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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u-λ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u-λ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。
Based on the finite element automatic generation system (FEPG), a finite element program using gradient plasticity theory was developed to solve the grid-dependent problem of strain softening. The u-λ algorithm with damping factor is proposed to solve the displacement equation and yield surface equation jointly, which can not only solve the displacement and plastic multipliers simultaneously, but also avoid the stress pull-back operation in the widely used stress return algorithm. In the D-P criterion, the softening modulus and the internal length of the material are introduced so that the constitutive model can consider the softening and gradient effects. The damping Newton method is used to solve the softening problem. The results show that the u-λ algorithm with damping factor can calculate the strain softening problem. Using the gradient plasticity theory expressed in the form of finite element weakness, the rational results can be obtained by using first- , In a certain grid range can get a stable stress-strain curve.