Paper Detail

A variational model of nonlinear poroelasticity

James H. Adler, Xiaozhe Hu, Arkadz Kirshtein

arxiv Score 9.0

Published 2026-09-18 · First seen 2026-09-21

Research Track A

Abstract

We derive a thermodynamically-consistent model of fluid flow through a poroelastic medium. Starting from elastic and fluid free-energy densities, an energy-dissipation rate, and a kinematic constraint, the force-balance equations are derived using variational principles, with the pressure--density constitutive relation emerging as a direct consequence of the variational structure; the same kinematic constraint also supplies the total-flux transport structure. In the ideal-gas limit, the model linearization recovers the classical linear Biot equations. For power-law fluid energies, it yields isentropic pressure--density relations. A key advantage of the variational formulation is that extensions to richer physics, such as thermal effects, chemical reactions, or multi-component fluids, can be incorporated systematically by augmenting the energy and dissipation functionals without redesigning the force-balance or transport closure. We support the model with an energy-compatible two-field discretization and study consolidation under a surface load with three lateral-boundary treatments and three fluid-compressibility exponents.

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BibTeX

@article{adler2026variational,
  title = {A variational model of nonlinear poroelasticity},
  author = {James H. Adler and Xiaozhe Hu and Arkadz Kirshtein},
  year = {2026},
  abstract = {We derive a thermodynamically-consistent model of fluid flow through a poroelastic medium. Starting from elastic and fluid free-energy densities, an energy-dissipation rate, and a kinematic constraint, the force-balance equations are derived using variational principles, with the pressure--density constitutive relation emerging as a direct consequence of the variational structure; the same kinematic constraint also supplies the total-flux transport structure. In the ideal-gas limit, the model li},
  url = {https://arxiv.org/abs/2609.21294},
  keywords = {math.AP, math.NA, physics.flu-dyn},
  eprint = {2609.21294},
  archiveprefix = {arXiv},
}

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