A finite element implementation of a coupled diffusion-deformation theory for elastomeric gels

The theory of Chester and Anand (2011) for fluid diffusion and large deformations of elastomeric gels is implemented as a user-defined element (UEL) subroutine in the commercial finite element software package ABAQUS. A specialized form of the constitutive equations and the governing partial differential equations of the theory are summarized, and the numerical implementation is described in detail. To demonstrate the robustness of the numerical implementation a few illustrative numerical simulation examples for axisymmetric, plane strain, and three-dimensional geometries are shown. For educational purposes, and also to facilitate the numerical implementation of other coupled multiphysics theories, the source code for the UEL is provided as an online supplement to this paper.

[1]  D. Owen,et al.  Design of simple low order finite elements for large strain analysis of nearly incompressible solids , 1996 .

[2]  Howon Lee,et al.  Prescribed pattern transformation in swelling gel tubes by elastic instability. , 2012, Physical review letters.

[3]  Eugenio Giner,et al.  An Abaqus implementation of the extended finite element method , 2009 .

[4]  Howard A. Stone,et al.  Bending and twisting of soft materials by non-homogenous swelling , 2011 .

[5]  James P. Keener,et al.  Kinetics of Swelling Gels , 2011, SIAM J. Appl. Math..

[6]  Z. Suo,et al.  Inhomogeneous swelling of a gel in equilibrium with a solvent and mechanical load , 2009 .

[7]  Shawn A. Chester,et al.  A large-deformation gradient theory for elastic–plastic materials: Strain softening and regularization of shear bands , 2012 .

[8]  Lallit Anand,et al.  Hydrogen in metals: A coupled theory for species diffusion and large elastic–plastic deformations , 2013 .

[9]  Takehiko Gotoh,et al.  Novel synthesis of thermosensitive porous hydrogels , 1998 .

[10]  Chih-Chang Chu,et al.  Thermoresponsive hydrogel with rapid response dynamics , 2003, Journal of materials science. Materials in medicine.

[11]  Zhigang Suo,et al.  A theory of constrained swelling of a pH-sensitive hydrogel†‡ , 2010 .

[12]  Simon Champ,et al.  New superabsorbent thermoreversible hydrogels , 2001 .

[13]  Wei Hong,et al.  INHOMOGENEOUS LARGE DEFORMATION KINETICS OF POLYMERIC GELS , 2013 .

[14]  R. McMeeking,et al.  Numerical analysis of hydrogen transport near a blunting crack tip , 1989 .

[15]  Alessandro Lucantonio,et al.  Transient analysis of swelling-induced large deformations in polymer gels , 2013 .

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

[17]  Z. Suo,et al.  Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels , 2011 .

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

[19]  Zhigang Suo,et al.  Poroelasticity of a covalently crosslinked alginate hydrogel under compression , 2010 .

[20]  James J Mason,et al.  Preparation and mechanical characterization of a PNIPA hydrogel composite , 2008, Journal of materials science. Materials in medicine.

[21]  Lallit Anand,et al.  A thermo-mechanically coupled theory for fluid permeation in elastomeric materials: Application to thermally responsive gels , 2011 .

[22]  Martijn Kleverlaan,et al.  Deployment of Swelling Elastomer Packers in Shell E&P , 2005 .

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

[24]  Zhigang Suo,et al.  Modeling and simulation of buckling of polymeric membrane thin film gel , 2010 .

[25]  Anupam Pandey,et al.  Swelling-induced deformations: a materials-defined transition from macroscale to microscale deformations. , 2013, Soft matter.

[26]  Rashmi Bhavsar,et al.  Intelligence in Novel Materials , 2008 .

[27]  Katia Bertoldi,et al.  Modeling of dielectric elastomers: Design of actuators and energy harvesting devices , 2013 .

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

[29]  Hanqing Jiang,et al.  Simulation of the Transient Behavior of Gels Based on an Analogy Between Diffusion and Heat Transfer , 2013 .

[30]  A. Khademhosseini,et al.  Hydrogels in Biology and Medicine: From Molecular Principles to Bionanotechnology , 2006 .

[31]  Lallit Anand,et al.  On modeling the oxidation of high-temperature alloys , 2013 .

[32]  Katia Bertoldi,et al.  Modeling of elasto-capillary phenomena. , 2014, Soft matter.

[33]  Robin H. Liu,et al.  Functional hydrogel structures for autonomous flow control inside microfluidic channels , 2000, Nature.

[34]  M. Gurtin,et al.  The Mechanics and Thermodynamics of Continua , 2010 .

[35]  Glaucio H. Paulino,et al.  Computational implementation of the PPR potential-based cohesive model in ABAQUS: Educational perspective , 2012 .

[36]  Lallit Anand,et al.  A Cahn–Hilliard-type phase-field theory for species diffusion coupled with large elastic deformations: Application to phase-separating Li-ion electrode materials , 2014 .

[37]  David J Mooney,et al.  New materials for tissue engineering: towards greater control over the biological response. , 2008, Trends in biotechnology.

[38]  Shawn A. Chester.  A constitutive model for coupled fluid permeation and large viscoelastic deformation in polymeric gels , 2012 .

[39]  Zhigang Suo,et al.  A finite element method for transient analysis of concurrent large deformation and mass transport in gels , 2009 .

[40]  Eric Nies,et al.  Phase transitions in the system poly(N-isopropylacrylamide)/water and swelling behaviour of the corresponding networks , 2000 .

[41]  Allan F. Bower,et al.  A simple finite element model of diffusion, finite deformation, plasticity and fracture in lithium ion insertion electrode materials , 2012 .

[42]  Khaled S. Al-Athel,et al.  Modeling decohesion of a top-coat from a thermally-growing oxide in a thermal barrier coating , 2013 .