Homogenization based two-scale modelling of unilateral contact in micropores of fluid saturated porous media

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F22%3A43966283" target="_blank" >RIV/49777513:23520/22:43966283 - isvavai.cz</a>

Result on the web

<a href="http://hdl.handle.net/11025/50391" target="_blank" >http://hdl.handle.net/11025/50391</a>

DOI - Digital Object Identifier

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Result language

angličtina

Original language name

Homogenization based two-scale modelling of unilateral contact in micropores of fluid saturated porous media

Original language description

We consider fluid-saturated poroelastic structures characterized by unilateral self-contact at the pore level of the periodic microstructure. The unilateral frictionless contact interaction is considered on matching pore surfaces of the elastic skeleton. Depending on the deformation due to applied macroscopic loads, the self-contact interaction alters the one between the solid and fluid phases. Both the disconnected and connected porosities are treated; in the latter case, quasistatic fluid flow is described by the Stokes model. We derive two-scale models of the homogenized porous media for the two types of porosities using the framework of the periodic unfolding homogenization. For the closed pore microstructures, a nonlinear elastic model is obtained at the macroscopic scale. For the connected porosity, a regularization is introduced, assuming the contact interaction never close perfectly the pores, which prevents the pore connectivity. The macroscopic model attains the form of a nonlinear Biot continuum, whereby the Darcy flow model governs the fluid redistribution. To respect that the permeability and other poroelastic coefficients depend on the deformation, an approximation based on the sensitivity analysis is employed.We propose and test new modifications of the original two-scale computational algorithm which is based on alternating micro- and macro-level steps. As a novelty, a dual formulation of the pore-level contact problems in the local representative cells provides actual active contact sets which enables to compute consistent effective elastic coefficients at particular macroscopic points. At the macroscopic level, a sequential linearization leads to an incremental equilibrium problem which is constrained by a projection arising from the homogenized contact constraint, such that the Uzawa algorithm can be used. At the local level, the finite element discretized contact problem attains the form of a nonsmooth equation which which is solved using the semi-smooth Newton method without any regularization, or a problem relaxation. Numerical examples of 2D deforming structures are presented.

Czech name

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Czech description

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Type

O - Miscellaneous

CEP classification

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OECD FORD branch

20302 - Applied mechanics

Project

<a href="/en/project/GF22-00863K" target="_blank" >GF22-00863K: Controllable metamaterials and smart structures: Nonlinear problems, modelling and experiments</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2022

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů