A variational model of nonlinear poroelasticity
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
@misc{adler2026variational,
title = {{A variational model of nonlinear poroelasticity}},
author = {James H. Adler and Xiaozhe Hu and Arkadz Kirshtein},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21294},
eprint = {2609.21294},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21294},
}
RIS
TY - UNPB
TI - A variational model of nonlinear poroelasticity
AU - James H. Adler
AU - Xiaozhe Hu
AU - Arkadz Kirshtein
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21294
UR - https://arxiv.org/abs/2609.21294
AB - 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.
ER -