线粘弹性材料中三维裂纹问题的加料有限元法  

The enriched finite element method for 3-D fracture problems in viscoelastic materials

作　　者：段静波[1] 雷勇军[1] 

机构地区：[1]国防科技大学航天与材料工程学院,湖南长沙410073

出　　处：《国防科技大学学报》2012年第3期6-11,共6页Journal of National University of Defense Technology

基　　金：教育部新世纪优秀人才支持计划资助项目(NCET-08-0148);高等学校博士学科点专项科研基金资助项目(20069998002);国家自然科学基金资助项目(11132012);国防科技大学科研计划资助项目(JC10-01-01)

摘　　要：将加料有限元法扩展应用于线粘弹性材料三维断裂问题。为了反映裂纹尖端的奇异性,在裂尖附近的奇异区采用若干八节点六面体加料单元和过渡单元,非奇异区采用常规八节点六面体单元。三种单元分区混合使用形成求解域网格划分。基于Boltzmann叠加原理,推导了粘弹性材料的增量型本构关系,进而获得了增量加料有限元列式,并通过附加自由度计算粘弹性介质中裂纹应变能量释放率。数值算例验证了方法的正确性和有效性。The enriched finite element method was developed for three-dimensional fracture problems in a linear viscoelastic body. To manifest the singularity at the crack tip, the 8-node hexahedral enriched elements and corresponding transition elements were employed, combined with ordinary elements on the zone far away from the crack tip. Three types of elements were used together to form the whole mesh. Based on the boltzmann superposition principle, the incremental constitutive relation for viscoelastic materials was formulated. Furthermore, the incremental formulations of the enriched FEM were derived. The strain energy release rate in a cracked viscoelastic body was obtained through the enriched degree of freedoms. The numerical results show that the present method is accurate and efficient.

关 键 词：线粘弹性体 三维断裂问题 六面体加料单元 六面体过渡单元 应变能量释放率 

分 类 号：O346.1[理学—固体力学]