Constitutive modeling of rock materials based on variable-order fractional theory

Abstract

In this work, we develop a novel variable-order fractional constitutive model to describe the uniaxial compressive behavior of rock materials. The varying-order function of the variable-order fractional model is assumed as a piecewise function of strain. The evolutions of mechanical properties in the closure, elastic, and yield stages within the stress-strain curve are captured by employing the varying-order function changing from 1 to 0. The peak post stage, that is, the strain softening stage, is described by varying-order function with the order exceeding 1. Based on the varying-order function corresponding to each deformation stage, the mechanical mechanisms for the four deformation stages are clearly identified. To validate the proposed model, a series of uniaxial compression tests are conducted on coal, salt rock, and mudstone samples under constant strain rates. We demonstrate that the proposed model is in a good agreement with the experimental data. A comparison indicates that the proposed model has an improved accuracy with the use of fewer parameters compared with other models. Consequently, the proposed variable-order fractional model is effective in describing the stress-strain relationships of rock materials.