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

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

南京航空航天大学, 南京 210016

计量
- 文章访问数: 2618
- HTML全文浏览量: 158
- PDF下载量: 658
- 被引次数: 0
出版历程
- 收稿日期: 1995-03-23
- 刊出日期: 1997-01-15

New Points of View on the Nonlocal Field Theory and Their Applications to the Fracture Mechanics (Ⅰ)——Fundamental Theory

Nanjing University of Aeronautics and Astronatutics, Nanjing 210016, P. R. China

摘要

摘要: 在线性非局部弹性理论中,具有均匀常应力边界的裂纹混合边界值问题的解是不存在的.本文从非局部场论的基本理论出发针对这一问题进行了研究.内容包括:对非局部能量守恒定律的客观性的考察,非局部热弹性体本构方程的推导,非局部体力的确定以及线性化理论,得到了一些新结果.其中,在线性化理论中所推出的应力边界条件不仅解决了本摘要开头所提到的问题,而且自然地包括了Barenblatt裂纹尖端的分子内聚力模型.
- 非局部场论 /
- 本构方程 /
- 应力边界条件 /
- 裂纹混合边界值问题
Abstract: In the linear nonlocal elasticity theory, the solution to the boundary-value problem of the crack with a constant stress boundary condition does not exist. This problem has been studied in this paper. The contents studicd contain of examining objectivity of the energy balance, deducing the constitutive equations of nonlocal thermoelastic bodies, and determining nonlocalforce and the linear nonlocal elasticity theory. Some new results are obtained. Among them, the stress boundary condition derived from the linear theory not only solves the problem mentioned at the beginning, but also contains the model of molecular cohesive stress on the shorp crack tip advanced by Barenblatt.
- nonlocal field theory /
- localization residuals /
- constitutive equations /
- stress boundary conditions

HTML全文

参考文献(19)

[1]	A. C. Eringen, C. G. Speziale and B. S. Kim, Crack tip problem in nonlocal elasticity, J.Mech. Phys. Solids, 25 (1977), 339.
[2]	A. C. Eringen, Line crack subject to shear, Int. J. Fracture, 14 (1978), 365.
[3]	A. C. Eringen, Nonlocal continuum mechanics and some applications, in: Nonlineare quations of physics and mathematics, Edited by A. O. Barut, Reidel Publishing Company, Dordrecht, Holland (1978), 271.
[4]	A. C. Eringen, On differential equations of nonlocal elasticity and soIutions of screwdis location and surface waves, J. Appl. Phys., 54 (1983), 4703.
[5]	A. C. Eringen, Theory of nonlocal elasticity and some applications, Res. Mech., 27 (4)(1987), 313.
[6]	虞吉林、郑哲敏,一种非局部弹塑性理论连续体模型与裂纹尖端附近的应力分布,力学学报,16(5) (1984), 485.
[7]	王锐,非局部弹性中的裂纹问题,中国科学(A), 34(10) (1989), 1056.
[8]	程品三,脆性断裂的非局部理论,力学学报,24(3) (1992), 329
[9]	C. Atkinson, On some recent crack tip stress calculations in nonlocal elasticity, Arch.Mech., 32, 2 (1980), 317.
[10]	C. Atkinson, Crack problems in nonlocaI elasticity, Arch. Mech., 32, 4 (1980), 597.
[11]	N. Ari and A. C. Eringen, Nonlocal stress field at Grifflth crack, Crystal Lattice Defects Amorph. Mat., 10 (1983), 33.
[12]	D. G. B. Edelen, Nonlocal field theoris, in Continuum Physics(IV), Edited by A. C.Eringen, Academic Press (1976), 75.
[13]	Wang Chong and Chen Zhida, Microrotation effects in material fracture and damage,Eng. Fract. Mech., 38, 2/3 (1991). 147.
[14]	C. Truesdell and R. A. Toupin, The classical field theories, Handbuch der Phvsik, Bd.Ⅲ/1, Springer (1960).
[15]	A. C,Eringen,《连续统力学》(程昌钧等译),科学出版社(1991), 150.
[16]	郭仲衡,《非线性弹性理论》,科学出版社(1980), 43.
[17]	R. A. Tapia, The differentiation and integration of nonlinear operators, in: Nonlinear Funclional Analysis and Applications Ed. by L. B. Rall, Academic Press, New York(1987).
[18]	M. Born and K. Huang, Dynamical Theory of Crystal Lattices Oxford (1954).
[19]	T. Bak, Phonons and Phonon Interactions, Benjamin, New York (1964).