A Comparative Analysis of Transient Finite-Strain Coupled Diffusion-Deformation Theories for Hydrogels

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External Research Organisations

  • Technische Universität Braunschweig
  • Tor Vergata University of Rome
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Details

Original languageEnglish
Pages (from-to)3767-3800
Number of pages34
JournalArchives of Computational Methods in Engineering
Volume31
Issue number7
Early online date30 Apr 2024
Publication statusPublished - Sept 2024

Abstract

This work presents a comparative review and classification between some well-known thermodynamically consistent models of hydrogel behavior in a large deformation setting, specifically focusing on solvent absorption/desorption and its impact on mechanical deformation and network swelling. The proposed discussion addresses formulation aspects, general mathematical classification of the governing equations, and numerical implementation issues based on the finite element method. The theories are presented in a unified framework demonstrating that, despite not being evident in some cases, all of them follow equivalent thermodynamic arguments. A detailed computational analysis is carried out where Taylor–Hood elements are employed in the spatial discretization to satisfy the inf-sup condition and to prevent spurious numerical oscillations. The resulting discrete problems are solved using the FEniCS platform through consistent variational formulations, employing both monolithic and staggered approaches. We conduct benchmark tests on various hydrogel structures, demonstrating that major differences arise from the chosen volumetric response of the hydrogel. The significance of this choice is frequently underestimated in the state-of-the-art literature but has been shown to have substantial implications on the resulting hydrogel behavior.

Keywords

    cs.CE, cond-mat.mtrl-sci, cond-mat.soft

ASJC Scopus subject areas

Cite this

A Comparative Analysis of Transient Finite-Strain Coupled Diffusion-Deformation Theories for Hydrogels. / Urrea-Quintero, Jorge Humberto; Marino, Michele; Wick, Thomas et al.
In: Archives of Computational Methods in Engineering, Vol. 31, No. 7, 09.2024, p. 3767-3800.

Research output: Contribution to journalReview articleResearchpeer review

Urrea-Quintero JH, Marino M, Wick T, Nackenhorst U. A Comparative Analysis of Transient Finite-Strain Coupled Diffusion-Deformation Theories for Hydrogels. Archives of Computational Methods in Engineering. 2024 Sept;31(7):3767-3800. Epub 2024 Apr 30. doi: 10.48550/arXiv.2403.08972, 10.1007/s11831-024-10101-x
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abstract = "This work presents a comparative review and classification between some well-known thermodynamically consistent models of hydrogel behavior in a large deformation setting, specifically focusing on solvent absorption/desorption and its impact on mechanical deformation and network swelling. The proposed discussion addresses formulation aspects, general mathematical classification of the governing equations, and numerical implementation issues based on the finite element method. The theories are presented in a unified framework demonstrating that, despite not being evident in some cases, all of them follow equivalent thermodynamic arguments. A detailed computational analysis is carried out where Taylor–Hood elements are employed in the spatial discretization to satisfy the inf-sup condition and to prevent spurious numerical oscillations. The resulting discrete problems are solved using the FEniCS platform through consistent variational formulations, employing both monolithic and staggered approaches. We conduct benchmark tests on various hydrogel structures, demonstrating that major differences arise from the chosen volumetric response of the hydrogel. The significance of this choice is frequently underestimated in the state-of-the-art literature but has been shown to have substantial implications on the resulting hydrogel behavior.",
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AU - Urrea-Quintero, Jorge Humberto

AU - Marino, Michele

AU - Wick, Thomas

AU - Nackenhorst, Udo

N1 - Publisher Copyright: © The Author(s) 2024.

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