Theoretical and numerical study on fracture mechanics of hydrogels

Date

2019-05-07

Authors

Yu, Yalin

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Abstract

Hydrogels consist of cross-linked polymer chains and water molecules. Due to the coupling between deformation of the polymer network and diffusion of the solvent molecules, the fracture behavior of hydrogels is quite different from that of polymers and rubbers. This dissertation presents theoretical and numerical studies on fracture behavior of hydrogels with linear and nonlinear theories.

For the study of stationary cracks, a centered crack model is used for hydrogel specimens under the plane strain condition. Asymptotic analysis of the crack tip fields is presented based on a linear poroelastic formulation for different chemical boundary conditions (immersed and not-immersed). For both cases, a finite element method is developed under different mechanical loading conditions (displacement-control and load-control). The evolution of the crack-tip energy release rate is calculated by a modified path-independent J-integral that takes the effect of energy dissipation due to solvent diffusion into account. Numerical results agree well with the asymptotic solutions of the crack-tip fields. Under load control, the crack-tip energy release rate increases over time, which suggests the onset of crack growth may be delayed until the crack-tip energy release rate reaches a critical value (fracture toughness).

For steady-state crack growth of hydrogels, a semi-infinite crack in a long strip specimen subject to plane-strain loading is studied with both asymptotic and numerical analysis. The crack-tip energy release rate is found to be smaller than the applied energy release rate due to poroelastic shielding. The characteristic size of the poroelastic crack-tip field is inversely proportional to the crack speed. For relatively fast crack growth, the crack-tip energy release rate decreases with increasing crack speed. For relatively slow crack growth, the energy release rate increases with increasing crack speed. The present results are found to be qualitatively consistent with previous experiments on the effects of velocity toughening, solvent viscosity and crack-tip soaking. Moreover, the effect of plane stress is examined with a cohesive zone model. Finally, the nonlinear effect due to large deformation is studied numerically based on a nonlinear poroelastic model.

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