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杜修力, 侯世伟, 路德春, 梁国平, 安超. 梯度塑性理论的计算方法与应用[J]. 岩土工程学报, 2012, 34(6): 1094-1101.
引用本文: 杜修力, 侯世伟, 路德春, 梁国平, 安超. 梯度塑性理论的计算方法与应用[J]. 岩土工程学报, 2012, 34(6): 1094-1101.
DU Xiu-li, HOU Shi-wei, LU De-chun, LIANG Guo-ping, AN Chao. Application of gradient plastic theory based on FEPG platform[J]. Chinese Journal of Geotechnical Engineering, 2012, 34(6): 1094-1101.
Citation: DU Xiu-li, HOU Shi-wei, LU De-chun, LIANG Guo-ping, AN Chao. Application of gradient plastic theory based on FEPG platform[J]. Chinese Journal of Geotechnical Engineering, 2012, 34(6): 1094-1101.

梯度塑性理论的计算方法与应用

Application of gradient plastic theory based on FEPG platform

  • 摘要: 基于有限元自动生成系统 (FEPG) ,开发使用梯度塑性理论的有限元程序,用于解决应变软化后的网格依赖性问题。提出带阻尼因子的 算法,联立求解位移方程和屈服面方程,既可同时解得位移和塑性乘子,又避免了广泛使用的应力返回算法中的应力拉回运算。在 D-P 准则中引入软化模量和材料内部特征长度,使本构模型能够考虑软化和梯度效应。在软化问题求解上使用阻尼牛顿法,算例结果表明,带阻尼因子的算法能够计算应变软化问题,以有限元弱形式表达的梯度塑性理论,使用一阶单元就能够得到合理的结果,在一定网格范围能够得到稳定的应力应变曲线。

     

    Abstract: Based on the FEPG platform, the finite element program using gradient plastic theory is developed to solve mesh dependence after strain softening. A algorithm with damp factor is proposed, which can solve the equation of displacement and yield surface simultaneously. The algorithm can not only get displacement and plastic multiplier together, but also avoid the stress haul back calculation in stress return algorithm widely used in finite element solution procedures. The softening modulus and the internal character length are introduced into D-P yield function, and the constitutive model can consider strain softening and gradient effect. The damp Newton algorithm is used to calculate softening problems. The results of a case study show that the algorithm with damp factor can be used to solve softening problems, the gradient plastic theory described by finite element weak form has no requirement of continuity, and appropriate outcome can be obtained by the first-order element, thus the mesh dependence of simulation is basically solved.

     

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