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The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…

Numerical Analysis · Mathematics 2022-02-11 Vladimír Lukeš , Eduard Rohan

By using dimension reduction and homogenization techniques, we study the steady flow of an incompresible viscoplastic Bingham fluid in a thin porous medium. A main feature of our study is the dependence of the yield stress of the Bingham…

Analysis of PDEs · Mathematics 2019-03-08 María Anguiano , Renata Bunoiu

This paper focuses on the simultaneous homogenization and dimension reduction of periodic composite plates within the framework of non-linear elasticity. The composite plate in its reference (undeformed) configuration consists of a periodic…

Analysis of PDEs · Mathematics 2026-02-03 Amartya Chakrabortty , Georges Griso , Julia Orlik

We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough…

Numerical Analysis · Mathematics 2018-12-27 Robert Altmann , Eric Chung , Roland Maier , Daniel Peterseim , Sai-Mang Pun

We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deformations across an interface, ensuring continuity of…

Numerical Analysis · Mathematics 2023-06-21 S. Badia , M. Hornkjøl , A. Khan , K. -A. Mardal , A. F. Martín , R. Ruiz-Baier

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 investigate solutions to a coupled system of partial differential equations that describe a multilayered filtration system. Namely, we study the interaction of a viscous incompressible flow with bulk poroelasticity, via a poroelastic…

Analysis of PDEs · Mathematics 2026-02-03 George Avalos , Galen Richard , Justin T. Webster

We consider the homogenisation of a coupled Stokes flow and advection-reaction-diffusion problem in a perforated domain with an evolving microstructure of size $\varepsilon$. Reactions at the boundaries of the microscopic interfaces lead to…

Analysis of PDEs · Mathematics 2024-04-05 Markus Gahn , Malte A. Peter , Iuliu Sorin Pop , David Wiedemann

This paper is the second part of a work devoted to the modelling of thin elastic plates with small, periodically distributed piezoelectric inclusions. We consider the equations of linear elasticity coupled with the electrostatic equation,…

Analysis of PDEs · Mathematics 2013-11-06 Eric Canon , Michel Lenczner

We analyze a quasi-static Biot system of poroelasticity for both compressible and incompressible constituents. The main feature of this model is a nonlinear coupling of pressure and dilation through the system's permeability tensor. Such a…

Analysis of PDEs · Mathematics 2021-03-23 Lorena Bociu , Justin T. Webster

In this work, we consider the popular P1-RT0-P0 discretization of the three-field formulation of Biot's consolidation problem. Since this finite-element formulation does not satisfy an inf-sup condition uniformly with respect to the…

Numerical Analysis · Mathematics 2018-08-15 Carmen Rodrigo , Xiaozhe Hu , Peter Ohm , James H. Adler , Francisco J. Gaspar , Ludmil Zikatanov

Biot's equations of poroelasticity contain a parabolic system for the evolution of the pressure, which is coupled with a quasi-stationary equation for the stress tensor. Thus, it is natural to extend the existing work on isogeometric…

Numerical Analysis · Mathematics 2021-02-17 Jeremias Arf , Bernd Simeon

We rigorously derive a Kirchhoff plate theory, via $\Gamma$-convergence, from a three-di\-men\-sio\-nal model that describes the finite elasticity of an elastically heterogeneous, thin sheet. The heterogeneity in the elastic properties of…

Analysis of PDEs · Mathematics 2018-07-17 Virginia Agostiniani , Alessandro Lucantonio , Danka Lučić

Modeling coupled systems of free flow adjacent to a porous medium by means of fully resolved Navier-Stokes equations is limited by the immense computational cost and is thus only feasible for relatively small domains. Model reduction allows…

Computational Physics · Physics 2019-08-07 Kilian Weishaupt , Alexandros Terzis , Ioannis Zarikos , Guang Yang , Matthijs de Winter , Rainer Helmig

Stochastic models for pore collapse in granular materials are developed. First, a general fluctuating stress-strain relation for a plastic flow rule is derived. The fluctuations account for non-associativity in plastic deformations…

Soft Condensed Matter · Physics 2020-03-02 Joseph Bakarji , Daniel M. Tartakovsky

We derive, via simultaneous homogenization and dimension reduction, the Gamma-limit for thin elastic plates whose energy density oscillates on a scale that is either comparable to, or much smaller than, the film thickness. We consider the…

Analysis of PDEs · Mathematics 2012-10-23 Peter Hornung , Stefan Neukamm , Igor Velcic

Energies and equilibrium equations for thin elastic plates are discussed, with emphasis on several issues pertinent to recent approaches in soft condensed matter. Consequences of choice of basis, choice of invariant strain measures, and of…

Soft Condensed Matter · Physics 2019-06-04 J. A. Hanna

In Part I of this two part series, we presented a multi-neighbor dependent contact model for adhesive elastic-plastic particles built upon the method of dimensionality reduction that is valid for the elastic and fully-plastic contact…

Soft Condensed Matter · Physics 2023-09-15 William Zunker , Ken Kamrin

The paper presents a new type of weakly nonlinear two-scale model of inflatable periodic poroelastic structures saturated by Newtonian fluids. The periodic microstructures incorporate fluid inclusions connected to the fluid channels by…

Analysis of PDEs · Mathematics 2025-08-28 Eduard Rohan , Vladimír Lukeš

We study a Stokes system posed in a thin perforated layer with a Navier-slip condition on the internal oscillating boundary from two viewpoints: 1) dimensional reduction of the layer and 2) homogenization of the perforated structure.…

Analysis of PDEs · Mathematics 2022-10-24 John Fabricius , Markus Gahn