考虑表面效应的空心圆柱大变形与失稳
Large deformation and instability of soft hollow cylinder with surface effects
摘要：
表面应力在经典弹性理论中一直被忽略，但近年来在高变形软固体力学中却成为一个重要的研究课题。本文分析了表面应力对软质空心圆柱体变形和失稳的影响。将表面能密度函数引入超弹性理论的本构模型中，得到了在均布压力加载和几何翻转条件下，空心圆柱体变形的显式解。发现表面张力对软圆柱的变形有明显的影响。具体而言，表面刚度抵抗变形，但残余表面应力倾向于更大的变形。探讨了表面应力对空心圆柱失稳的影响。对于压力加载和几何外翻条件，折痕的临界条件的显着变化，发现通过改变表面参数。研究结果表明，在有限变形条件下，表面能对软质空心圆柱体的变形和失稳均有明显的影响。所得结果将有助于更准确地理解和预测软结构的力学行为。
英文摘要：
Surface stress, which is always neglected in classical elastic theories, has recently emerged as a key role in the mechanics of highly deformable soft solids. In this paper, the effect of surface stress on the deformation and instability of soft hollow cylinder are analyzed. By incorporating surface energy density function into the constitutive model of a hyper-elastic theory, explicit solutions are obtained for the deformation of soft hollow cylinder under the conditions of uniform pressure loading and geometric everting. It is found that surface tension evidently alters the deformation of the soft cylinder. Specifically, the surface stiffness resists the deformation, but the residual surface stress is inclined to larger deformation. Effects of surface stress on the instability of the soft hollow cylinder is also explored. For both the pressure loading and geometric everting conditions, significant changes in critical condition of the creases are found by varying the surface parameter. The results in this work reveal that surface energy obviously influences both the deformation and the instability of soft hollow cylinder at finite deformation. The obtained results will be helpful for understanding and predicting the mechanical behavior of soft structures accurately.
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