Effective governing equations for poroelastic growing media

Penta, R. , Ambrosi, D. and Shipley, R. J. (2014) Effective governing equations for poroelastic growing media. Quarterly Journal of Mechanics and Applied Mathematics, 67(1), pp. 69-91. (doi: 10.1093/qjmam/hbt024)

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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.

Item Type:Articles
Additional Information:R.P. and D.A. acknowledge the financial support of the ERC Advanced Grant Mathcard (number 227058).
Glasgow Author(s) Enlighten ID:Penta, Dr Raimondo
Authors: Penta, R., Ambrosi, D., and Shipley, R. J.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Quarterly Journal of Mechanics and Applied Mathematics
Publisher:Oxford University Press
ISSN (Online):1464-3855
Published Online:21 January 2014
Copyright Holders:Copyright © 2014 The Authors
First Published:First published in Quarterly Journal of Mechanics and Applied Mathematics 67(1):69-91
Publisher Policy:Reproduced under a Creative Commons License

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