@article {58, title = {On polymer network rupture in gels in the limit of very slow straining or a very slow crack propagation rate}, journal = {Journal of the Mechanics and Physics of Solids}, volume = {136}, year = {2020}, pages = {103754}, abstract = {

The J-integral is formulated in a direct manner for a gel consisting of a cross-linked polymer network and a mobile solvent. The form of the J-integral is given for a formulation that exploits the Helmholtz energy density of the gel and expressions are provided for it in both the unswollen reference configuration of the polymer network and in the current swollen configuration of the gel when small strains are superimposed on the swollen state. Similarly, the form of the J-integral is developed for an approach that exploits the Landau energy density of the gel and its reference and current configuration expressions are also developed. The Flory-Rehner model of the gel is used to obtain expressions for both the densities of Helmholtz energy and the Landau energy, with the chemical potential of the solvent derived from the Helmholtz energy used in the Legendre transformation that generates the Landau energy. Both the Helmholtz and Landau energies are expanded asymptotically for small strains superimposed on the swollen state of the gel. The results for the various forms of the energies are then used to obtain the elasticity law and the incompressibility constraint for the gel, each derived from both the Helmholtz and the Landau energies. The results are then inserted into the J-integral and fracture mechanics insights obtained for the rapid and slow loading of a gel body with a stationary crack and for a gel body with a crack that is experiencing slow, steady propagation. It is found that the Landau energy form of the J-integral is particularly useful for the slow loading of stationary cracks and for the slow steady propagation of the crack. It is noted that solvent flux during crack growth can cause an increase in the effective fracture toughness of the gel. However, it is found that there is an absence of such diffusional toughening in the rapidly loaded stationary crack case, the very slowly loaded stationary crack case and for the crack experiencing extremely slow but steady propagation. It is further found that, for cracks propagating very slowly, diffusional toughening rises linearly with crack propagation rate up to a critical crack growth rate, above which the diffusional toughening becomes insensitive to the crack propagation rate. The critical crack propagation rate for this transition is found to be dependent on the linear dimension of the gel body and on constitutive parameters for the gel elasticity and solvent diffusion.\ 

}, keywords = {J-integral, polymer gel, Rupture, Slow crack growth, Toughness}, doi = {10.1016/j.jmps.2019.103754}, author = {Robert M McMeeking and Alessandro Lucantonio and Giovanni Noselli and Vikram S Deshpande} } @article {41, title = {Poroelastic toughening in polymer gels: A theoretical and numerical study}, journal = {Journal of the Mechanics and Physics of Solids}, volume = {94}, year = {2016}, pages = {33-46}, abstract = {

We explore the Mode I fracture toughness of a polymer gel containing a semi-infinite, growing crack. First, an expression is derived for the energy release rate within the linearized, small-strain setting. This expression reveals a crack tip velocity-independent toughening that stems from the poroelastic nature of polymer gels. Then, we establish a poroelastic cohesive zone model that allows us to describe the micromechanics of fracture in gels by identifying the role of solvent pressure in promoting poroelastic toughening. We evaluate the enhancement in the effective fracture toughness through asymptotic analysis. We confirm our theoretical findings by means of numerical simulations concerning the case of a steadily propagating crack. In broad terms, our results explain the role of poroelasticity and of the processes occurring in the fracturing region in promoting toughening of polymer gels.

}, keywords = {crack propagation, fracture, polymer gel, swelling, toughening}, doi = {10.1016/j.jmps.2016.04.017}, author = {Giovanni Noselli and Alessandro Lucantonio and Robert M McMeeking and Antonio DeSimone} }