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)

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.

• Item Type: Articles
• Additional Information: R.P. and D.A. acknowledge the financial support of the ERC Advanced Grant Mathcard (number 227058).
• Status: Published
• Refereed: Yes
• 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: 0033-5614
• 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