冀宾,陈万吉,王胜军.偶应力/应变梯度弹塑性理论有限元实现[J].,2010,(1):9-14 |
偶应力/应变梯度弹塑性理论有限元实现 |
Finite element methods in couple stress/strain gradient elasto-plasticity theory |
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DOI:10.7511/dllgxb201001002 |
中文关键词: 偶应力 应变梯度 C 0-1 分片检验 剪切带 |
英文关键词: couple stress strain gradient C 0-1 patch test shear band |
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中文摘要: |
引入了偶应力弹塑性理论的增量形式,并提出了一种新的应变梯度理论,该理论引入了两个细观材料长度,结构较为简便.采用RCT9+RT9单元对软化材料的剪切带问题进行分析,该单元无多余零能模式且满足 C 0-1 分片检验,即同时满足 C 1 常曲率分片检验和 C 0 线性应力分片检验.数值结果表明,利用传统弹塑性理论分析剪切带问题会出现显著的网格依赖性现象,而偶应力/应变梯度理论可以有效地避免这一问题,使计算结果收敛,此外,剪切带宽度随细观材料长度的减小而变窄. |
英文摘要: |
The flow theory of couple stress gradient elasto-plasticity is derived and a new strain gradient theory is introduced, which includes only two length scales and has a simple structure. A RCT9+RT9 plane triangular element is applied to shear band problem of softening materials. This element has no spurious zero energy modes and passes the \%C\% 0-1 patch test, namely passing the \%C\% 1 constant curvature patch test and the \%C\% 0 linear stress patch test simultaneously. Numerical results show that pathological mesh dependence as obtained in traditional finite element computations with conventional continuum models is no longer encountered. The width of shear band grows more narrow with smaller length scales. |
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