A numerical strategy for investigating the kinetic response of stimulus-responsive hydrogels

Dolbow, John E.; Fried, Eliot; Ji, Huidi

doi:10.1016/j.cma.2004.12.004

Cited by 66 publications

(39 citation statements)

References 43 publications

(36 reference statements)

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“…For example, on numerical implementations, one may refer to the related scientific papers by NematNasser and Li [35] , De et al [33] , Baek and Srinivasa [29] , Dolbow et al [36] , Li et al [34] , Swaminathan et al [37] , and many others. A detailed numerical model usually assumes or implies a combination of the free-energy function and kinetic laws.…”

Section: Equilibrium Models Of Polymeric Gelsmentioning

confidence: 98%

Continuum Models of Stimuli-responsive Gels

Hong

2012

Advances in Soft Matter Mechanics

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Immersed in a solution of small molecules and ions, a network of long-chain polymers may imbibe the solution and swell, resulting in a polymeric gel. Depending on the molecular structure of the polymers, the amount of swelling can be regulated by moisture, mechanical forces, ionic strength, electric field, pH value, and many other types of stimuli. Starting from the basic principles of non-equilibrium thermodynamics, this chapter formulates a field theory of the coupled large deformation and mass transportation in a neutral polymeric gel. The theory is then extended to study polyelectrolyte gels with charge-carrying networks by accounting for the electromechanical coupling and migration of solute ions. While the theoretical framework is adaptable to various types of material models, some representative ones are described through specific free-energy functions and kinetic laws. A specific material law for pH-sensitive gels -a special type of polyelectrolyte gels -is introduced as an example of incorporating chemical reactions in modeling stimuli-responsive gels. Finally, a simplified theory for the equilibrium but inhomogeneous swelling of a polymeric gel is deduced. The theory and the specific material models are illustrated through several examples.

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Section: Equilibrium Models Of Polymeric Gelsmentioning

confidence: 98%

Continuum Models of Stimuli-responsive Gels

Hong

2012

Advances in Soft Matter Mechanics

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“…The body heat source term that needs to be applied to all elements results from substituting Equation (19) in the differential equation:…”

Section: Single Uniform Heat Sourcementioning

confidence: 99%

Generalized finite element enrichment functions for discontinuous gradient fields

Aragón

Duarte

Geubelle

2009

Numerical Meth Engineering

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SUMMARYA general GFEM/XFEM formulation is presented to solve two-dimensional problems characterized by C 0 continuity with gradient jumps along discrete lines, such as those found in the thermal and structural analysis of heterogeneous materials or in line load problems in homogeneous media. The new enrichment functions presented in this paper allow solving problems with multiple intersecting discontinuity lines, such as those found at triple junctions in polycrystalline materials and in actively cooled microvascular materials with complex embedded networks. We show how the introduction of enrichment functions yields accurate finite element solutions with meshes that do not conform to the geometry of the discontinuity lines. The use of the proposed enrichments in both linear and quadratic approximations is investigated, as well as their combination with interface enrichment functions available in the literature. Through a detailed convergence study, we demonstrate that quadratic approximations do not require any correction to the method to recover optimal convergence rates and that they perform better than linear approximations for the same number of degrees of freedom in the solution of these types of problems. In the linear case, the effectiveness of correction functions proposed in the literature is also investigated.

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“…They find application in a wide range of problems of interest to the engineering and materials science communities. For example, consider the recent work on fluid-structure interaction [1], cohesive crack growth [2], and sharp phase transitions [3], just to name a few.…”

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confidence: 99%

A bubble‐stabilized finite element method for Dirichlet constraints on embedded interfaces

Mourad

Dolbow

Harari

2006

Numerical Meth Engineering

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100

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SUMMARYWe examine a bubble-stabilized finite element method for enforcing Dirichlet constraints on embedded interfaces. By 'embedded' we refer to problems of general interest wherein the geometry of the interface is assumed independent of some underlying bulk mesh. As such, the robust imposition of Dirichlet constraints using a Lagrange multiplier field is not trivial. To focus issues, we consider a simple one-sided problem that is representative of a wide class of evolving-interface problems. The bulk field is decomposed into coarse and fine scales, giving rise to coarse-scale and fine-scale one-sided sub-problems. The fine-scale solution is approximated with bubble functions, permitting static condensation and giving rise to a stabilized form bearing strong analogy with a classical method. Importantly, the method is simple to implement, readily extends to multiple dimensions, obviates the need to specify any free stabilization parameters, and can lead to a symmetric, positive-definite system of equations. The performance of the method is then examined through several numerical examples. The accuracy of the Lagrange multiplier is compared to results obtained using a local version of the domain integral method. The variational multiscale approach proposed herein is shown to both stabilize the Lagrange multiplier and improve the accuracy of the post-processed fluxes.

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A numerical strategy for investigating the kinetic response of stimulus-responsive hydrogels

Cited by 66 publications

References 43 publications

Continuum Models of Stimuli-responsive Gels

Continuum Models of Stimuli-responsive Gels

Generalized finite element enrichment functions for discontinuous gradient fields

A bubble‐stabilized finite element method for Dirichlet constraints on embedded interfaces

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