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.

在这项工作中，我们开发了一种新颖的可变阶分数阶本构模型来描述岩石材料的单轴压缩行为。可变阶分数模型的变化阶函数被假定为应变的分段函数。通过使用从1到0的变化函数来捕获应力-应变曲线内闭合，弹性和屈服阶段的力学性能演变。描述了峰值后阶段，即应变软化阶段。通过阶次超过1的阶次函数，基于与每个变形阶段相对应的阶次函数，可以清楚地识别出四个变形阶段的机械机制。为了验证所提出的模型，在煤，盐岩，和在恒定应变率下的泥岩样品。我们证明了所提出的模型与实验数据非常吻合。比较表明，与其他模型相比，所提出的模型使用较少的参数具有更高的准确性。因此，所提出的变阶分数阶模型对于描述岩石材料的应力-应变关系是有效的。