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Cyclic loading is a common feature in poroelastic systems, the material response depending non-trivially on the exact form of boundary conditions, pore structure, and mechanical properties. The situation becomes more complex when…

Soft Condensed Matter · Physics 2025-10-08 Zoe C. Godard , Derek E. Moulton , Sarah L. Waters

Detailed understanding of the coupling between fluid flow and solid deformation in porous media is crucial for the development biomedical devices and novel energy technologies relating to a wide range of geological and biological processes.…

Fluid Dynamics · Physics 2021-09-22 Francisco J. Carrillo

A mathematical model for poro-visco-plastic compaction and pressure solution in porous sediments has been formulated using the Voigt-type rheological constitutive relation as derived from experimental data. The governing equations reduce to…

Geophysics · Physics 2010-03-30 Xin-She Yang

We present a time-dependent Ginzburg-Landau model of nonlinear elasticity in solid materials. We assume that the elastic energy density is a periodic function of the shear and tetragonal strains owing to the underlying lattice structure.…

Statistical Mechanics · Physics 2009-11-10 Akira Onuki , Akira Furukawa , Akihiko Minam

Many metastable complex fluids such as colloidal glasses and gels show distinct nonlinear viscoelasticity with increasing oscillatory-strain amplitude; the storage modulus decreases monotonically as the strain amplitude increases whereas…

Soft Condensed Matter · Physics 2009-11-11 Kunimasa Miyazaki , Hans M. Wyss , D. A. Weitz , David R. Reichman

We develop a computational model to study the interaction of a fluid with a poroelastic material. The coupling of Stokes and Biot equations represents a prototype problem for these phenomena, which feature multiple facets. On one hand it…

Numerical Analysis · Mathematics 2023-07-19 Martina Bukac , Ivan Yotov , Rana Zakerzadeh , Paolo Zunino

In this paper we study the interaction problem between a nonlinear thermoelastic plate and a compressible viscous fluid with the adiabatic constant $\gamma>12/7$. The existence of a weak solution for this problem is obtained by constructing…

Analysis of PDEs · Mathematics 2020-10-06 Srđan Trifunović , Ya-Guang Wang

We attempt to formalise the relationship between the poroelasticity theory and the effective medium theory of micromechanics. The assumptions of these two approaches vary, but both can be linked by considering the undrained response of a…

Geophysics · Physics 2023-03-09 Filip P. Adamus , David Healy , Philip G. Meredith , Thomas M. Mitchell

We consider the Stokes system in a thin porous medium $\Omega_\varepsilon$ of thickness $\varepsilon$ which is perforated by periodically distributed solid cylinders of size $\varepsilon$. On the boundary of the cylinders we prescribe…

Analysis of PDEs · Mathematics 2018-10-10 María Anguiano , Francisco J. Suárez-Grau

We propose, analyze and implement a virtual element discretization for an interfacial poroelasticity-elasticity consolidation problem. The formulation of the time-dependent poroelasticity equations uses displacement, fluid pressure, and…

Numerical Analysis · Mathematics 2023-06-07 Sarvesh Kumar , David Mora , Ricardo Ruiz-Baier , Nitesh Verma

In this paper, we study the stability and convergence of a decoupled and linearized mixed finite element method (FEM) for incompressible miscible displacement in a porous media whose permeability and porosity are discontinuous across some…

Numerical Analysis · Mathematics 2014-06-18 Buyang Li , Hongxing Rui , Chaoxia Yang

We present benchmark computations of dynamic poroelasticity modeling fluid flow in deformable porous media by a coupled hyperbolic-parabolic system of partial differential equations. A challenging benchmark setting and goal quantities of…

Numerical Analysis · Mathematics 2023-07-06 Mathias Anselmann , Markus Bause , Nils Margenberg , Pavel Shamko

In this paper we demonstrate the influence of the pore pressure to the development of a hydraulically-driven fracture in a poroelastic medium. We present a novel numerical model for propagation of a planar hydraulic fracture and prove its…

Fluid Dynamics · Physics 2016-08-30 Sergey V. Golovin , Alexey N. Baykin

A stabilized conforming mixed finite element method for the three-field (displacement, fluid flux and pressure) poroelasticity problem is developed and analyzed. We use the lowest possible approximation order, namely piecewise constant…

Numerical Analysis · Mathematics 2016-09-23 Lorenz Berger , Rafel Bordas , David Kay , Simon Tavener

In this paper, we develop a discretization for the non-linear coupled model of classical Darcy-Forchheimer flow in deformable porous media, an extension of the quasi-static Biot equations. The continuous model exhibits a generalized…

Numerical Analysis · Mathematics 2021-05-24 Jakub Wiktor Both , Jan Martin Nordbotten , Florin Adrian Radu

Poroelasticity describes the interaction of deformation and fluid flow in saturated porous media. A fully-mixed formulation of Biot's poroelasticity problem has the advantage of producing a better approximation of the Darcy velocity and…

Numerical Analysis · Mathematics 2025-04-25 Michele Botti , Daniele Prada , Anna Scotti , Michele Visinoni

A mathematical model for crack-tip fields is proposed in this paper for the response of a three-dimensional (3-D) porous elastic solid whose material moduli are dependent on the density. Such a description wherein the generalized Lam\`e…

Numerical Analysis · Mathematics 2025-03-11 Kun Gou , S. M. Mallikarjunaiah

Using a combination of theory, experiment and simulation we investigate the nonlinear response of dense colloidal suspensions to large amplitude oscillatory shear flow. The time-dependent stress response is calculated using a recently…

Soft Condensed Matter · Physics 2015-05-20 J. M. Brader , M. Siebenbuerger , M. Ballauff , K. Reinheimer , M. Wilhelm , S. J. Frey , F. Weysser , M. Fuchs

We analyse a PDE system modelling poromechanical processes (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes in the medium. We investigate the…

A linear system of differential equations describing a joint motion of thermoelastic porous body and thermofluid occupying porous space is considered. Although the problem is linear, it is very hard to tackle due to the fact that its main…

Analysis of PDEs · Mathematics 2007-05-23 Anvarbek M. Meirmanov