Recent Investigations on Strain and Stress-Rates in Nonlinear Continuum Mechanics

Guo Zhong-heng

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1983 > 4(5): 587-594

Guo Zhong-heng. Recent Investigations on Strain and Stress-Rates in Nonlinear Continuum Mechanics[J]. Applied Mathematics and Mechanics, 1983, 4(5): 587-594.

Citation:

Guo Zhong-heng. Recent Investigations on Strain and Stress-Rates in Nonlinear Continuum Mechanics[J]. Applied Mathematics and Mechanics, 1983, 4(5): 587-594.

Citation:

Guo Zhong-heng. Recent Investigations on Strain and Stress-Rates in Nonlinear Continuum Mechanics[J]. Applied Mathematics and Mechanics, 1983, 4(5): 587-594.

PDF( 517 KB)

Recent Investigations on Strain and Stress-Rates in Nonlinear Continuum Mechanics

Guo Zhong-heng

Department of Mathematics, Peking University, Beijing

Received Date: 1982-12-01
Publish Date: 1983-10-15

Abstract

Abstract

Presenting some recent considerations and results, the present paper deals with two basic concepts of the continuum mechanics, strain- and stress-rates. Upon a brief systematic survey of concepts of strain and stress, a so far unknown explicit expression for the rate of the right stretch tensor is offered in absolute notation. This paper then suggests to distinguish two ways of defining objective stress-rates, Following the second procedure, after analyzing several particular cases, the author proposes a generalized daumann flux, which contains the majority of the existing definitions for stress-rate and the Hill's result as well.

FullText(HTML)

References(10)

References

[1]	Seth,B,R.,Generalized strain measure with applications to physical,Second-Order Effects in Elasticity,Plasticity and Fluid Dynamics,edited by M,Refiner and D,Abir,New York,Macmillan(1984),162-171.
[2]	Hill,R.,Aspects of invariance in solid mechanics,Adv,in Appl,Mech.,18(1978).1-75.
[3]	郭仲衡.《非线性弹性理论》北京.科学出版社(1980).
[4]	Guo Zhong-heng,Rates of stretch tensors,(将发表于Tournal of Elasticity),
[5]	Macveau,D,B.,Die Elementararbeit in einem Kontinuum and die Zuordnuag von Spannung-and Verzerrungstensoren,Z,A,M,P.,19(1968).157-185.
[6]	Truesdell,C.,W,Noll,The Non-Liaear Field Theories of Mechanics,Handbuch der physik,Vol,Ⅲ/3,Berlin-Heidelberg-New York,Springer,(1965).
[7]	Guo Zhong-heng,Time derivative of tensor fields in non-linear continuum mechanics,Arch,Mech,Stos.,15.1(1963).131-163.
[8]	Eringen,A,C.,Continuum Physics Vol,Ⅱ.New York,Acad,press,(1975)
[9]	Green,A,E B,C,McInnis,Generalized hypo-elasticity,Proc,Roy,Soc,Edinburgh,A 87(1967).Part Ⅱ,220-230
[10]	Dienes,J,K.,On the analysis of rotation and stress rate in deforming bodies,Acta Mech.39(1979),217-232.