Garyfallogiannis Konstantinos, Purohit Prashant K, Bassani John L
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104, USA.
J Mech Phys Solids. 2022 Oct;167. doi: 10.1016/j.jmps.2022.105009. Epub 2022 Jul 18.
The rupture of hydrogels and swellable elastomers involves large deformations, and there exists a large literature devoted to their experimental characterization including methods for measuring and enhancing fracture toughness. Analytical investigations of the fracture of hydrogels have recognized the importance of large deformations and the contributions of liquid flow, but they have largely been restricted to plane-strain formulations that ignore through-thickness effects. In this paper, boundary-initial value problems for cracked specimens are solved in plane-strain and three dimensions for both permeable and impermeable boundary conditions and various rates of loading. The transient stress, strain and chemical potential fields near the crack tip/front are found to be notably different than the asymptotic solutions of linear poroelasticity and large deformation plane-strain formulations. The energy release rate is computed using a poroelastic path-independent integral , and generally that also is a function of the liquid flow. It is shown for moderately thin three-dimensional specimens that liquid flow is largely in the out-of-plane direction under permeable boundaries and largely in-plane for impermeable boundaries; thus, liquid flow makes larger contributions to the energy release in the latter. In agreement with experiments, the energy release rate tends to be larger at higher loading rates due to the contributions of liquid flow. Finally, criteria for crack growth based on the critical stretch ahead of the crack are adopted to predict the critical energy release rate as a function of solid volume fraction, and the possibility of a non-monotone dependence of energy release on solid volume fraction is uncovered. The methods presented in this paper can be utilized to analyze a wide variety of problems in the rupture of hydrogels including applications to soft tissues and fibrous gels.
水凝胶和可膨胀弹性体的破裂涉及大变形，并且有大量文献致力于对其进行实验表征，包括测量和提高断裂韧性的方法。对水凝胶断裂的分析研究已经认识到了大变形的重要性以及液体流动的贡献，但这些研究在很大程度上仅限于忽略厚度方向效应的平面应变公式。在本文中，针对具有裂纹的试样，求解了平面应变和三维情况下的边界 - 初值问题，考虑了可渗透和不可渗透边界条件以及各种加载速率。结果发现，裂纹尖端/前沿附近的瞬态应力、应变和化学势场与线性多孔弹性和大变形平面应变公式的渐近解有显著不同。使用一个与多孔弹性路径无关的积分来计算能量释放率，通常它也是液体流动的函数。结果表明，对于适度薄的三维试样，在可渗透边界条件下液体流动主要沿平面外方向，而在不可渗透边界条件下主要沿平面内方向；因此，液体流动对后者的能量释放贡献更大。与实验结果一致，由于液体流动的贡献，在较高加载速率下能量释放率往往更大。最后，采用基于裂纹前方临界伸长的裂纹扩展准则来预测作为固体体积分数函数的临界能量释放率，并发现了能量释放对固体体积分数可能存在非单调依赖关系。本文提出的方法可用于分析水凝胶破裂中的各种问题，包括应用于软组织和纤维凝胶方面。
