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三维非均匀脆性材料破坏过程的数值模拟
引用本文:陈永强,郑小平,姚振汉.三维非均匀脆性材料破坏过程的数值模拟[J].力学学报,2002,34(3):351-361.
作者姓名:陈永强  郑小平  姚振汉
作者单位:清华大学工程力学系,北京,100084
摘    要:采用有限元方法模拟了三维均匀固体材料在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。

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
修稿时间:2000年2月26日

NUMERICAL SIMULATION OF FAILURE PROCESSES IN 3-D HETEROGENEOUS BRITTLE MATERIAL
Chen Yongqiang Zheng Xiaoping Yao Zhenhan.NUMERICAL SIMULATION OF FAILURE PROCESSES IN 3-D HETEROGENEOUS BRITTLE MATERIAL[J].chinese journal of theoretical and applied mechanics,2002,34(3):351-361.
Authors:Chen Yongqiang Zheng Xiaoping Yao Zhenhan
Institution:Chen Yongqiang Zheng Xiaoping Yao ZhenhanDepartment of Engineering Mechanics,Tsinghua University,Beijing 100084,China
Abstract: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" phenomenon presented in references, which shows that the heterogeneity ofmaterial properties is a cause responsible for strain softening. And the more inhomogeneous thedistribution of material properties, the more obvious the phenomenon of strain softening and thehigher the residual strength after peak load. Most dissipated energy is distributed in stages afterpeak load, so the heterogeneity is helpful to prevent structures from paroxysmal failure and playa role in protections. Several 3-D visual appearances of fracture patterns are also presented, i.e.apart fracture patterns in 392nd and 425th load-step and the ultimate fracture patterns.We can expect that the present analysis method may shed new light on some promising fields,such as strength analysis of structural components, optimization and design of composite materials,stability and safety of underground opening engineering, etc.
Keywords:3-D heterogeneity  fracture process  lattice model  statistical methods  numericalsimulation  
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