Goriely Alain, Ben Amar Martine
Department of Mathematics, University of Arizona, Tucson, 85721, USA.
Phys Rev Lett. 2005 May 20;94(19):198103. doi: 10.1103/PhysRevLett.94.198103. Epub 2005 May 17.
Differential growth in elastic materials can produce stress either through incompatibility of growth or by interaction with the surrounding medium. In many situations, this stress can be sufficient to induce shape instability in the growing medium. To gain better insight in growth-induced instabilities, the growth of an elastic shell loaded with hydrostatic pressure or embedded in an elastic medium is studied. The residual stress arising from the incompatibility of growth and the contact stress arising from the interaction with the surrounding medium are computed with respect to growth and geometric parameters and critical values for instability are obtained. Depending on these parameters, different modes of instability can be obtained.
弹性材料中的差异生长可通过生长不相容性或与周围介质的相互作用产生应力。在许多情况下，这种应力足以在生长介质中引发形状不稳定性。为了更好地理解生长诱导的不稳定性，研究了承受静水压力或嵌入弹性介质中的弹性壳的生长。计算了由生长不相容性引起的残余应力以及与周围介质相互作用产生的接触应力相对于生长和几何参数的情况，并获得了不稳定性的临界值。根据这些参数，可以得到不同的不稳定性模式。
