角点型非共轴模型的半隐式应力积分算法及应用

Semi-implicit integration algorithm for non-coaxial model based on vertex theory and its application

针对基于屈服面角点非共轴理论建立的弹塑性本构模型,提出了对应的半隐式应力积分算法。在考虑非共轴项的应力更新方程中,塑性流动方向采用显示表示。构建非共轴塑性流动的Gram-Schmidt正交化过程则是基于已知应力条件定义。根据张量之间的正交性,进一步简化模型的应力更新方程,再推导该方程的牛顿迭代格式。然后将该算法编写进ABAQUS的材料用户子程序Vumat,将该非共轴模型应用于有限元分析。在Explict分析模块中,分析了不同非共轴模型参数模拟单剪试验和活动门问题的效果,并与共轴模型结果进行了对比。结果显示该半隐式算法收敛性好,强健有效,适用于工程分析。

A semi-implicit integration algorithm is presented for the non-coaxial model based on the yield vertex theory. In the stress updating considering the non-coaxial terms, the plastic flow direction is expressed explicitly. The Gram-Schmidt orthogonalization process aiming to formulate the non-coaxial flow is conducted under the given stress condition. According to the orthogonality among tensors, the stress updating equation is further simplified, and the Newton-Raphson iteration is established based on the simplified equation. With this algorithm programmed into the user subroutines, Vumat, the constitutive model is implemented into the finite element analysis based on ABAQUS. Through the explicit procedure, the simple shear tests and trapdoor problems are simulated with different non-coaxial model parameters. The results are compared to those of the coaxial model. The calculated results show that the proposed algorithm is converged and robust, and is be suitable for the numerical analysis.