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A thermodynamically consistent and numerically stable formulation for the description of diffusion in polymeric gels
Author(s) -
Krischok Andreas,
Tkachuk Mykola,
Linder Christian
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410231
Subject(s) - discretization , finite element method , gravitational singularity , compressibility , displacement (psychology) , mathematics , flow (mathematics) , diffusion , incompressible flow , work (physics) , field (mathematics) , mechanics , mathematical analysis , geometry , physics , thermodynamics , psychology , psychotherapist , pure mathematics
This work proposes a stable equal‐order element formulation for polymeric gels at finite deformations. From the numerical point of view the description of flow in incompressible elastic media such as gels leads to singularities in the coupled system of equations of the corresponding finite element discretization unless certain requirements are met to satisfy the Ladyženskaja‐Babuška‐Brezzi (LBB) condition. The proposed computationally efficient mixed enhanced assumed strain method allows to satisfy the LBB condition and to account for locking phenomena without the requirement of higher order interpolations for the displacement field. The proposed model can be employed in various fields where the modeling of flow in incompressible media undergoing finite deformations is of interest such as Computational Soil Mechanics or Computational Biomechanics. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)