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.

Nonlocal models offer a unified framework for describing long-range spatial interactions and temporal memory effects. The review briefly outlines several representative physical problems, including anomalous diffusion, material fracture, viscoelastic wave propagation, and electromagnetic scattering, to illustrate the broad applicability of nonlocal systems. However, the intrinsic global coupling and historical dependence of these models introduce significant computational challenges, particularly in high-dimensional settings. From the perspective of algorithmic strategies, the review systematically summarizes high-dimensional numerical methods applicable to nonlocal equations, emphasizing core approaches for overcoming the curse of dimensionality, such as structured solution frameworks based on FFT, spectral methods, probabilistic sampling, physics-informed neural networks, and asymptotically compatible schemes. By integrating recent advances and common computational principles, the review establishes a dual “problem review + method review” structure that provides a systematic perspective and valuable reference for the modeling and high-dimensional numerical simulation of nonlocal systems.