This paper presents a micromechanically based constitutive model within the framework of the continuum mechanics to characterize the inelastic elastomeric and swelling behaviors of double network (DN) hydrogels, such as the stress-softening, necking instability, hardening, and stretch-induced anisotropy. The strain-energy density function of the material is decomposed into two independent contributions from the tight and brittle first network and the soft and loose second network, each of which is obtained by integrating the strain energy of one-dimensional (1D) polymer chains in each direction of a unit sphere. The damage process is derived from the irreversible breakages of sacrificial chains in the first network and characterized by the directional stretch-dependent evolution laws for the equivalent modulus and the locking stretch in the non-Gauss statistical model of a single polymer chain. The constitutive model with the optimized-material evolution law predicts stress–stretch curves in a good agreement with the experimental results during loading, unloading, and reloading paths for both ionic and covalent DN hydrogels. The deformation-induced anisotropy is investigated and demonstrated by the constitutive model for the free swelling of damaged specimen. The constitutive model is embedded into the finite-element (FE) procedure and proved to be efficient to model the necking and neck propagation in the plane-strain uniaxial elongation. Based on the procedure, the effects of imperfection and boundary conditions on the loading path and the material evolution during different stages of deformation are investigated.
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February 2016
Research-Article
A Micromechanically Based Constitutive Model for the Inelastic and Swelling Behaviors in Double Network Hydrogels
Yin Liu,
Yin Liu
State Key Laboratory of Structural Analysis for
Industrial Equipment,
Department of Engineering Mechanics,
Faculty of Vehicle Engineering and Mechanics,
Dalian University of Technology,
Dalian 116024, China
Industrial Equipment,
Department of Engineering Mechanics,
Faculty of Vehicle Engineering and Mechanics,
Dalian University of Technology,
Dalian 116024, China
Search for other works by this author on:
Hongwu Zhang,
Hongwu Zhang
State Key Laboratory of Structural
Analysis for Industrial Equipment,
Department of Engineering Mechanics,
Faculty of Vehicle Engineering and Mechanics,
Dalian University of Technology,
Dalian 116024, China
Analysis for Industrial Equipment,
Department of Engineering Mechanics,
Faculty of Vehicle Engineering and Mechanics,
Dalian University of Technology,
Dalian 116024, China
Search for other works by this author on:
Yonggang Zheng
Yonggang Zheng
State Key Laboratory of Structural
Analysis for Industrial Equipment,
Department of Engineering Mechanics,
Faculty of Vehicle Engineering and Mechanics,
Dalian University of Technology,
Dalian 116024, China
e-mail: zhengyg@dlut.edu.cn
Analysis for Industrial Equipment,
Department of Engineering Mechanics,
Faculty of Vehicle Engineering and Mechanics,
Dalian University of Technology,
Dalian 116024, China
e-mail: zhengyg@dlut.edu.cn
Search for other works by this author on:
Yin Liu
State Key Laboratory of Structural Analysis for
Industrial Equipment,
Department of Engineering Mechanics,
Faculty of Vehicle Engineering and Mechanics,
Dalian University of Technology,
Dalian 116024, China
Industrial Equipment,
Department of Engineering Mechanics,
Faculty of Vehicle Engineering and Mechanics,
Dalian University of Technology,
Dalian 116024, China
Hongwu Zhang
State Key Laboratory of Structural
Analysis for Industrial Equipment,
Department of Engineering Mechanics,
Faculty of Vehicle Engineering and Mechanics,
Dalian University of Technology,
Dalian 116024, China
Analysis for Industrial Equipment,
Department of Engineering Mechanics,
Faculty of Vehicle Engineering and Mechanics,
Dalian University of Technology,
Dalian 116024, China
Yonggang Zheng
State Key Laboratory of Structural
Analysis for Industrial Equipment,
Department of Engineering Mechanics,
Faculty of Vehicle Engineering and Mechanics,
Dalian University of Technology,
Dalian 116024, China
e-mail: zhengyg@dlut.edu.cn
Analysis for Industrial Equipment,
Department of Engineering Mechanics,
Faculty of Vehicle Engineering and Mechanics,
Dalian University of Technology,
Dalian 116024, China
e-mail: zhengyg@dlut.edu.cn
1Corresponding author.
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 8, 2015; final manuscript received October 26, 2015; published online November 16, 2015. Assoc. Editor: Thomas Siegmund.
J. Appl. Mech. Feb 2016, 83(2): 021008 (14 pages)
Published Online: November 16, 2015
Article history
Received:
September 8, 2015
Revised:
October 26, 2015
Citation
Liu, Y., Zhang, H., and Zheng, Y. (November 16, 2015). "A Micromechanically Based Constitutive Model for the Inelastic and Swelling Behaviors in Double Network Hydrogels." ASME. J. Appl. Mech. February 2016; 83(2): 021008. https://doi.org/10.1115/1.4031897
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