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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
Double network (DN) hydrogels are hydrogels consist of two different networks to make them both tough and extensible. This thesis focuses on understanding the time-dependent mechanical behavior of DN hydrogels through constitutive modeling and numerical simulation. We start by working with a poly(vinyl alcohol) (PVA) gel which is chemically cross-linked by glutaraldehyde and physically cross-linked by Borax ions. This PVA gel serves as a model system because of its well-defined simple chemical structure. Based on the steady state breaking and healing kinetics of the temporary (physical) cross-links, a time-dependent large deformation constitutive model for this model system is developed. This constitutive model is compared against a large set of experimental data, including uniaxial tension tests of loading-holding-unloading at different rates, and torsional rheology tests at temperatures ranging from 13 to 50 degrees Celsius; all results agree very well. A standard procedure for determining the material parameters is also presented. Using the steady state constitutive model, an asymptotic analysis for the dominant stress and strain fields near the tip of a plane stress crack is carried out. This model is then implemented into a commercial finite element (FE) software, ABAQUS, through a user defined material subroutine (UMAT) with a novel time integration scheme. This enables us to run numerical simulations with complex geometries and loading conditions. Currently we are able to numerically simulate the PVA gel with undamaged polymer chains that follow Gaussian chain statistics. A possible way to incorporate strain hardening into ABAQUS using polynomial strain energy density functions is also discussed. Model prediction, FE simulation, and experimental data are compared for samples with high stress and strain concentrations (cracked or notched samples). Comparisons range from full field responses to local singularities as well as 3D and 2D simulations; all results agree very well. However, a limitation of the PVA model system is that the bond breaking and healing kinetics are independent of stress, while bond dissociations in most polymeric materials are stress-induced. A more general constitutive model for a polyampholyte (PA) gel that considers stress-dependent breaking kinetics for the temporary cross-links is investigated. Physical meanings of each material parameter and how to fit for them are presented. Using this stress-dependent model along with the steady state model, differences between nonlinear and linear viscoelasticity are discussed, and two cases with stress concentrations as analogs of crack problems are examined to study the role of nonlinear viscoelasticity at crack tip fields.
The Mechanics of Hydrogels: Mechanical Properties, Testing, and Applications offers readers a systematic description of the mechanical properties and characterizations of hydrogels. Practical topics such as manufacturing hydrogels with controlled mechanical properties and the mechanical testing of hydrogels are covered at length, as are areas such as inelastic and nonlinear deformation, rheological characterization, fracture and indentation testing, mechanical properties of cellularly responsive hydrogels, and more. Proper instrumentation and modeling techniques for measuring the mechanical properties of hydrogels are also explored. Links the mechanical and biological behaviors and applications of hydrogels Looks at the manufacturing and mechanical testing of hydrogels Discusses the design and use of hydrogels in a wide array of applications
Swelling of a polymer gel is a kinetic process coupling mass transport and mechanical deformation. A comparison between a nonlinear theory for polymer gels and the classical theory of linear poroelasticity is presented. It is shown that the two theories are consistent within the linear regime under the condition of a small perturbation from an isotropically swollen state of the gel. The relationships between the material properties in the linear theory and those in the nonlinear theory are established by a linearization procedure. Both linear and nonlinear solutions are presented for swelling kinetics of substrate-constrained and freestanding hydrogel layers. A new procedure is suggested to fit the experimental data with the nonlinear theory. A nonlinear, transient finite element formulation is presented for initial boundary value problems associated with swelling and deformation of hydrogels, based on nonlinear continuum theories for hydrogels with compressible and incompressible constituents. The incompressible instantaneous response of the aggregate imposes a constraint to the finite element discretization in order to satisfy the LBB condition for numerical stability of the mixed method. Three problems of practical interests are considered: constrained swelling, flat-punch indentation, and fracture of hydrogels. Constrained swelling may lead to instantaneous surface instability. Indentation relaxation of hydrogels is simulated beyond the linear regime under plane strain conditions, and is compared with two elastic limits for the instantaneous and equilibrium states. The effects of Poisson's ratio and loading rate are discussed. On the study of hydrogel fracture, a method for calculating the transient energy release rate for crack growth in hydrogels, based on a modified path-independent J-integral, is presented. The transient energy release rate takes into account the energy dissipation due to diffusion. Numerical simulations are performed for a stationary center crack loaded in mode I, with both immersed and non-immersed chemical boundary conditions. Both sharp crack and blunted notch crack models are analyzed over a wide range of applied remote tensile strains. Comparisons to linear elastic fracture mechanics are presented. A critical condition is proposed for crack growth in hydrogels based on the transient energy release rate. The applicability of this growth condition for simulating concomitant crack propagation and solvent diffusion in hydrogels is discussed.
This book perfects the theoretical system of fracture mechanics of nonhomogeneous materials through the establishment of the piecewise exponential model and expands the fracture research scope to nonhomogeneous materials containing complex interfaces through proposing the domain-independent interaction integral concept. The piecewise exponential model has overcome the problem of fracture mechanics of nonhomogeneous materials and clarified the doubt of traditional exponential models in recent 30 years. The domain-independent interaction integral method is not affected by material nonhomogeneity and discontinuity, which greatly facilitates its numerical implementation in the investigation of fracture behaviors of nonhomogeneous materials with complex interfaces.
This volume covers experimental and theoretical advances on the relationship between composition, structure and macroscopic mechanical properties of novel hydrogels containing dynamic bonds. The chapters of this volume focus on the control of the mechanical properties of several recently discovered gels with the design of monomer composition, chain architecture, type of crosslinking or internal structure. The gels discussed in the different chapters have in common the capability to dissipate energy upon deformation, a desired property for mechanical toughness, while retaining the ability to recover the properties of the virgin material over time or to self-heal when put back in contact after fracture. Some chapters focus on the synthesis and structural aspects while others focus on properties or modelling at the continuum or mesoscopic scale. The volume will be of interest to chemists and material scientists by providing guidelines and general structure-property considerations to synthesize and develop innovative gels tuned for applications. In addition it will provide physicists with a better understanding of the role of weak interactions between molecules and physical crosslinking on macroscopic dissipative properties and self-healing or self-recovering properties.
Fracture, and particularly brittle fracture, is a good example of an instability. For a homogeneous solid, subjected to a uniform stress field, a crack may appear anywhere in the structure once the threshold stress is reached. However, once a crack has been nucleated in some place, further damage in the solid will in most cases propagate from the initial crack, and not somewhere else in the solid. In this sense fracture is an unstable process. This property makes the process extremely sensitive to any heterogeneity present in the medium, which selects the location of the first crack nucleated. In particular, fracture appears to be very sensitive to disorder, which can favor or impede local cracks. Therefore, in most realistic cases, a good description of fracture mechanics should include the effect of disorder. Recently this need has motivated work in this direction starting from the usual description of fracture mechanics. Parallel with this first trend, statistical physics underwent a very important development in the description of disordered systems. In particular, let us mention the emergence of some "new" concepts (such as fractals, scaling laws, finite size effects, and so on) in this field. However, many models considered were rather simple and well adapted to theoretical or numerical introduction into a complex body of problems. An example of this can be found in percolation theory. This area is now rather well understood and accurately described.
Volume is indexed by Thomson Reuters CPCI-S (WoS). This book, which comprises contributions from researchers in 20 countries, was designed to be a forum within which to promote and exchange the latest experimental and theoretical research work on structural integrity, durability and failure analysis; with the emphasis being placed on fracture and damage mechanics.
The papers in this volume represent a considerable cross-section of the field of fracture mechanics, a testimony to the breadth of interest that Mel and Max Williams' friends share with them. Several are expanded versions of papers that were given in special sessions honoring them at the 1997 Ninth International Conference on Fracture Mechanics in Sydney, Australia. The subjects treated in this volume can be classified as follows: dynamic fracture problems as viewed primarily from a classical continuum point of view; analysis of relatively general crack geometrics; fracture problems of polymers and other relatively ductile materials; scaling rules that allow extension of results obtained at one size to be translated into behavior at different size scales; problems dealing with interactions that produce complex stress fields; fracture problems directly appropriate to composite materials; analysis of stress concentrations in anisotropic, elastic solids; and the problem of cracks in thin plates bending. This volume will be of interest to engineers and scientists working on all aspects of the physics and mechanics of fracture.