Wrinkling as a mechanical instability in growing annular hyperelastic plates
Wrinkling as a mechanical instability in growing annular hyperelastic plates
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DOI：
10.1016/j.ijmecsci.2022.107481
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发表时间：
2022-03
影响因子：
7.3
通讯作者：
S. Mehta;G. Raju;P. Saxena
中科院分区：
文献类型：
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作者：
S. Mehta;G. Raju;P. Saxena
生长诱导的不稳定性在生物系统中普遍存在，并导致以褶皱、折叠和折痕形式的多种形态。目前的工作集中在不可压缩环形超弹性板中生长诱导的扭曲不稳定性背后的机制。本文利用变分原理，在厚度方向上不作任何先验运动学假设，导出了二维板系统的控制微分方程。通过线性分叉分析，研究了在轴对称和非对称扰动下，超弹性环板的稳定性。然后使用复合矩阵法数值求解所产生的微分方程，以评估导致起皱的临界生长因子。研究了边界约束、环板厚度和环板半径比对临界增长因子的影响。对于大多数的情况下，一个不对称的分叉是一个环形板的不稳定的首选模式。我们的研究结果对于模拟生长平面软组织、膨胀水凝胶中的起皱现象以及在弹性基底上生长的二维薄膜中的图案转变的物理过程非常有用。
Growth-induced instabilities are ubiquitous in biological systems and lead to diverse morphologies in the form of wrinkling, folding, and creasing. The current work focusses on the mechanics behind growth-induced wrinkling instabilities in an incompressible annular hyperelastic plate. The governing differential equations for a two-dimensional plate system are derived using a variational principle with no apriori kinematic assumptions in the thickness direction. A linear bifurcation analysis is performed to investigate the stability behaviour of the growing hyperelastic annular plate by considering both axisymmetric and asymmetric perturbations. The resulting differential equations are then solved numerically using the compound matrix method to evaluate the critical growth factor that leads to wrinkling. The effect of boundary constraints, thickness, and radius ratio of the annular plate on the critical growth factor is studied. For most of the considered cases, an asymmetric bifurcation is the preferred mode of instability for an annular plate. Our results are useful to model the physics of wrinkling phenomena in growing planar soft tissues, swelling hydrogels, and pattern transition in two-dimensional films growing on an elastic substrate.