Applied Mathematics and Mechanics

, Volume 20, Issue 7, pp 764–772 | Cite as

New points of view on the nonlocal field theory and their applications to the fracture mechanics(II)—re-discuss nonlinear constitutive equations of nonlocal thermoelastic bodies

  • Huang Zaixing


In this paper, nonlinear constitutive equations are deduced strictly according to the constitutive axioms of rational continuum mechanics. The existing judgments are modified and improved. The results show that the constitutive responses of nonlocal thermoelastic body are related to the curvature and higher order gradient of its material space, and there exists an antisymmetric stress whose average value in the domain occupied by thermoelastic body is equal to zero. The expressions of the antisymmetric stress and the nonlocal residuals are given. The conclusion that the directions of thermal conduction and temperature gradient are consistent is reached. In addition, the objectivity about the nonlocal residuals and the energy conservation law of nonlocal field is discussed briefly, and a formula for calculating the nonlocal residuals of energy changing with rigid motion of the spatial frame of reference is derived.

Key words

nonlocal field theory nonlocal thermoelastic body constitutive equations antisymmetric stress nonlocal residuals 

CLC number

O346.1 O343 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Eringen A C. Theory of nonlocal thermoelasticity[J].Int J Engng Sci, 1974,12(6): 1063.MATHCrossRefGoogle Scholar
  2. [2]
    Eringen A C. Nonlocal continuum mechanics and some applications[A]. In: A O Barut Ed.Nonlinear Equations of Physics and Mathematics[C]. Reidel Publishing Company, 1978.Google Scholar
  3. [3]
    Edelen D G B. Nonlocal field theories[A]. In: A C Eringen Ed.Continuum Physics(IV) [C]. New York: Academic Press 1976.Google Scholar
  4. [4]
    Huang Zaixing, Fan Weixun, Huang Weiyang. New points of view on the nonlocal field theory and applications to the fracture mechanics (I)—Fundamental theory [J].Applied Mathematics and Mechanics (English Ed), 1997,18(1): 45–54.MathSciNetGoogle Scholar
  5. [5]
    Truesdell C, Noll R A.The Classical Field Theories Handbuch der Physik[M]. Vol. III/1 Berlin: Springer-Verlag, 1960.Google Scholar
  6. [6]
    Eringen A C.Mechanics of Continua (Second edition) [M]. New York: R E Krieger Publishing Company, 1980.Google Scholar
  7. [7]
    Mason J.Methods of Founctional Analysis for Application in Solid Mechanics[M]. Amsterdam: Elsevier Science Publishing Company, 1985.Google Scholar
  8. [8]
    Chadwick P.Continuum Mechanics-Concise Theory and Problems[M]. Reidel Publishing Company, 1979.Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 1999

Authors and Affiliations

  • Huang Zaixing
    • 1
  1. 1.Nanjing University of Aeronautics and AstronauticsNanjingP R China

Personalised recommendations