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Applied Mathematics and Mechanics

, Volume 40, Issue 1, pp 49–62 | Cite as

Fractional-order visco-plastic constitutive model for uniaxial ratcheting behaviors

  • Wenjie Zhao
  • Shaopu YangEmail author
  • Guilin Wen
  • Xuehong Ren
Article
  • 25 Downloads

Abstract

This paper proposes a novel unified visco-plastic constitutive model for uniaxial ratcheting behaviors. The cyclic deformation of the material presents remarkable time-dependence and history memory phenomena. The fractional (fractional-order) derivative is an efficient tool for modeling these phenomena. Therefore, we develop a cyclic fractional-order unified visco-plastic (FVP) constitutive model. Specifically, within the framework of the cyclic elasto-plastic theory, the fractional derivative is used to describe the accumulated plastic strain rate and nonlinear kinematic hardening rule based on the Ohno-Abdel-Karim model. Moreover, a new radial return method for the back stress is developed to describe the unclosed hysteresis loops of the stress-strain properly. The capacity of the FVP model used to predict the cyclic deformation of the SS304 stainless steel is verified through a comparison with the corresponding experimental data found in the literature (KANG, G. Z., KAN, Q. H., ZHANG, J., and SUN, Y. F. Time-dependent ratcheting experiments of SS304 stainless steel. International Journal of Plasticity, 22(5), 858–894 (2006)). The FVP model is shown to be successful in predicting the rate-dependent ratcheting behaviors of the SS304 stainless steel.

Key words

cyclic visco-plastic constitutive fractional derivative fractional-order unified visco-plastic (FVP) model rate-dependent ratcheting 

Chinese Library Classification

O345 

2010 Mathematics Subject Classification

74C10 

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Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Wenjie Zhao
    • 1
  • Shaopu Yang
    • 2
    Email author
  • Guilin Wen
    • 1
  • Xuehong Ren
    • 1
  1. 1.State Key Laboratory of Advanced Design and Manufacturing for Vehicle BodyHunan UniversityChangshaChina
  2. 2.State Key Laboratory of Mechanical Behavior in Traffic Engineering Structure and System SafetyShijiazhuang Tiedao UniversityShijiazhuangChina

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