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赵杰 陈万吉 冀宾. 关于两种二阶应变梯度理论[J]. 力学学报, 2010, 42(1): 138-145. DOI: 10.6052/0459-1879-2010-1-2008-517
引用本文: 赵杰 陈万吉 冀宾. 关于两种二阶应变梯度理论[J]. 力学学报, 2010, 42(1): 138-145. DOI: 10.6052/0459-1879-2010-1-2008-517
Jie Zhao, Wanji Chen, Bin Ji. A study on the two second-order strain gradient theories[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(1): 138-145. DOI: 10.6052/0459-1879-2010-1-2008-517
Citation: Jie Zhao, Wanji Chen, Bin Ji. A study on the two second-order strain gradient theories[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(1): 138-145. DOI: 10.6052/0459-1879-2010-1-2008-517

关于两种二阶应变梯度理论

A study on the two second-order strain gradient theories

  • 摘要: 对常见的两种应变梯度理论进行了深入的理论分析,比较了它们在公式推导、能量表达、物理解释和应用领域方面的差异. 选择钢筋拉拔弹性阶段和超薄悬臂梁受压弯曲两个典型的算例,采用可以通过C^0\hbox-1分片检验的18自由度应变梯度平面三角形单元和轴对称三角形单元,通过数值计算比较了两种理论在描述细观力学性能方面的差异.

     

    Abstract: There are various strain gradient theories derived fromphenomenal theory and nonlocal continuum mechanics. Meanwhile, there are twopopular second-order strain gradient theories in which strain gradient termwas introduced into the constitutive law with positive and negative signsrespectively. In this paper, these two theories are discussed in the aspectof formula derivation, energy expression, and application fields. By usingthe 18-DOF triangle strain gradient plan element (RCT9+RT9) and axisymmetricelement (BCIZ+ART9) which can pass C^0\hbox-1 patch test, the elasticpull-out processes of the reinforced concrete bond specimen and thedeformation of a cantilever beam are simulated to compare the limitation ofthe two theories in the analysis of microstructures.

     

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