有限变形计算中的体积不可压缩问题  

Volume Invariability in Calculation of Finite Deformation

作　　者：周喆[1] 李明瑞[1] 黄文彬[1] 杨青春[2] 

机构地区：[1]中国农业大学,北京100083 [2]机械工业部北京机电研究所,北京100083

出　　处：《应用力学学报》2002年第2期81-84,共4页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金资助项目 (5 9875 0 2 8)

摘　　要：在金属材料塑性成形的数值模拟中 ,由于变形通常很大 ,有限变形理论被广泛采用。但由于有限变形下 ,塑性本构理论的研究相对欠缺 ,还未建立起较为公认的理论。塑性体积不可压缩是公认的结果 ,但在有限变形下如何描述体积不可压缩则必须为人们所关注。本文重点讨论了这一问题 ,认为必须完全抛弃以εii=0作为体积不可压缩条件 ,否则不仅将会给计算带来很大误差 。In metal forming processes simulation, the deformation usually is quiet big. And the finite deformation theory is adopted widely in the field. But, study of plastic constitutive theory is not sufficient in finite deformation field. So, a generally recognized theory has not yet been established. As the volume invariability in plastic deformation is generally recognized, the problem on what is the volume invariability condition described in finite deformation field must be noted. This problem is discussed in the paper. Usually, volume invariability condition in small deformation is equivalent to ε ii =0. But if this condition is still adopted, all strain measures except the logarithm strain, will bring various problems——volume change and unconvergence. Therefore, the condition ε ii =0 must be abandoned completely in finite deformation for the other strain measures. Otherwise, it will bring not only big mistake, but also caused calculation unconvergence.

关 键 词：有限变形 塑性本构 体积不可压缩 金属材料 数值模拟 

分 类 号：O344[理学—固体力学]