基于半隐式积分方案统一强度理论ANSYS二次开发  

ANSYS secondary development of unified strength theory with semi-implicit integral

作　　者：柯锦福 吴爱祥[3] KE Jin-fu WU Ai-xiang(State Key Laboratory of Geomechanics and GeotechnicaI Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, Hubei 430071, China University of Chinese Academy of Sciences, Beijing 100049, China School of Civil and Environment Engineering, University of Science and Technology Beijing, Beijing 100083, China)

机构地区：[1]中国科学院武汉岩土力学研究所岩土力学与工程国家重点实验室,湖北武汉430071 [2]中国科学院大学,北京100049 [3]北京科技大学土木与环境工程学院,北京100083

出　　处：《岩土力学》2017年第10期3048-3052,3080,共6页Rock and Soil Mechanics

基　　金：国家科技支撑计划课题(No.2012BAB08B02)~~

摘　　要：目前,岩土工程中常用的塑性屈服准则多为局部不可导的分段函数,在隐式有限元求解中均采用显式向前欧拉法更新应力和Newton-Raphson迭代法求解方程。但显式向前欧拉法容易导致应力偏离屈服面和计算不收敛,而Newton-Raphson迭代法需频繁求导,对于分段函数而言这些方法均不利于求解。为此,提出了采用半隐式向后欧拉法和免导数的Steffensen迭代法联合更新应力与一致切线模量的方案。根据上述方案,利用ANSYS提供的User Mat模块编写了基于统一强度理论与拉破坏复合屈服准则的理想塑性模型。用自定义的本构模型模拟深埋圆形巷道弹塑性开挖过程,数值模拟结果与理论解很好地吻合,验证了模型代码和所提出方案的正确性和可行性。采用半隐式向后欧拉法与Steffensen迭代法相结合的手段,可简化应力与一致切线模量的求解,该方法避免了应力偏离屈服面和求解流动函数偏导,算法简便,易于推广应用。Currently, locally non-differential piecewise functions, the explicit forward Euler method（EFEM）, and the Newton-Raphson iteration method（NRIM） are commonly adopted plastic yield criterions for implicit finite element solution. However, the EFEM will cause stress deviation from the yield surface and lead to non-convergent result, and the NRIM needs to frequently calculate derivative of yield criterion. They are both inconvenient for non-differential functions. A method combining the semi-implicit backward Euler method and the Steffensen iterative method is proposed for these piecewise yield criterions to update stress and consistent tangent modulus. The combination method is applied to write code in ANSYS＇s User Mat module for an elastic-perfect plastic constitutive model, based on a composite unified strength criterion with unified strength theory and tension cut-off. Then the custom constitutive model is applied to simulate excavation process of a deep circular tunnel, and the numerical simulation results fit well with the theoretical solutions, which verifies the correctness and practicability of the model and the combination method. The combination method can prevent stress deviation from the yield surface and does not need to solve partial derivatives of the plastic flow function. It is simple and easy for popularization and application.

关 键 词：半隐式向后欧拉法 Steffensen迭代法 统一强度理论 拉伸截断 ANSYS二次开发 

分 类 号：O241[理学—计算数学]