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首页> 外文期刊>ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees >A study on the Gurtin-Murdoch model for spherical solids with surface tension
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A study on the Gurtin-Murdoch model for spherical solids with surface tension

机译：具有表面张力的球形固体的古霉菌模型研究

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摘要

An investigation is made on the Gurtin-Murdoch (GM) model for soft spherical elastic solids with surface tension-induced bulk residual stress. Unlike the original GM model which treats the surface tension as a finite value but the surface tension-induced bulk residual stress as infinitesimal, the present model treats both consistently as finite values. Detailed comparisons between the present model and the GM model show that for a solid sphere (for which the surface tension-induced bulk residual stress remains uniform in the entire body), the GM model deviates considerably from the present model. Conversely, for a small cavity in an infinite body (for which the surface tension-induced bulk residual stress is significant only nearby the cavity's surface but quickly diminishes with radial distance), the deviation between the present model and the original GM model is negligible. It is concluded that the surface tension-induced bulk residual stress, which is addressed in the present paper but ignored in the GM model, can have a significant effect on deformation and vibration of soft elastic solids when its magnitude does not vanishingly diminish within the body.
机译：研究了表面张力引起的体积残余应力作用下的球形软弹性固体的Gurtin-Murdoch（GM）模型。与原始GM模型不同，该模型将表面张力视为有限值，但表面张力引起的体积残余应力是无穷小的，本模型将两者一致地视为有限值。本模型与GM模型之间的详细比较表明，对于实心球体（其表面张力引起的体积残余应力在整个身体内保持均匀），GM模型与本模型有很大差异。相反，对于无限体中的小空腔（表面张力引起的体积残余应力仅在空腔表面附近显著，但随径向距离迅速减小），当前模型与原始GM模型之间的偏差可以忽略不计。结果表明，当表面张力引起的体积残余应力的大小在人体内不消失时，其对软弹性固体的变形和振动会产生显著的影响。本文讨论了该问题，但在GM模型中忽略了该问题。

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