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.
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References
Cosserat E, Cosserat F.Theorie des Corpes Deformable [M]. Paris: Hermann et Fils, 1909.
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)
CHEN Zhi-da.Rational Mechanics [M]. Xuzhou: China University of Ming and Technology Press, 1988. (in Chinese)
Eringen A C.Continuum Physics, Vol II [M]. New York and London: Academic Press, 1975.
Mase G E.Theory and Problems of Continuum Mechanics [M]. New York: McGraw-Hill Book Company, 1970.
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.
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.
Eringen A C.Continuum Physics, Vol. IV [M]. New York and London: Academic Press, 1976.
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)
GAO Jian, DAI Tian-min. Nonlocal elastic theory with body moments [J].Acta Mechanica Sinica, 1990,22(4):446–455. (in Chinese)
GAO Jian, CHEN Zhi-da. Nonlocal asymmetric plasticity [J].Acta Mechanica Sinica, 1994,26 (5):570–581 (in Chinese)
GAO Jian. An asymmetric theory of nonlocal elasticity—Part 1, Quasicontinuum theory [J].Int J Solids Structures, 1999,36:2947–2956.
GAO Jian. An asymmetric theory of nonlocal elasticity—Part 2, Continuum field [J].Int J Solids Structures, 1999,36:2959–2971.
DAI Tian-min. The mixed boundary-value problem for nonlocal asymmetric elasticity [J].Applied Mathematics and Mechanics (English Ed), 2000,21(1):27–32.
Eringen A C.Mechanics of Continua [M]. Inc: Robert E Krieger Publishing Company, 1980.
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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
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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
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DOI: https://doi.org/10.1007/BF02437877
Key words
- local asymmetric
- nonlocal asymmetric
- continuum mechanics
- conservation laws of energy
- balance equations of energy
- C-D inequalities