论文标题

脱水引起的活性弹性球形壳中的机械不稳定性

Dehydration induced mechanical instabilities in active elastic spherical shells

论文作者

Curatolo, Michele, Napoli, Gaetano, Nardinocchi, Paola, Turzi, Stefano

论文摘要

主动弹性不稳定性是具有突然机械形变方面的自然世界中的常见现象。通常,不稳定性机制的驱动力具有化学机械性质,这使得这种不稳定性与标准弹性不稳定性截然不同。在本文中,我们描述并研究了在溶解过程中,在肿胀的球形封闭壳中发生的活动弹性不稳定性,在水腔中汇总了水腔。该描述是通过基于应力扩散模型的一些数值实验的结果给出的,该模型可以浏览现象。这项研究是从化学机械角度进行的,通过一些简化的假设,可以得出半分析模型,该模型在不稳定性开始时考虑了应力状态和水浓度到壳的壁上。此外,还考虑了不可能立即更改充满水的腔体体积的不稳定性时腔体体积的不变性。它显示为半分析模型非常匹配数值实验的结果。当考虑不均匀的壳时,即使可以通过少数参数描述不均匀性,也可以显示为更广泛的机械不稳定性。

Active-elastic instabilities are common phenomena in the natural world which have the aspect of sudden mechanical morphings. Frequently, the driving force of the instability mechanisms has a chemo-mechanical nature which makes these kind of instabilities very different from standard elastic instabilities. In this paper, we describe and study the active-elastic instability occurring in a swollen spherical closed shell, bounding a water filled cavity, during a de-hydration process. The description is given through the outcomes of a few numerical experiments based on a stress-diffusion model which allows to glance at the phenomenon. The study is carried on from a chemo-mechanical perspective through a few simplifying assumptions which allow to derive a semi-analytical model which takes into account both the stress state and the water concentration into the walls of the shell at the onset of the instability. Moreover, also the invariance of the cavity volume at the onset of instability, which is due to the impossibility to instantaneously change the cavity volume filled with water, is considered. It is shown as the semi-analytic model matches very well the outcome of the numerical experiments. It is also shown as a wider range of mechanical instabilities can be produced when inhomogeneous shells are considered, even when the inhomogeneities can be described by a small number of parameters.

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