Motivated by experiments on dendritic actin networks exhibiting surface growth, we address the problem of the stability of this growth process. We choose as a simple, reference geometry a biaxially stressed half-space growing at its boundary. The actin network is modeled as a neo-Hookean material. A kinetic relation between growth velocity and a stress-dependent driving force for growth is utilized. The stability problem is formulated and results are discussed for different loading and boundary conditions, with and without surface tension. Connections are drawn with Biot’s 1963 surface instability threshold.

中文翻译：

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预拉伸半空间的表面吸积：重新审视 Biot 的问题

受表现出表面生长的树突肌动蛋白网络实验的启发，我们解决了这种生长过程的稳定性问题。我们选择在其边界处生长的双轴应力半空间作为简单的参考几何。肌动蛋白网络被建模为新胡克材料。利用生长速度和依赖于应力的生长驱动力之间的动力学关系。制定了稳定性问题，并讨论了具有和不具有表面张力的不同载荷和边界条件的结果。使用 Biot 的 1963 年表面不稳定性阈值绘制连接。