一类不可压缩材料平面应力问题的裂纹尖端场  

The Plane Stress Crack-Tip field for an Incompressible Rubber Material

作　　者：石志飞 高玉臣[1] 

机构地区：[1]哈尔滨船舶工程学院,哈尔滨工业大学

出　　处：《应用数学和力学》1994年第5期471-477,共7页Applied Mathematics and Mechanics

基　　金：国家自然科学基金

摘　　要：本文采用完全非线性弹性理论，研究了一类不可压缩橡皮类材料￣［１］在Ⅰ型荷载作用下的平面应力问题。指出裂尖变形由两个收缩区和一个扩张区三部分组成。裂纹尖端应力、应变分别具有Ｒ￣（－１）、Ｒ￣（－１／ｎ）的奇异性，当趋近裂尖时，厚度以Ｒ￣（１／４ｎ）的方式趋于零，ｎ为材料常数。The crack-tip field under plane stress condition for an incompressible rubber material [1] is investigated by use of the fully nonlinear equilibrium theory. It is found that the crack-tip field ls composed of two shrink sectors and one expa-nsion sector. At the crack-tip, stress and strain possess the singularity of R￣(-1) and R￣(-1/n), respectively, (R is the distance to the crack-tip before deformation, n is the material constant). When the crack-tip is approached , the thickness of the sheet shrinks to zero with the order of R￣(-1/4n). The results obtained in this paper are consistent with that obtained in [5] when s→∞.

关 键 词：不可压缩材料 平面应力 裂纹尖端场 

分 类 号：O346.1[理学—固体力学]