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基于偶应力理论剪切带问题的弹塑性有限元分析

Elastoplastic finite element analysis of shear band with couple stress theory

  • 摘要: 对于软化材料的剪切带问题,传统弹塑性有限元分析遇到了困难,进入弹塑性阶段,计算结果对网格划分敏感,出现所谓的有限元网格依赖性问题,随着网格的细分,计算常常因不收敛导致失效. 用有限元软件ABAQUS计算了3个例题,证实了传统弹塑性有限元分析软化材料剪切带问题的局限性,同时证实对于无剪切带的厚壁筒问题不会出现上述问题. 进一步引入细观非局部化理论,对非局部理论含有的细观参数\ell进行了深入讨论,并采用可通过C0 -1分片检验的18参偶应力三角形单元,重新计算了3个例题,结果避免了上述问题,说明细观偶应力有限元尤其适用于分析剪切带问题.

     

    Abstract: The problems of mesh dependence and mesh refinement areexhibited in shear bands computations of softening materials withconventional finite element method, and recognized with three numericalcases by a finite element software ABAQUS. Numerical analysis shows themesh-dependence problem does not occur for the thick-walled cylinderswithout shear bands. Couple stress theory is introduced to solve thesenumerical problems as a mesoscale non-local theory and the length scaleparameter \ell is investigated \ell in details. 18-DOF triangle couplestress element, which can pass C0 - 1 patch test, is used for the abovethree numerical cases. Numerical results show that the finite elementmethods of mesoscale couple stress theory are suitable for the shear bandscomputations.

     

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