Energy release rate for cracks in hydrogels undergoing finite deformations

Area of Science:

• Materials Science
• Solid Mechanics
• Biomechanics

Background:

• Hydrogel and elastomer rupture involves large deformations and is extensively studied for fracture toughness.
• Previous analytical models often neglect through-thickness effects and focus on plane-strain formulations.
• The influence of liquid flow on fracture behavior requires further investigation in three-dimensional scenarios.

Purpose of the Study:

• To analyze the fracture behavior of hydrogels and elastomers in three dimensions, considering both permeable and impermeable boundary conditions.
• To investigate the transient stress, strain, and chemical potential fields near crack tips.
• To compute the energy release rate using a poroelastic integral and explore its dependence on liquid flow and loading rates.

Main Methods:

• Solving boundary-initial value problems for cracked specimens in plane-strain and three dimensions.
• Utilizing a poroelastic path-independent integral (J*) to compute the energy release rate.
• Applying crack growth criteria based on critical stretch to predict energy release rate as a function of solid volume fraction.

Main Results:

• Transient fields near crack tips differ from asymptotic solutions of linear poroelasticity and large deformation plane-strain models.
• Liquid flow direction (in-plane vs. out-of-plane) depends on boundary permeability, influencing energy release.
• Higher loading rates and impermeable boundaries increase the energy release rate due to liquid flow contributions.
• A non-monotone dependence of energy release on solid volume fraction was uncovered.

Conclusions:

• Liquid flow is a critical factor in hydrogel and elastomer fracture, affecting energy release rates.
• The developed poroelastic models provide a more comprehensive understanding of crack propagation in these materials.
• The findings are applicable to diverse problems, including the rupture of soft tissues and fibrous gels.