A unified fractional-order viscoplastic fatigue damage model for rock materials under cyclic loading with creep effects

Abstract

This study presents a fractional-order viscoplastic fatigue–damage model to investigate the long-term deformation behavior of rock materials considering creep effects. Fatigue damage is interpreted as progressive microstructural degradation, formulated through a convolution-based evolution law, while time-dependent creep effects are captured via a viscoplastic yield function. Fractional calculus is introduced to establish a unified constitutive framework that couples viscoplastic deformation with damage evolution. The established model is implemented numerically using a return-mapping algorithm and validated through applications to four sets of experimental data reported in the literature, showing excellent agreement in terms of strain-rate dependency, cumulative deformation, confining pressure effects and fatigue life. Moreover, the proposed model successfully reproduces the transition of volumetric strain from compaction to dilation during cyclic loading, demonstrating its capability to capture the coupled fatigue–creep behavior of rock materials.