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

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Article Navigation > Applied Mathematics and Mechanics > 1999 > 20(7): 713-720

Huang Zaixing. 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[J]. Applied Mathematics and Mechanics, 1999, 20(7): 713-720.

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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

Najjing University of Aeronautics and Astronautics, Nanjing 210016, P R China

Received Date: 1998-05-05
Rev Recd Date: 1999-04-20
Publish Date: 1999-07-15

Abstract

Abstract

In this paper,nonlinear constitutive equations are deduced strictly according to the constitutive axioms of rational continuum mechanics.The existing judgements 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 enrgy 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.
- nonlocal field theory,
- nonlocal themoelastic body,
- constitutive equations,
- antisymmetric stress,
- nonlocal residuals

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References(8)

References

[1]	Eringen A C. Theory of nonlocal thermoelasticity[J].Int J Engng Sci,1974,12(6):1063.
[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.
[3]	Edelen D G B. Nonlocal field theories[A]. In: A C Eringen Ed.Continuum Physics(Ⅳ)[C]. New York: Academic Press,1976.
[4]	黄再兴,樊蔚勋,黄维扬.关于非局部场论的几个新观点及其在断裂力学中的应用(Ⅰ)——基本理论部分[J].应用数学和力学,1997,18(1):45～54.
[5]	Truesdell C, Noll R A. The Classical Field Theories Hangbuch der Physik[M].Vol.Ⅲ/1,Berlin: Springer-Verlag,1960.
[6]	Eringen A C. Mechanics of Continua(Second edition)[M]. New York: R E Krieger Publishing Company,1980.
[7]	Mason J. Methods of Founctional Analysis for Application in Solid Mechanics[M]. Amsterdam: Elsevier Science Publishing Company,1985.
[8]	Chadwick P. 简明理论和例题[A].连续介质力学[M].傅依斌译,天津:天津大学出版社,1992.