Environmental control of crack propagation in polymer hydrogels

Abstract

Hydrogels are highly hydrated polymer networks. The synergistic association of a fluid and an elastic phase is the key of numerous applications of hydrogels as food or cosmetic products, drug delivery vectors, wound dressings, scaffolds for tissue regeneration... Since the natural environment for many of these applications is a wet or liquid one, exchange of fluid or solute may occur via the liquid continuum which exists between the environment and the constitutive solvent. In addition to purely osmotic forces, stresses acting on the network are able to drive solvent flow. This is the basis of poroelasticity, initially studied within the framework of consolidated, fluid saturated rocks. The specificity of hydrogels lies on their high stretchability, which makes extended non-linear elasticity the rule rather than the exception when dealing with fracture mechanics. The association of poro-and non-linear elasticity brings the study of rupture of hydrogels at the forefront of research in mechanics. Along this review, we intend to explore the various ways the environment may affect the nucleation, growth and path stability of a crack in a hydrogel. This goal is pursued from a physicist and experimentalist point of view, with special emphasis on dimensionless relevant parameters and order-of-magnitude estimates. A substantial part of the paper is devoted to an introduction to the specific features of soft gel fracture mechanics. We then try and put forward the wide variety of theoretical and experimental issues relevant to environmental crack control with some tentative insight into tissue engineering and living tissue biomechanics. Keywords Hydrogels • Poroelasticity • Fracture mechanics • Delayed fracture • Drug delivery • Tissue engineering List of main symbols and abbreviations χ Flory parameter for solvent quality δ Crack tip opening displacement Volumetric strain in Eq. (4) η Solvent viscosity Degree of rehydration of the cohesive zone defined in Eq. (43) Fracture energy (generic) 0 Threshold for crack growth int Intrinsic fracture energy visc Viscous dissipation term eff Effective fracture energy dry,wet Fracture energy of a dry (resp. wet) crack κ Darcy permeability ν Drained Poisson ratio λ 3 eq Equilibrium swelling ratio λ 3 0

How hidden 3D structure within crack fronts reveals energy balance

“…For example, why do elastomers have such a strong and monotonically increasing fracture energy dependence for low values of v? One might expect that the opposite would take place; prior to any crack extension due to fracture of the material, the tangled polymer chains that make up a gel, if given sufficient time (small v) should undergo large elongation and alignment, as well as internal friction of the polymer strands (Yang et al, 2019;Baumberger and Ronsin, 2020). In this picture, many of these dissipative processes would, conceivably, not have time to develop at high values of v, so that naively one might expect the fracture energy to decrease with v. As Figs.…”

3D characterization of kinematic fields and poroelastic swellingnear the tip of a propagating crack in a hydrogel

“…Linear elastic fracture mechanics (LEFM) is the most welldeveloped theory for brittle fracture, with wide adoption in engineering science [1][2][3]; it confines the fracture process to a small-scale yielding zone near the crack tip and accurately describes the deformation fields outside this region, with the canonical '1/ √ r' diverging stress field [1][2][3][4]. Within this small region, however, the deformation can be extremely large under the diverging stresses; this large deformation can lead to nonlinear material responses [5][6][7], and further induce cohesive loss or poroelastic solvent flux [8][9][10][11][12][13][14][15]. Furthermore, LEFM is developed for predominantly planar cracks that are translationally invariant along z, but a real crack can be complex with 3D features [16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”

Rate-dependent fracture behavior of gelatin-based hydrogels

“…It is crucial that the fracture properties of hydrogels are understood because of their growing use in applications, and consequently numerous investigators have addressed this in recent years (see for example, Long and Hui, 2016;Baumberger and Ronsin, 2020). Most hydrogels exhibit rate dependent fracture behavior.…”