超弹性圆板中的生长诱导不稳定性
Growth induced instabilities in a circular hyperelastic plate
摘要：
在这项工作中，我们探讨了各向同性超弹性圆板的增长引起的机械不稳定性。用变分法导出了一般有限应变下板的一致二维控制方程。导出的板方程求解两种情况下的轴对称增长条件-纯径向，径向和周向相结合的增长使用的复合矩阵法。对于不同的厚度值的板的屈曲行为（特别是，临界增长因子和相关的屈曲模态形状）的增长的影响进行了研究。这些结果适用于模型生长诱导变形的平面软组织，如皮肤。
英文摘要：
In this work, we have explored growth-induced mechanical instability in an isotropic circular hyperelastic plate. Consistent two-dimensional governing equations for a plate under a general finite strain are derived using a variational approach. The derived plate equations are solved using the compound matrix method for two cases of axisymmetric growth conditions - purely radial, and combined radial and circumferential growth. The effect of growth on the buckling behaviour of the plate (in particular, the critical growth factor and the associated buckling mode shapes) is investigated for different thickness values. These results are applicable to model growth induced deformation in planar soft tissues such as skin.
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