Finite‐strain poro‐visco‐elasticity with degenerate mobility

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 and Kelvin–Voigt‐type viscosity. 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 and 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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• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Finite‐strain poro‐visco‐elasticity with degenerate mobility ; day:25 ; month:03 ; year:2024 ; extent:22 ; ZAMM ; (25.03.2024) (gesamt 22)

Contributors, Places and Time

• Creator: van Oosterhout, Willem J. M. ; Liero, Matthias

Further information

• DOI: 10.1002/zamm.202300486
• URN: urn:nbn:de:101:1-2024032613071264281143
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.