Study on the generalized k-Hilfer–Prabhakar fractional viscoelastic–plastic model. (March 2022)

• Record Type: Journal Article
• Authors: Feng, Yi-Ying; Yang, Xiao-Jun; Liu, Jian-Gen; Chen, Zhan-Qing
• Is Part Of: Mathematics and mechanics of solids. Volume 27:Number 3(2022)
• Page Start: 491
• Page End: 500
• Publication Date: 2022-03
• Subjects: k-Hilfer–Prabhakar fractional derivative -- Laplace transform -- creep damage analysis -- constitutive model -- sensitivity analysis; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/10812865211025813
• Languages: English
• ISSNs: 1081-2865

Abstract

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 elementE ( 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 orderμ and parameter k on the creep process are investigated through the sensitivity analyses with two- and three-dimensional plots.