一种基于平均场理论的格栅材料均匀化方法
A homogenization method for the lattice material based on the average-field theory
查看参考文献14篇
|
文摘
|
将颗粒材料中发展的一种基于平均场理论的解析均匀化方法应用于二维周期格栅材料；依据尺度分离原理和统计均匀表征元概念构建了格栅材料的两尺度均匀化模型，包括细观杆件单元的本构关系、细观位移-宏观应变关系式以及应力的细观力学表达式；推导了两种二维周期格栅材料等效弹性参数包括弹性模量、泊松比和剪切弹性模量的细观力学表达式。结果表明：等边三角形结构等效为各向同性连续体时，弹性参数表达式与文献中其他方法所得结果一致；正方形结构均匀化为正交各向异性连续体时，主平面内弹性模量等于杆件单元轴向刚度，泊松比和剪切弹性模量分别由杆件单元的泊松比和剪切刚度决定，符合正方形格栅材料的力学特性；对于非主平面内的正方形本构矩阵，选取坐标轴与材料主轴夹角为45°的方向为例进行推导，本文方法与坐标变换方法所得结果一致。以上结果均验证了本文所发展方法的有效性。 |
|
其他语种文摘
|
An analytical homogenization method for granular materials based on the average-field theory is applied to the derivation of macro effective elastic properties for 2-D periodic lattice materials, including elastic modulus, Poisson ratio and shear ealstic modulus. The two-scale homogenization model is introduced on the basis of the scale separation principe and the statistically homogeneous representative volume element. The model consists of three aspects, i.e. the micro constitutive relation of the rod element, micromechanically based expression of the macro stress tensor, and the macro strains-micro displacements relaiton. Two typical 2-D periodic lattice structures are analyzed and discussed. The equilateral triangle lattice is homogenized as isotropic continuum and expressions of effective elastic parameters are consistent with the existing results in the literatures. The square lattice is homogenized as orthotropic continuum. In the material principal plane, the ealstic modulus expression is equal to the axial stiffness of the rod element, the Poisson ratio and the shear ealstic modulus is determined by the Poisson ratio and the shear stiffness of the rod element, respectively. These results accord with the mechanical characteristic of square lattice. For the constitutive behavior in other planes, taking the 45° direction between coordinate axis and material principal axis as an example, the constitutive matrix via the present method is consistent with the result from the coordinate transformation. These results show the validity of the presented approach. |
|
来源
|
应用力学学报
,2014,31(1):43-48 【核心库】
|
|
DOI
|
10.11776/cjam.31.01.d007
|
|
关键词
|
平均场理论
;
格栅材料
;
均匀化
;
等效弹性参数
|
|
地址
|
1.
大连交通大学土木与安全工程学院, 大连, 116028
2.
中国科学院力学研究所, 北京, 100190
|
|
语种
|
中文 |
|
文献类型
|
研究性论文 |
|
ISSN
|
1000-4939 |
|
学科
|
力学 |
|
基金
|
国家自然科学基金
|
|
文献收藏号
|
CSCD:5046810
|
参考文献 共
14
共1页
|
|
1.
Gibson L J.
Cellular solids: structures and properties,1997
|
被引
248
次
|
|
|
|
|
2.
Wang A J. In-plane stiffness and yield strength of periodic metal honeycombs.
ASME Journal of Engineering Materials and Technology,2004,126:137-156
|
被引
52
次
|
|
|
|
|
3.
王飞. 用均匀化理论分析蜂窝结构的等效弹性参数.
力学学报,2002,34(6):914-923
|
被引
21
次
|
|
|
|
|
4.
Gonella S. Homogenization and equivalent in-plane properties of two-dimensional periodic lattice.
International Journal of Solids and Structures,2008,45:2897-2915
|
被引
6
次
|
|
|
|
|
5.
Hohe J. Effective elastic properties of triangular grid structures.
Composite Structures,1999,45:131-145
|
被引
13
次
|
|
|
|
|
6.
Kumar R S. Generalized continuum modeling of 2-D periodic cellular solids.
International Journal of Solids and Structures,2004,41:7399-7422
|
被引
15
次
|
|
|
|
|
7.
阎军. 周期性点阵类桁架材料等效弹性性能预测及尺度效应.
固体力学学报,2005,26(4):421-427
|
被引
18
次
|
|
|
|
|
8.
Kruyt N P. Statics and kinematics of discrete Cosserat-type granular materials.
International Journal of Solids and Structures,2003,40:511-534
|
被引
6
次
|
|
|
|
|
9.
Chang C S. On virtual work and stress in granular media.
International Journal of Solids and Structures,2005,42:3773-3793
|
被引
13
次
|
|
|
|
|
10.
刘其鹏. 基于细观方向平均模型的颗粒材料宏观Cosserat连续体本构关系.
计算力学学报,2011,28(5):682-687
|
被引
1
次
|
|
|
|
|
11.
胡更开. 复合材料有效弹性性质分析方法.
力学进展,2001,31(3):361-393
|
被引
44
次
|
|
|
|
|
12.
Christoffersen J. A micromechanical description of granular material behavior.
ASME Journal of Applied Mechanics,1981,48:339-344
|
被引
45
次
|
|
|
|
|
13.
Arroyo M. An atomistic-based finite deformation membrane for single layer crystalline film.
Journal of the Mechanics and Physics of Solids,2002,50:1941-1977
|
被引
13
次
|
|
|
|
|
14.
陈建桥.
复合材料力学概论,2006:17-19
|
被引
1
次
|
|
|
|
|
了解气象卫星更多信息，请访问