一类不可压缩材料平面应力问题的裂纹尖端场

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基金项目: 国家自然科学基金

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

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.
- 不可压缩材料 /
- 平面应力 /
- 裂纹尖端场 /
- 完全非线性弹性理论
Abstract: The crack-tip field under plane stress condition for an incompressible rubber material^[1] is investigated by.the use of the fully nonlinear equilibrium theory.It is found thai the crack-tip field is composed of two shrink sectors and one expansion se-ctor.At the crack-tip,stress and strain possess the singularity of R^-1 and R^-1n,respec-tively,(R is the distance to the crack-tip before deformation,n is the material const-ant).When the crack-tip is approached,the thickness of the sheet shrinks to zerowith the order of R^1.4n.The results obtained in this paper are consistent with that ob-tained in [8] when s→χ.
- incompressible material /
- plane stress condition /
- crack-tip field /
- fully nonlinear equilibrium theory

[1]	Gao,Y.C.,A constitutive relation of rubber-like materials(to be published).
[2]	Knowles,J.K.,and E,Stern berg,An asp mptotic finite dEformation analysis of the elastostatic field near the tip of a crack,J,Elas.,(1973).
[3]	Knowles,J.K.and E Stcrnbcrg.An asymptom finite deformation analysis of the elastostatic field near the tip of a crack,J.of Elas.3(1973),67
[4]	Gao Y.C.,Elastostatic crack tip behavior for a rubber-like material,Theoretical and Aflblied Fracture Mechanics,14(1990).
[5]	Gao,Y.C.,and D,Durban,The crack tip field in a rubber-like thin sheet(to appear).