Transversely Isotropic Hyper-Elastic Material Rectangular Plate With Voids Under a Uniaxial Extension
-
摘要: 利用横观各向同性超弹性材料的广义neo-Hookean应变能函数研究了含有多个微孔的超弹性矩形板在单向拉伸作用下的有限变形和受力分析.给出了含有某种对称性分布的多个微孔的矩形板的变形模式,通过求解该变形模式满足的微分方程,将它用两个参数表示出来.可应用最小势能原理导出变分近似解,从而得到矩形板的变形和应力分布的解析解.分析了板中微孔的增长及微孔边缘应力的分布情况,讨论了板的各向异性程度及微孔的大小和孔间距离的影响,得到了单个、三个及五个微孔板中微孔的增长变形和孔边应力分布的一些基本规律规律,并进行了相互比较.Abstract: The finite deformation and stress analyses for a transversely isotropic rectangular plate with voids and made of hyper-elastic material with the generalized neo-Hookean strain energy function under a uniaxial extension are studied.The deformation functions of plates with voids that are symmetrically distributed in a certain manner are given and the functions are expressed by two parameters by solving the differential equations.The solution may be approximately obtained from the minimum potential energy principle.Thus,the analytic solutions of the deformation and stress of the plate are obtained.The growth of the voids and the distribution of stresses along the voids are analyzed and the influences of the degree of anisotropy,the size of the voids and the distance between the voids are discussed.The characteristics of the growth of the voids and the distribution of stresses of the plates with one void,three or five voids are obtained and compared.
-
[1] Horgan C O,Polignone D A.Cavitation in nonlinear elastic solids:A review[J].Applied Mechanics Review,1995,48(8):471-485. [2] Chou-Wang M-S,Horgan C O.Void nuclearation and growth for a class of incompressible nonlinearly elastic materials[J].Int J Solids Structures,1989,25(11):1239-1254. [3] 任九生,程昌钧.不可压超弹性材料中的空穴分叉[J].应用数学和力学,2002,23(8):783-789. [4] REN Jiu-sheng,CHENG Chang-jun.Bifurcation of cavitation solutions for incompressible transversely isotropic hyper-elastic materials[J].Journal of Engineering Mathematics,2002,44(3):245-257. [5] Horgan C O,Abeyaratne R.A bifurcation problem for a compressible nonlinearly elastic medium:growth of a micro-void[J].J Elasticity,1986,16(1):189-200. [6] Horgan C O.Void nucleation and growth for compressible nonlinearly elastic materials:an example[J].Int J Solids Structures,1992,29(2):279-291. [7] 程昌钧,尚新春.超弹性矩形板单向拉伸时微孔的增长[J].应用数学和力学,1997,18(6):573-578. [8] REN Jiu-sheng,CHENG Chang-jun,SHANG Xin-chun.The growth of a void in a rubber rectangular plate under uniaxial extension[J].Journal of Shanghai University,2001,5(3):177-182. [9] 任九生,程昌钧.多孔Mooney-Rivlin材料矩形板的单向拉伸[J].力学季刊,2002,23(3):347-353. [10] Polignone D A,Horgan C O.Cavitation for incompressible anisotropic nonlinearly elastic spheres[J].J Elasticity,1993,33(1):27-65. -
点击查看大图
计量
- 文章访问数: 2171
- HTML全文浏览量: 67
- PDF下载量: 572
- 被引次数: 0
下载:
