混凝土类材料弹塑性损伤问题的全隐式迭代法  

Full implicit iterative method for elastoplastic damage of concrete-like materials

作　　者：张立[1] 李广凯[1] 马怀发[2,3] ZHANG Li;LI Guangkai;MA Huaifa(Shandong Taishan Pumped Storage Power Station Co.,Ltd.,Taian 271000,China;State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin,China Institute of Water Resources and Hydropower Research,Beijing 100038,China;Earthquake Engineering Research Center,China Institute of Water Resources and Hydropower Research,Beijing 100048,China)

机构地区：[1]山东泰山抽水蓄能电站有限责任公司,山东泰安271000 [2]中国水利水电科学研究院流域水循环模拟与调控国家重点实验室,北京100038 [3]中国水利水电科学研究院工程抗震研究中心,北京100048

出　　处：《水利学报》2020年第8期947-956,共10页Journal of Hydraulic Engineering

基　　金：国家自然科学基金项目(51679265);中国水利水电科学研究院“十三五”重点专项(EB0145B412016);国家电网新源公司项目(SGXYKJ-2019-011)。

摘　　要：弹塑性全隐式迭代法将联立隐式迭代求解屈服条件、塑性流动方程和平衡方程。为了提高算法的收敛性,本文在迭代过程中引入了屈服应力的局部回映迭代。考虑到混凝土弹塑性损伤模型既可反映其塑性(不可恢复)变形又可反映其材料刚度的损伤弱化,因此可将混凝土类材料弹塑性损伤问题分解为弹塑性问题和损伤问题,应用弹塑性全隐式迭代法在有效应力空间计算弹塑性变形,再基于应变等效的原则,并通过损伤参数将有效应力转换为物理空间的实际应力。由此形成了混凝土类材料弹塑性损伤问题的全隐式迭代法。通过混凝土试件弯拉损伤破坏过程的数值模拟验证了该算法。数值计算表明,在有效应力空间的塑性变形处于强化状态下,损伤参数的大小只会影响实际应力,而不会影响塑性变形迭代求解的稳定性。另外,本文提出的全隐式迭代法可用于求解混凝土坝及其坝基岩体的弹塑性损伤问题。由于隐式迭代格式以全量的形式给出,在分析高混凝土坝非线性地震响应时,也可以全量的形式输入地震动荷载。The full implicit iterative method for the elastoplastic problems can be used to solve the yield condition,plastic flow equation and equilibrium equations simultaneously.In order to improve the conver⁃gence of the algorithm,local return-mapping iteration of yield stress is introduced in this paper.Consider⁃ing that an elastoplastic damage model can reflect both its plastic(unrecoverable)deformation and the dam⁃age weakening of the stiffness of concrete-like materials,the elastoplastic damage problem is decomposed into elastoplastic problem and damage problem of concrete materials.Therefore,the full implicit iterative method of the elastoplastic problem is used to calculate the plastic deformation in the effective stress space,and then,based on the principle of strain equivalence,and by means of damage parameters,the effective stress is converted into the actual(nominal)stress in the physical space.The method has been verified by the numerical simulation of flexural damage and failure process of concrete specimen.It is shown that when the plastic deformation in the effective stress space is strengthened,the magnitude of the damage parameter only affect the nominal stress,but not the stability of the numerical iteration of the plas⁃tic deformation.In addition,the full implicit iterative method proposed is not only suitable for solving the elastoplastic damage problem of concrete dam,but also for solving that of rock mass of dam foundation.Since the iterative scheme is fully implicit,it is convenient to input the full seismic load when applying this method to analyze the nonlinear responses of high concrete dams.

关 键 词：混凝土类材料 非线性 弹塑性损伤 屈服函数 隐式迭代法 

分 类 号：TV311[水利工程—水工结构工程] TU311[建筑科学—结构工程]