Environmental control of crack propagation in polymer hydrogels
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REVIEW PAPER
Environmental control of crack propagation in polymer hydrogels Tristan Baumberger1,2
· Olivier Ronsin1,2
Received: 12 July 2020 / Accepted: 13 August 2020 / Published online: 19 November 2020 © Springer Nature Switzerland AG 2020
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 Viscous dissipation term visc eff Effective fracture energy dry,wet Fracture energy of a dry (resp. wet) crack κ Darcy permeability ν Drained Poisson ratio Equilibrium swelling ratio λ3eq λ30 Preparation state swelling ratio Chain contour length (see Fig. 3) Tristan Baumberger
[email protected] 1
Sorbonne Universit´es, CNRS, Institut des nanosciences de Paris 4, place Jussieu, F-75005 Paris, France
2
Universit´e de paris, F-75006 Paris, France
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μ μ0 σij σc σY τij τporo ξ dA a a C CL CZ d e Dcoll Dsol E, E ∗ Eel FEM G G tip G ext G0ext G h J∗ K tip KI KIext 0 diff f law sol L LNL LEFM NLEFM NP n N p Pe PEFM SSY tf , tˆf UCL Ubond V Vporo
Solvent chemical potential S
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