proposed model via a sandstone compress creep numerical test, and the results show that the latter can simulate nonlinear creep behavior more efficiently. Additionally, the numerical simulation of practical engineering is conducted. Compared with constant-order time-fractional peridynamics, the proposed model can improve the simulation accuracy by 16.7% with fewer model parameters.