Reduced model and nonlinear analysis of localized instabilities of residually stressed cylinders under axial stretch

被引:1
作者
Liu, Yang [1 ,2 ]
Yu, Xiang [3 ]
Dorfmann, Luis [4 ]
机构
[1] Tianjin Univ, Sch Mech Engn, Dept Mech, Tianjin, Peoples R China
[2] Tianjin Key Lab Modern Engn Mech, Tianjin, Peoples R China
[3] Dongguan Univ Technol, Sch Comp Sci & Technol, Dept Math, Dongguan, Peoples R China
[4] Tufts Univ, Dept Civil & Environm Engn, Medford, MA 02155 USA
基金
中国国家自然科学基金;
关键词
Necking; bulging; one-dimensional model; residual stress; bifurcation analysis; nonlinear analysis; INFLATED CIRCULAR-CYLINDERS; CYLINDRICAL-TUBES; ELASTIC-MATERIAL; NECKING; BIFURCATION; STABILITY;
D O I
10.1177/10812865241242432
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
In this paper, we present a dimensional reduction to obtain a one-dimensional model to analyze localized necking or bulging in a residually stressed circular cylindrical solid. The nonlinear theory of elasticity is first specialized to obtain the equations governing the homogeneous deformation. Then, to analyze the nonhomogeneous part, we include higher-order correction terms of the axisymmetric displacement components leading to a three-dimensional form of the total potential energy functional. Details of the reduction to the one-dimensional form are given. We focus on a residually stressed Gent material and use numerical methods to solve the governing equations. Two loading conditions are considered. First, the residual stress is maintained constant, while the axial stretch is used as the loading parameter. Second, we keep the pre-stretch constant and monotonically increase the residual stress until bifurcation occurs. We specify initial conditions, find the critical values for localized bifurcation, and compute the change in radius during localized necking or bulging growth. Finally, we optimize material properties and use the one-dimensional model to simulate necking or bulging until the Maxwell values of stretch are reached.
引用
收藏
页码:1879 / 1899
页数:21
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