Skip to main content
Log in

New conservation laws of energy and C-D inequalities in continua without microstructure

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Fundamental laws and balance equations as well as C-D inequalities in continuum mechanics are carefully restudied, incompleteness of existing balance laws of angular momentum and conservation laws of energy as well as C-D inequalities are pointed out, and finally new and more general conservation laws of energy and corresponding balance equations of energy as well as C-D inequalities in local and nonlocal asymmetric continua are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Cosserat E, Cosserat F.Theorie des Corpes Deformable [M]. Paris: Hermann et Fils, 1909.

    Google Scholar 

  2. CHIEN Wei-zang, GUO Zhong-heng, DAI Tian-min. Rational mechanics [A]. In:The Chinese Encyclopedia [C]. Beijing, Shanghai: Publisher of The Chinese Encyclopedia, 1985, 288–290 (in Chinese)

    Google Scholar 

  3. CHEN Zhi-da.Rational Mechanics [M]. Xuzhou: China University of Ming and Technology Press, 1988. (in Chinese)

    Google Scholar 

  4. Eringen A C.Continuum Physics, Vol II [M]. New York and London: Academic Press, 1975.

    Google Scholar 

  5. Mase G E.Theory and Problems of Continuum Mechanics [M]. New York: McGraw-Hill Book Company, 1970.

    Google Scholar 

  6. CHEN Zhi-da. Application of Chien's theorem to general variational principle in finite elasticity with body couple [J].Applied Mathematics and Mechanics (English Ed), 1981,2(2):209–214.

    Google Scholar 

  7. SONG Yan-qi, CHEN Zhi-da. Variational principles of asymmetric elasticity theory of finite deformation [J].Applied Mathematics and Mechanics (English Ed), 1999,20(11):1200–1206.

    Google Scholar 

  8. Eringen A C.Continuum Physics, Vol. IV [M]. New York and London: Academic Press, 1976.

    Google Scholar 

  9. GAO Jian, Some important problems in nonlocal field theories [D]. Doctor degree dissertation, Beijing: China University of Mining and Technology, Beijing Campus, 1999. (in Chinese)

    Google Scholar 

  10. GAO Jian, DAI Tian-min. Nonlocal elastic theory with body moments [J].Acta Mechanica Sinica, 1990,22(4):446–455. (in Chinese)

    Google Scholar 

  11. GAO Jian, CHEN Zhi-da. Nonlocal asymmetric plasticity [J].Acta Mechanica Sinica, 1994,26 (5):570–581 (in Chinese)

    Google Scholar 

  12. GAO Jian. An asymmetric theory of nonlocal elasticity—Part 1, Quasicontinuum theory [J].Int J Solids Structures, 1999,36:2947–2956.

    Article  Google Scholar 

  13. GAO Jian. An asymmetric theory of nonlocal elasticity—Part 2, Continuum field [J].Int J Solids Structures, 1999,36:2959–2971.

    Article  Google Scholar 

  14. DAI Tian-min. The mixed boundary-value problem for nonlocal asymmetric elasticity [J].Applied Mathematics and Mechanics (English Ed), 2000,21(1):27–32.

    Google Scholar 

  15. Eringen A C.Mechanics of Continua [M]. Inc: Robert E Krieger Publishing Company, 1980.

Download references

Author information

Authors and Affiliations

Authors

Additional information

Paper from DAI Tian-min, Member of Editorial Committee, AMM

Foundation item: the National Natural Science Foundation of China(19672023); the Fundamental Research (Class A) of the Education Committee of Liaoning Province

Biography: DAI Tian-min (1931-), Professor, Doctor

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tian-min, D. New conservation laws of energy and C-D inequalities in continua without microstructure. Appl Math Mech 22, 127–134 (2001). https://doi.org/10.1007/BF02437877

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02437877

Key words

CLC number

Navigation