We employ the finite deformation theory to analyze the inhomogeneous large deformation of a heterogeneous spherical hydrogel subjected to chemo-mechanical loadings. The heterogeneous spherical hydrogel is composed of two concentric spherical hydrogel layers with different material properties. The Gent model is employed for the free energy function of the polymer stretching part in order to tackle the effect of the limiting chain extensibility. The heterogeneous spherical hydrogel is assumed to be perfectly bonded at the interface and is traction free at the external surface. At the internal surface, two boundary conditions are considered: one is internally fixed and the other is internally pressurized. Numerical examples are performed to describe the nonlinear behaviors of a heterogeneous spherical hydrogel when subjected to the swelling and mechanical loadings. For internally fixed case, numerical results show that the limiting chain extensibility and the initial swelling ratio have significant effect on the actuation deformation of a heterogeneous spherical hydrogel. For internally pressurized case, we find that the swelling-induced snap-through instability can be triggered under specified conditions. It is shown that the chemo-mechanical behaviors of the heterogeneous spherical hydrogels can be adjusted by tuning the material properties and the initial swelling ratios.

中文翻译：

---

量化异质球形水凝胶的平衡溶胀反应和溶胀诱导的快速穿透

我们采用有限变形理论来分析受到化学机械载荷的异质球形水凝胶的不均匀大变形。异质球形水凝胶由两个具有不同材料特性的同心球形水凝胶层组成。聚合物拉伸部分的自由能函数采用 Gent 模型，以解决有限链延展性的影响。假设异质球形水凝胶在界面处完美结合，在外表面无牵引力。在内表面，考虑了两种边界条件：一种是内部固定的，另一种是内部加压的。执行数值示例来描述异质球形水凝胶在受到膨胀和机械载荷时的非线性行为。对于内部固定的情况，数值结果表明，极限链伸长率和初始溶胀比对异质球形水凝胶的致动变形有显着影响。对于内部加压的情况，我们发现可以在指定条件下触发膨胀引起的快速通过不稳定性。结果表明，异质球形水凝胶的化学力学行为可以通过调整材料特性和初始溶胀率来调节。数值结果表明，极限链伸长率和初始溶胀比对异质球形水凝胶的致动变形有显着影响。对于内部加压的情况，我们发现在特定条件下可以触发膨胀引起的快速通过不稳定性。结果表明，异质球形水凝胶的化学力学行为可以通过调整材料特性和初始溶胀率来调节。数值结果表明，极限链伸长率和初始溶胀比对异质球形水凝胶的致动变形有显着影响。对于内部加压的情况，我们发现可以在指定条件下触发膨胀引起的快速通过不稳定性。结果表明，异质球形水凝胶的化学力学行为可以通过调整材料特性和初始溶胀率来调节。