三维非均匀脆性材料破坏过程的数值模拟  

NUMERICAL SIMULATION OF FAILURE PROCESSES IN 3-DHETEROGENEOUS BRITTLE MATERIAL

作　　者：陈永强[1] 郑小平[1] 姚振汉[1] 

机构地区：[1]清华大学工程力学系,北京100084

出　　处：《力学学报》2002年第3期351-361,共11页Chinese Journal of Theoretical and Applied Mechanics

摘　　要：采用有限元方法模拟了三维非均匀固体材料的宏观等效力学性质和破坏过程．首先采用格形(lattice)方法把试件离散成三维均匀网格,在每个单元格中将材料按照均匀处理,根据给定的统计规则来确定不同单元格中的材料常数以反映材料的非均匀性．然后对非均匀脆性材料选用简单的本构关系与断裂准则,采用自适应选取载荷步长对试件进行加载,通过非平衡迭代技术对刚度矩阵进行不断修正,实现了非均匀脆性材料的弹性行为及破坏过程的数值模拟．在此基础上,通过数值计算研究了材料的非均匀分布对宏观等效力学性质和破坏过程的影响,给出了破坏全过程的非线性载荷－位移曲线以及不同载荷阶段的三维损伤破坏的演化图．In this paper, a numerical approach based on FEM is developed to simulate the macro-scopic equivalent mechanical properties and fracture process in three-dimensional heterogeneousbrittle materials for both compressive and tensile cases.The lattice model is adopted to divide the specimen into 3-D uniform lattice. The material ineach element is treated as homogeneous. The elastic constants and failure strength are randomlyallocated according to some known statistical distribution to reflect the initial heterogeneity ofdistribution of material properties. Since in each load-step stage the problem is linear a self-adaptive loading method is adopted, which may automatically determine the size of displacementload-step so that only as less elements as possible fail in each load step. Displacement-controlledload are acted on the specimen and the element is considered broken by making the Young modulusvery flexible when the maximum tensile principal stress computed at an elemeat exceeds the tensilestrength. The specimen is considered totally fractured if its resultant force at any cross-sectionreaches a value most close to zero.The uniaxial tension test of specimen with rectangular cross-section is considered as an exampleof application. The initial heterogeneity of modulus and strength are simulated by normal distribu-tion and Weibull distribution. The numerical simulation results indicate that the equivalent Youngmodulus and bearing capacity increase with the decrease of the heterogeneity,this illustrating thewell known phenomenon that mechanical properties of practical material are always more inferiorto theoretical ones; the failure processes of two kinds of random fields are surprisingly different. Thenormal distribution makes the failure process rather brittle while the Weibull distribution is verysuitable to simulate the 'strain-softening' phenomenon. The non-linear macroscopic stress-straincurves obtained by the method preseated in this paper are in good agreement with data concern-ing 'strain softening' phenomeno

关 键 词：破坏过程 格形模型 数值模拟 有限元法 载荷步长 非平衡迭代技术 演化演 三维非均匀脆性材料 

分 类 号：TB301[一般工业技术—材料科学与工程]