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.

针对具有表面张力引起的整体残余应力的软球形弹性固体，对Gurtin-Murdoch（GM）模型进行了研究。不同于原始的GM模型将表面张力视为有限值，而将表面张力引起的整体残余应力视为极小值，本模型将这两者始终视为有限值。本模型与GM模型之间的详细比较表明，对于一个实心球（其表面张力引起的整体残余应力在整个体内保持均匀），GM模型与本模型有很大的偏差。相反，对于无限物体中的小腔体（对于这种腔体，表面张力引起的整体残余应力仅在腔体表面附近才显着，但随着径向距离而迅速减小），当前模型与原始GM模型之间的偏差可以忽略不计。结论是，当表面张力引起的本体残余应力已在本模型中得到解决，但在GM模型中被忽略时，当其强度在体内不减小时，会对软弹性固体的变形和振动产生重大影响。 。