期刊
INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES
卷 80, 期 -, 页码 28-37出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijsolstr.2015.10.018
关键词
Strain gradient elasticity; Constitutive behavior; Microstructure; Size effects
类别
资金
- National Natural Science Foundation of China [11272186]
- Specialized Research Fund for the Doctoral Program of Higher Education of China [20120131110045]
- Natural Science Fund of Shandong Province of China [ZR2012AM014]
The general isotropic strain gradient elasticity theory with five higher-order elastic constants is reformulated by introducing two different orthogonal decompositions of the strain gradient tensor. Just applying the mathematical reformulations, no extra conditions needed, the constitutive relations, equilibrium equation and boundary conditions are reformulated. In the reformulated theory, the number of independent higher-order elastic constants is proved to be three for isotropic materials, which indicates that the five higher-order elastic constants in the general isotropic strain gradient elasticity theory are dependent with each other. Therefore, the general strain gradient elasticity theory contains only three independent material length-scale parameters for isotropic materials in addition to the Lame constants. The new theory is different from the existed strain gradient elasticity theory with one or three material length-scale parameters, which introduces extra conditions during deriving process. Moreover, the reformulated theory can be directly reduced to that of incompressible materials by assuming the terms associated with hydrostatic strains to be zero. Some examples, such as torsion of cylindrical bars, shearing of fixed-end layers, and pure bending of thin beams, are performed to reveal the necessity of including multi-length-scale parameters in the strain gradient elasticity theory to predict size effects at micron scale. (C) 2015 Elsevier Ltd. All rights reserved.
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