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Applied Mathematics and Mechanics

, Volume 29, Issue 1, pp 67–74 | Cite as

Strain analysis of nonlocal viscoelastic Kelvin bar in tension

  • Zhao Xue-chuan  (赵雪川)
  • Lei Yong-jun  (雷勇军)Email author
  • Zhou Jian-ping  (周建平)
Article

Abstract

Based on viscoelastic Kelvin model and nonlocal relationship of strain and stress, a nonlocal constitutive relationship of viscoelasticity is obtained and the strain response of a bar in tension is studied. By transforming governing equation of the strain analysis into Volterra integration form and by choosing a symmetric exponential form of kernel function and adapting Neumann series, the closed-form solution of strain field of the bar is obtained. The creep process of the bar is presented. When time approaches infinite, the strain of bar is equal to the one of nonlocal elasticity.

Key words

nonlocal theory Kelvin viscoelasticity Neumann series bar strain analysis 

Chinese Library Classification

O345 

2000 Mathematics Subject Classification

74K20 70K28 74S30 

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Copyright information

© Editorial Committee of Appl. Math. Mech. and Springer-Verlag 2008

Authors and Affiliations

  • Zhao Xue-chuan  (赵雪川)
    • 1
  • Lei Yong-jun  (雷勇军)
    • 1
    Email author
  • Zhou Jian-ping  (周建平)
    • 1
  1. 1.College of Aerospace and Material EngineeringNational University of Defense TechnologyChangshaP. R. China

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