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.

在这项工作中，我们探索了各向同性圆形超弹性板中生长引起的机械不稳定性。使用变分方法推导了在一般有限应变下板的一致二维控制方程。对于两种轴对称生长条件（纯径向的，以及径向和周向组合生长）的情况，使用复合矩阵方法求解导出的板方程。对于不同的厚度值，研究了生长对板屈曲行为（特别是临界生长因子和相关的屈曲模式形状）的影响。这些结果可用于模拟平面软组织（如皮肤）中的生长诱导变形。