非局部非对称弹性固体理论
Theory of Nonlocal Asymmetric Elastic Solids
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摘要: 本文基于非局部连续统场论和非线性连续体力学理论,建立了非局部非对称弹性固体的非线性理论.它完善和发展了Eringen等人所建立的非局部弹性场论.将文献[1]中所建立的非局部非对称弹性力学的线性理论推广到有限变形.证明了在非局部弹性固体中存在着非局部体力矩.非局部体力矩引起应力的非对称性,而非局部体力矩则由原子晶格相互作用形成的共价键所产生的.并应用本文建立的理论合理地解释了平面横波和纵波色散系关的不相似性.Abstract: In this paper, a nonlinear theory of nonlocal asymmetric, elastic solids is developed on the basis of basic theories of nonlocal continuum field theory and nonlinear continuum mechanics. It perfects and expands the nonlocal elastic field theory developed by Eringen and others. The linear theory of nonlocal asymmetric elasticity developed in [1] expands to the finite deformation. We show that there is the nonlocal body moment in the nonlocal elastic solids. The nonlocal body moment causes the stress asymmetric and itself is caused by the covalent bond formed by the reaction between atoms. The theory developed in this paper is applied to explain reasonably that curves of dispersion relation of one-dimensional plane longitudinal waves are not similar with those of transverse waves.
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Key words:
- non-symmetrical stress /
- nonlocal theory /
- body couple stress
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[1] 高键,非局部非对称弹性固沐的线性理论,中国矿业大学北京研究生部博士论文,北京(1988),14. [2] Kunin,I.A,,Elastic Media with Microstructurel,Springer-Verlag,Berlin(1983). [3] Eringen,A.C,Continuum Physics Vol,Ⅱ-Ⅳ.Academic Press,New York(1976). [4] 陈至达,《有理力学》,中国矿业大学出版社,徐州(1986). [5] 陈至达,论连续体力学非线性场论中有限转动的表现,应用数学和力学,7(11)(1986),959. [6] Mason,J.M.,Variational,Incremental and Energy Methods in Solids Mechanics and Shell Theory,Amsterdam Oxford,New York(1980). [7] Friedman and Katz,A representation theorem for additive functional,Arch.Ratl.Mech.Anal.,21(1966),49-57. [8] Omar,M,A,,《固体物理学基础》,北京师范大学出版社,北京(1986). -
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