Effect of Solvent Diffusion on Crack-Tip Fields and Driving Force for Fracture of Hydrogels

Hydrogels are used in a variety of applications ranging from tissue engineering to soft robotics. They often undergo large deformation coupled with solvent diffusion, and structural integrity is important when they are used as structural components. This paper presents a thermodynamically consistent method for calculating the transient energy release rate for crack growth in hydrogels based on a modified path-independent J-integral. The transient energy release rate takes into account the effect of solvent diffusion, separating the energy lost in diffusion from the energy available to drive crack growth. Numerical simulations are performed using a nonlinear transient finite element method for center-cracked hydrogel specimens, subject to remote tension under generalized plane strain conditions. The hydrogel specimen is assumed to be either immersed in a solvent or not immersed by imposing different chemical boundary conditions. Sharp crack and rounded notch models are used for small and large far-field strains, respectively. Comparisons to linear elastic fracture mechanics (LEFM) are presented for the crack-tip fields and crack opening profiles in the instantaneous and equilibrium limits. It is found that the stress singularity at the crack tip depends on both the far-field strain and the local solvent diffusion, and the latter evolves with time and depends on the chemical boundary conditions. The transient energy release rate is predicted as a function of time for the two types of boundary conditions with distinct behaviors due to solvent diffusion. Possible scenarios of delayed fracture are discussed based on evolution of the transient energy release rate. [DOI: 10.1115/1.4030587]

[1]  Abimael F. D. Loula,et al.  On stability and convergence of finite element approximations of biot's consolidation problem , 1994 .

[2]  Joseph Jagur-Grodzinski,et al.  Polymers for tissue engineering, medical devices, and regenerative medicine. Concise general review of recent studies , 2006 .

[3]  J. Qu,et al.  A path-independent integral for fracture of solids under combined electrochemical and mechanical loadings , 2014 .

[4]  A. Rogalsky,et al.  On the measurement of fracture toughness of soft biogel , 2011 .

[5]  W. Hong,et al.  A visco-poroelastic theory for polymeric gels , 2012, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[6]  C. Caroli,et al.  Fracture of a biopolymer gel as a viscoplastic disentanglement process , 2006, The European physical journal. E, Soft matter.

[7]  A. K. Agarwal,et al.  Adaptive liquid microlenses activated by stimuli-responsive hydrogels , 2006, Nature.

[8]  Min Zhou,et al.  Coupled mechano-diffusional driving forces for fracture in electrode materials , 2013 .

[9]  Mary F. Wheeler,et al.  Overcoming the problem of locking in linear elasticity and poroelasticity: an heuristic approach , 2009 .

[10]  Joshua A. White.  Stabilized finite element methods for coupled flow and geomechanics , 2009 .

[11]  Lallit Anand,et al.  A coupled theory of fluid permeation and large deformations for elastomeric materials , 2010 .

[12]  C. Hui,et al.  Stress Relaxation Near the Tip of a Stationary Mode I Crack in a Poroelastic Solid , 2013 .

[13]  D. Mooney,et al.  Hydrogels for tissue engineering. , 2001, Chemical Reviews.

[14]  Chad M. Landis,et al.  A nonlinear, transient finite element method for coupled solvent diffusion and large deformation of hydrogels , 2015 .

[15]  Zhigang Suo,et al.  Stress-relaxation behavior in gels with ionic and covalent crosslinks. , 2010, Journal of applied physics.

[16]  Emmanuel M Detournay,et al.  Plane strain analysis of a stationary hydraulic fracture in a poroelastic medium , 1991 .

[17]  Andy Ruina.  Influence Of Coupled Deformation-Diffusion Effects On The Retardation Of Hydraulic Fracture , 1978 .

[18]  K. Shull,et al.  Ionically Cross-Linked Triblock Copolymer Hydrogels with High Strength , 2010 .

[19]  Rui Huang,et al.  Swelling kinetics of polymer gels: comparison of linear and nonlinear theories , 2012 .

[20]  Fan Yang,et al.  The energy release rate for hygrothermal coupling elastic materials , 2006 .

[21]  Emmanuel M Detournay,et al.  Plane strain propagation of a hydraulic fracture in a permeable rock , 2008 .

[22]  C. Hui,et al.  Finite strain crack tip fields in soft incompressible elastic solids. , 2008, Langmuir : the ACS journal of surfaces and colloids.

[23]  J. Dolbow,et al.  Chemically induced swelling of hydrogels , 2004 .

[24]  Robert M. McMeeking,et al.  Finite deformation analysis of crack-tip opening in elastic-plastic materials and implications for fracture , 1977 .

[25]  T. Baumberger,et al.  Cooperative effect of stress and ion displacement on the dynamics of cross-link unzipping and rupture of alginate gels. , 2010, Biomacromolecules.

[26]  Philippe H. Geubelle,et al.  Finite deformation effects in homogeneous and interfacial fracture , 1995 .

[27]  J. Lewis,et al.  Evaluation of fracture toughness of cartilage by micropenetration , 2004, Journal of materials science. Materials in medicine.

[28]  M. Oyen,et al.  Poroviscoelastic characterization of particle-reinforced gelatin gels using indentation and homogenization. , 2011, Journal of the mechanical behavior of biomedical materials.

[29]  G. Whitesides,et al.  Indentation of polydimethylsiloxane submerged in organic solvents , 2011 .

[30]  J. Rice,et al.  Some basic stress diffusion solutions for fluid‐saturated elastic porous media with compressible constituents , 1976 .

[31]  J. Fineberg,et al.  The 1/r singularity in weakly nonlinear fracture mechanics , 2009, 0902.2121.

[32]  J. G. Williams,et al.  Modelling and experimental characterisation of the rate dependent fracture properties of gelatine gels , 2015 .

[33]  Z. Suo,et al.  A theory of coupled diffusion and large deformation in polymeric gels , 2008 .

[34]  Richard Schapery,et al.  A theory of crack initiation and growth in viscoelastic media II. Approximate methods of analysis , 1975, International Journal of Fracture.

[35]  G. Herrmann,et al.  Conservation Laws for Thermo or Poroelasticity , 1996 .

[36]  David Martina,et al.  Solvent control of crack dynamics in a reversible hydrogel , 2006, Nature materials.

[37]  T. Iwatsubo,et al.  A Study upon Durability of the Artificial Knee Joint with PVA Hydrogel Cartilage , 2004 .

[38]  Richard Schapery,et al.  A theory of crack initiation and growth in viscoelastic media , 1975 .

[39]  P. Hood,et al.  A numerical solution of the Navier-Stokes equations using the finite element technique , 1973 .

[40]  W. Hong,et al.  Delayed fracture in gels , 2012 .

[41]  Walter Noll,et al.  The thermodynamics of elastic materials with heat conduction and viscosity , 1963 .

[42]  D. Mooney,et al.  Hydrogels for tissue engineering: scaffold design variables and applications. , 2003, Biomaterials.

[43]  Ilya Prigogine,et al.  Introduction to Thermodynamics of Irreversible Processes , 1967 .

[44]  K. Broberg.  Cracks and Fracture , 1999 .

[45]  John R. Rice,et al.  Mathematical analysis in the mechanics of fracture , 1968 .

[46]  A. Needleman,et al.  A COMPARISON OF METHODS FOR CALCULATING ENERGY RELEASE RATES , 1985 .

[47]  Eliot Fried,et al.  A theory for species migration in a finitely strained solid with application to polymer network swelling , 2010 .

[48]  Z. Suo,et al.  Highly stretchable and tough hydrogels , 2012, Nature.

[49]  Choon Chiang Foo,et al.  Stretchable, Transparent, Ionic Conductors , 2013, Science.

[50]  P. Calvert.  Hydrogels for Soft Machines , 2009 .

[51]  Richard Schapery.  Correspondence principles and a generalizedJ integral for large deformation and fracture analysis of viscoelastic media , 1984 .

[52]  David J. Mooney,et al.  Growth Factors, Matrices, and Forces Combine and Control Stem Cells , 2009, Science.

[53]  Z. Suo,et al.  Poroelastic swelling kinetics of thin hydrogel layers: comparison of theory and experiment , 2010 .

[54]  Xuanhe Zhao,et al.  Multi-scale multi-mechanism design of tough hydrogels: building dissipation into stretchy networks. , 2014, Soft matter.

[55]  N. Bouklas.  Modelling and simulations of hydrogels with coupled solvent diffusion and large deformation , 2014 .

[56]  Louis J. Durlofsky,et al.  Stabilized Finite Element Methods for Coupled Geomechanics - Reservoir Flow Simulations , 2003 .

[57]  Kinam Park,et al.  Environment-sensitive hydrogels for drug delivery , 2001 .

[58]  Jian Ping Gong,et al.  Why are double network hydrogels so tough , 2010 .

[59]  Ying Luo,et al.  A photolabile hydrogel for guided three-dimensional cell growth and migration , 2004, Nature materials.

[60]  J. Rice.  A path-independent integral and the approximate analysis of strain , 1968 .

[61]  Richard Schapery,et al.  A theory of crack initiation and growth in viscoelastic media , 1975 .

[62]  Z. Suo,et al.  Viscoelasticity and Poroelasticity in Elastomeric Gels , 2012 .

[63]  J. Williams,et al.  Determination of large deformation and fracture behaviour of starch gels from conventional and wire cutting experiments , 2009 .

[64]  Shigeru Aoki,et al.  On the path independent integral-Ĵ , 1980 .

[65]  Fracture energy of gels , 2000, cond-mat/0003474.

[66]  Bonn,et al.  Delayed fracture of an inhomogeneous soft solid , 1998, Science.

[67]  D. Mooney,et al.  Independent Control of Rigidity and Toughness of Polymeric Hydrogels , 2003 .

[68]  Zhibing Hu,et al.  Swelling Kinetics of Polymer Gels , 1997 .