WIAS Preprint No. 3027, (2023)

Finite-strain poro-visco-elasticity with degenerate mobility


Authors

  • van Oosterhout, Willem
    ORCID: 0009-0003-0956-7222
  • Liero, Matthias
    ORCID: 0000-0002-0963-2915

2020 Mathematics Subject Classification

  • 35K55 35K65 35Q74 74A30 35A01 76S05 35K51 74B20

Keywords

  • Poro-visco-elasticity, finite-strain elasticity, diffusion equation, energy-dissipation inequality, energy estimates, time-incremental scheme

DOI

10.20347/WIAS.PREPRINT.3027

Abstract

A quasistatic nonlinear model for poro-visco-elastic solids at finite strains is considered in the Lagrangian frame using the concept of second-order nonsimple materials. The elastic stresses satisfy static frame-indifference, while the viscous stresses satisfy dynamic frame-indifference. The mechanical equation is coupled to a diffusion equation for a solvent or fluid content. The latter is pulled-back to the reference configuration. To treat the nonlinear dependence of the mobility tensor on the deformation gradient, the result by Healey & Krömer is used to show that the determinant of the deformation gradient is bounded away from zero. Moreover, the focus is on the physically relevant case of degenerate mobilities. The existence of weak solutions is shown using a staggered time-incremental scheme and suitable energy-dissipation inequalities.

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