基于微平面模型和正则化的脆性岩石损伤破裂模拟方法  

Simulation Method of Damage and Fracture for Brittle Rock Based on Microplane Model and Regularization

作　　者：袁阳 徐涛[1] 周广磊 勒治华 YUAN Yang;XU Tao;ZHOU Guang-lei;LE Zhi-hua(School of Resources&Civil Engineering,Northeastern University,Shenyang 110819,China;College of Energy and Mining Engineering,Shandong University of Science and Technology,Qingdao 266590,China)

机构地区：[1]东北大学资源与土木工程学院,辽宁沈阳110819 [2]山东科技大学能源与矿业工程学院,山东青岛266590

出　　处：《东北大学学报（自然科学版）》2022年第8期1141-1148,共8页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(51974062,42172312);“十三五”国家重点研发计划项目(2017YFC1503101).

摘　　要：为解决有限元计算在模拟脆性岩石损伤过程方面的网格依赖性问题,本文基于微平面模型和正则化方法建立了改进的微平面损伤模型,将单轴压缩条件下的岩石实验结果与数值模型进行了对比.引入不同非均质系数对三点弯曲岩石试样的损伤发展进行模拟,结果表明非均质系数越高损伤区域越集中.此外,通过引入高阶梯度正则化方法对不同特征长度的三点弯曲实验进行数值模拟.特征长度为1 mm时,在不同网格尺寸下的正则化微平面模型的损伤演化结果基本相同,而没有采用正则化方法的微平面损伤模型在不同网格尺寸下出现明显的网格依赖性.最后,通过对比普通模型和正则化模型的载荷-位移曲线,发现网格密度对采用高阶梯度正则化后的微平面损伤模型损伤演化影响较低.To solve the mesh dependence of finite element method in simulating the failure of brittle rock,an improved microplane damage model was built based on the microplane model and regularization method.And the numerical simulations were compared with the experimental results under uniaxial compression test.Heterogeneous indexes were introduced for the damage process simulation of three points bending tests.The results showed that the damage area was more concentrated at the high heterogeneous index.In addition,the three points bending tests with different characteristic length were simulated by regularization based on higher-order deformation gradients.The results showed that the damage evolution of microplane damage models with regularization are analogous when the characteristic length is 1 mm,while the microplane damage model without regularization has a significant mesh-dependence at different mesh size.Finally,the load-displacement relationship of normal model and regularization model was contrasted.Mesh density has little effect on the microplane damage model based on regularization with higher-order deformation gradients.

关 键 词：微平面模型 非均质 损伤演化 正则化 数值模拟 

分 类 号：TD853[矿业工程—金属矿开采]