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首页> 外文期刊>International journal of non-linear mechanics >Constitutive branching analysis of cylindrical bodies under in-plane equibiaxial dead-load tractions
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Constitutive branching analysis of cylindrical bodies under in-plane equibiaxial dead-load tractions

机译：平面等双轴静载荷作用下圆柱体的本构分支分析

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摘要

Finite homogeneous deformations of hyperelastic cylindrical bodies subjected to in-plane equibiaxial dead-load tractions are analyzed. Four basic equilibrium problems are formulated considering incompressible and compressible isotropic bodies under plane stress and plane deformation condition. Depending on the form of the stored energy function, these plane problems, in addition to the obvious symmetric solutions, may admit asymmetric solutions. In other words, the body may assume an equilibrium configuration characterized by two unequal in-plane principal stretches corresponding to equal external forces. In this paper, a mathematical condition, in terms of the principal invariants, governing the global development of the asymmetric deformation branches is obtained and examined in detail with regard to different choices of the stored energy function. Moreover, explicit expressions for evaluating critical loads and bifurcation points are derived. With reference to neo-Hookean, Mooney-Rivlin and Ogden-Ball materials, a broad numerical analysis is performed and the qualitatively more interesting asymmetric equilibrium branches are shown. Finally, using the energy criterion, a number of considerations are put forward about the stability of the computed solutions.
机译：分析了平面内等双轴静载荷牵引下的超弹性圆柱体的有限均质变形。考虑平面应力和平面变形条件下的不可压缩和可压缩各向同性体，提出了四个基本平衡问题。根据存储的能量函数的形式，除了明显的对称解之外，这些平面问题还可能允许不对称解。换句话说，主体可以采取平衡构型，其特征在于对应于相等的外力的两个不相等的平面内主拉伸。在本文中，获得了关于主不变量的数学条件，该条件控制着不对称变形分支的整体发展，并针对存储能量函数的不同选择进行了详细研究。此外，导出了用于评估临界载荷和分叉点的明确表达式。参照新胡克，穆尼-里夫林和奥格登-鲍尔的材料，进行了广泛的数值分析，并显示了质上更有趣的不对称平衡分支。最后，使用能量准则，对计算解的稳定性提出了许多考虑。

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