Double poroelasticity derived from the microstructure

Miller, L. and Penta, R. (2021) Double poroelasticity derived from the microstructure. Acta Mechanica, 232(10), pp. 3801-3823. (doi: 10.1007/s00707-021-03030-4)

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We derive the balance equations for a double poroelastic material which comprises a matrix with embedded subphases. We assume that the distance between the subphases (the local scale) is much smaller than the size of the domain (the global scale). We assume that at the local scale both the matrix and subphases can be described by Biot’s anisotropic, heterogeneous, compressible poroelasticity (i.e. the porescale is already smoothed out). We then decompose the spatial variations by means of the two-scale homogenization method to upscale the interaction between the poroelastic phases at the local scale. This way, we derive the novel global scale model which is formally of poroelastic-type. The global scale coefficients account for the complexity of the given microstructure and heterogeneities. These effective poroelastic moduli are to be computed by solving appropriate differential periodic cell problems. The model coefficients possess properties that, once proved, allow us to determine that the model is both formally and substantially of poroelastic-type. The properties we prove are a) the existence of a tensor which plays the role of the classical Biot’s tensor of coefficients via a suitable analytical identity and b) the global scale scalar coefficient M¯ is positive which then qualifies as the global Biot’s modulus for the double poroelastic material.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Penta, Dr Raimondo and Miller, Dr Laura
Authors: Miller, L., and Penta, R.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Acta Mechanica
ISSN (Online):1619-6937
Published Online:12 July 2021
Copyright Holders:Copyright © 2021 The Authors
First Published:First published in Acta Mechanica 232(10): 3801-3823
Publisher Policy:Reproduced under a Creative Commons License

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
172865EPSRC DTP 16/17 and 17/18Tania GalabovaEngineering and Physical Sciences Research Council (EPSRC)EP/N509668/1Research and Innovation Services
303232EPSRC Centre for Multiscale soft tissue mechanics with MIT and POLIMI (SofTMech-MP)Xiaoyu LuoEngineering and Physical Sciences Research Council (EPSRC)EP/S030875/1M&S - Mathematics
308255The SofTMech Statistical Emulation and Translation HubDirk HusmeierEngineering and Physical Sciences Research Council (EPSRC)EP/T017899/1M&S - Statistics