考虑损伤的修正梯度弹性理论

赵冰; 刘韬; 贺剑辉; 朱浩睿; 李威

doi:10.21656/1000-0887.370285

考虑损伤的修正梯度弹性理论

doi: 10.21656/1000-0887.370285

长沙理工大学土木与建筑学院, 长沙 410004

详细信息

作者简介:
赵冰(1972—), 男, 副教授, 博士（通讯作者. E-mail: zhaob_m-y@163.com）.

中图分类号: O346.5
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- 被引次数: 0
出版历程
- 收稿日期: 2016-09-20
- 修回日期: 2016-11-13
- 刊出日期: 2017-09-15

A Modified Gradient Elastic Theory Considering Damage

School of Civil Engineering and Architecture, Changsha University of Science and Technology, Changsha 410004, P.R.China

摘要

摘要: 梯度弹性理论在描述材料微结构起主导作用的力学行为时具有显著优势，将其与损伤理论相结合，可在材料破坏研究中考虑微结构的影响.基于修正梯度弹性理论，将应变张量、应变梯度张量和损伤变量作为Helmholtz自由能函数的状态变量，并在自然状态附近对自由能函数作Taylor展开，进而由热力学基本定律，推导出修正梯度弹性损伤理论本构方程的一般形式.编制有限元程序，模拟土样损伤局部化带的发展演化过程.结果表明，修正梯度弹性损伤理论消除了网格依赖性；损伤局部化带不是与损伤同时发生，而是在损伤发展到一定程度后再逐渐显现出来.
- 损伤局部化 /
- 应变梯度 /
- 内部特征长度 /
- 网格依赖性
Abstract: To describe the material mechanics behaviors depending on microstructure, the gradient elastic theory with significant advantages was investigated. The gradient elastic theory was combined with the damage theory to consider the influence of microstructure on material failure. Then a modified gradient elasticity damage theory was proposed, based on which the basic law of thermodynamics, the strain tensor, the damage variable and the scalar strain gradient tensor were taken as the state variables of the Helmholtz free energy. The Taylor expansion of the Helmholtz free energy function was conducted near the natural state, and the general expressions of the modified gradient elasticity damage constitutive functions were derived. The finite element code was programmed to simulate the development process of damage localization in soil specimens. The results show that, the traditional mesh dependence in numerical simulation can be removed under the modified gradient elasticity damage theory. The band of the damage localization does not concur with the damage, but occurs after the damage development to some extent.
- damage localization /
- strain gradient /
- internal length scale /
- mesh dependence

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参考文献(25)

[1]	Askes H, Aifantis E C. Numerical modeling of size effects with gradient elasticity—formulation, meshless discretization and examples[J]. International Journal of Fracture,2002,117(4): 347-358.
[2]	SONG Zhan-ping, ZHAO Bing, HE Jian-hui, et al. Modified gradient elasticity and its finite element method for shear boundary layer analysis[J]. Mechanics Research Communications,2014,62: 146-154.
[3]	Cosserat E, Cosserat F. Théorie des corps déformables[J]. Hermann Archives,1909.
[4]	Toupin R A. Elastic materials with couple-stresses[J]. Archive for Rational Mechanics and Analysis,1962,11(1): 385-414.
[5]	Toupin R A. Theories of elasticity with couple-stress[J]. Archive for Rational Mechanics and Analysis,1964,17(2): 85-112.
[6]	Mindlin R D, Tiersten H F. Effects of couple-stresses in linear elasticity[J]. Archive for Rational Mechanics and Analysis,1962,11(1): 415-448.
[7]	Mindlin R D. Micro-structure in linear elasticity[J]. Archive for Rational Mechanics and Analysis,1964,16(1): 51-78.
[8]	Mindlin R D. Second gradient of strain and surface-tension in linear elasticity[J]. International Journal of Solids and Structures,1965,1(4): 417-438.
[9]	Mindlin R D. Theories of Elastic Continua and Crystal Lattice Theories [M]//Krner E, ed. Mechanics of Generalized Continua . Berlin: Springer, 1968: 312-320.
[10]	Eringen A C. Theories of nonlocal plasticity[J]. International Journal of Engineering Science,1983,21(7): 741-751.
[11]	Eringen A C. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves[J]. Journal of Applied Physics,1983,54(9): 4703-4710.
[12]	Triantafyllidis N, Aifantis E C. A gradient approach to localization of deformation: I. hyperelastic materials[J]. Journal of Elasticity,1986,16(3): 225-237.
[13]	Aifantis E C. On the role of gradients in the localization of deformation and fracture[J]. International Journal of Engineering Science,1992,30(10): 1279-1299.
[14]	Altan S B, Aifantis E C. On the structure of the mode III crack-tip in gradient elasticity[J]. Scripta Metallurgica et Materialia,1992,26(2): 319-324.
[15]	Ru C Q, Aifantis E C. A simple approach to solve boundary-value problems in gradient elasticity[J]. Acta Mechanica,1993,101(1): 59-68.
[16]	徐晓建, 邓子辰. 多层简化应变梯度Timoshenko梁的变分原理分析[J]. 应用数学和力学, 2016,37(3): 235-244. (XU Xiao-jian, DENG Zi-chen. The variational principle for multi-layer Timoshenko beam systems based on the simplified strain gradient theory[J]. Applied Mathematics and Mechanics,2016,37(3): 235-244.(in Chinese))
[17]	Pijaudier-Cabot G, Baant Z P. Nonlocal damage theory[J]. Journal of Engineering Mechanics,1987,113(10): 1512-1533.
[18]	Baant Z P, Jirásek M. Nonlocal integral formulations of plasticity and damage: survey of progress[J]. Journal of Engineering Mechanics,2002,128(11): 1119-1149.
[19]	Baant Z P, Pijaudier-Cabot G. Nonlocal continuum damage, localization instability and convergence[J]. Journal of Applied Mechanics,1988,55(2): 287-293.
[20]	Frémond M, Nedjar B. Damage, gradient of damage and principle of virtual power[J]. International Journal of Solids and Structures,1996,33(8): 1083-1103.
[21]	赵吉东, 周维垣, 刘元高, 等. 岩石类材料应变梯度损伤模型研究及应用[J]. 水利学报, 2002(7): 70-74.(ZHAO Ji-dong, ZHOU Wei-yuan, LIU Yuan-gao, et al. Strain gradient enhanced damage model for rock material and its application[J]. Journal of Hydraulic Engineering,2002(7): 70-74.(in Chinese))
[22]	唐雪松, 蒋持平, 郑健龙. 各向同性弹性损伤本构方程的一般形式[J]. 应用数学和力学, 2001,22(12): 1317-1323.(TANG Xue-song, JIANG Chi-ping, ZHENG Jian-long. General expressions of constitutive equations for isotropic elastic damaged materials[J]. Applied Mathematics and Mechanics,2001,22(12): 1317-1323.(in Chinese))
[23]	沈珠江. 结构性粘土的非线性损伤力学模型[J]. 水利水运科学研究, 1993(3): 247-255.(SHEN Zhu-jiang. A nonlinear damage model for structured clay[J]. Hydro-Science and Engineering,1993(3): 247-255.(in Chinese))
[24]	Belytschko T, Baant Z P, Yul-Woong H, et al. Strain-softening materials and finite-element solutions[J]. Computers & Structures, 1986,23(2): 163-180.
[25]	Baant Z P, CHANG Ta-peng. Nonlocal finite element analysis of strain-softening solids[J]. Journal of Engineering Mechanics,1987,113(1): 89-105.