The general fractional operator shows its great predominance in the construction of constitutive model owing to its agility in choosing the embedded parameters. A generalized fractional viscoelastic–plastic constitutive model with the sense of the k-Hilfer–Prabhakar (k-H-P) fractional operator, which has the character recovering the known classical models from the proposed model, is established in this article. In order to describe the damage in the creep process, a time-varying elastic element $E(t)$ is used in the proposed model with better representation of accelerated creep stage. According to the theory of the kinematics of deformation and the Laplace transform, the creep constitutive equation and the strain of the modified model are established and obtained. The validity and rationality of the proposed model are identified by fitting with the experimental data. Finally, the influences of the fractional derivative order $\mu$ and parameter k on the creep process are investigated through the sensitivity analyses with two- and three-dimensional plots.

广义分数算子在选择嵌入参数时表现出其在本构模型构建中的巨大优势。本文建立了具有k -Hilfer-Prabhakar( k - HP)分数算子意义的广义分数粘弹-塑性本构模型，该模型具有从所提出的模型中恢复已知经典模型的特性。为了描述蠕变过程中的损伤，一个时变弹性单元$乙(吨)$用于所提出的模型中，以更好地表示加速蠕变阶段。根据变形运动学理论和拉普拉斯变换，建立并得到了修正模型的蠕变本构方程和应变。通过与实验数据的拟合，验证了所提出模型的有效性和合理性。最后，分数阶导数的影响$\mu$通过二维和三维绘图的敏感性分析研究了蠕变过程中的参数k。