Miller, L., Di Stefano, S., Grillo, A. and Penta, R. (2023) Homogenised governing equations for pre-stressed poroelastic composites. Continuum Mechanics and Thermodynamics, 35, pp. 2275-2300. (doi: 10.1007/s00161-023-01247-3)
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Abstract
We propose the governing equations for a pre-stressed poroelastic composite material. The structure that we investigate possesses a porous elastic matrix with embedded elastic subphases with an incompressible Newtonian fluid flowing in the pores. Both the matrix and individual subphases are assumed to be linear elastic and pre-stressed. We are able to apply the asymptotic homogenisation technique by exploiting the length-scale separation that exists between the porescale and the overall size of the material (the macroscale). We derive the novel macroscale model which describes a poroelastic composite material where the elastic phases possess a pre-stress. We extend the current literature for poroelastic composites by addressing the role of the pre-stresses in the functional form of the new system of derived partial differential equations and its coefficients. The latter are computed by solving appropriate periodic cell differential problems which encode the specific contribution related to the pre-stresses. The model in the first instance is derived in the most general scenario and then specified for a variety of particular cases which are associated with different macroscale behaviour of materials.
| Item Type: | Articles |
|---|---|
| Additional Information: | LM is funded by EPSRC with Project Number EP/N509668/1. RP is partially supported by EPSRC grants EP/S030875/1 and EP/T017899/1 and conducted the research according to the inspiring scientific principles of the national Italian mathematics association Indam ( “Istituto nazionale di Alta Matematica”), GNFM group. SDS acknowledges Regione Puglia in the context of the REFIN research project “Riciclo di materiali e sostenibilit`a modelli di delaminazione per dispositivi laminati”. AG acknowledges PRIN project n. 2020F3NCPX on “Mathematics for industry 4.0 (Math4I4)” and PRIN project n. 2017KL4EF3 on “Mathematics of active materials From mechanobiology to smart devices.” |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Miller, Dr Laura and Penta, Dr Raimondo |
| Authors: | Miller, L., Di Stefano, S., Grillo, A., and Penta, R. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Continuum Mechanics and Thermodynamics |
| Publisher: | Springer |
| ISSN: | 0935-1175 |
| ISSN (Online): | 1432-0959 |
| Published Online: | 09 August 2023 |
| Copyright Holders: | Copyright © 2023 The Author(s) |
| First Published: | First published in Continuum Mechanics and Thermodynamics 35:2275–2300 |
| Publisher Policy: | Reproduced under a Creative Commons license |
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