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EFFECTIVE GOVERNING EQUATIONS FOR POROELASTIC GROWING MEDIA

Penta, R; Ambrosi, D; Shipley, RJ; (2014) EFFECTIVE GOVERNING EQUATIONS FOR POROELASTIC GROWING MEDIA. QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS , 67 (1) 69 - 91. 10.1093/qjmam/hbt024. Green open access

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Abstract

A new mathematical model is developed for the macroscopic behaviour of a porous, linear elastic solid, saturated with a slowly flowing incompressible, viscous fluid, with surface accretion of the solid phase. The derivation uses a formal two-scale asymptotic expansion to exploit the well-separated length scales of the material: the pores are small compared to the macroscale, with a spatially periodic microstructure. Surface accretion occurs at the interface between the solid and fluid phases, resulting in growth of the solid phase through mass exchange from the fluid at a prescribed rate (and vice versa). The averaging derives a new poroelastic model, which reduces to the classical result of Burridge and Keller in the limit of no growth. The new model is of relevance to a large range of applications including packed snow, tissue growth, biofilms and subsurface rocks or soils.

Type: Article
Title: EFFECTIVE GOVERNING EQUATIONS FOR POROELASTIC GROWING MEDIA
Open access status: An open access version is available from UCL Discovery
DOI: 10.1093/qjmam/hbt024
Publisher version: http://dx.doi.org/10.1093/qjmam/hbt024
Additional information: This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Mechanical Engineering
URI: https://discovery.ucl.ac.uk/id/eprint/1420944
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