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Appl. Sci. 2017, 7(9), 917; doi:10.3390/app7090917

A Review of Mixture Theory for Deformable Porous Media and Applications

Department of Mathematics, York Campus, Penn State University, York, PA 17403-3326, USA
Department of Mathematics, Capital University of Science and Technology, Islamabad 44000, Pakistan
College of Electrical and Mechanical Engineering, National University of Sciences and Technology, Islamabad 44000, Pakistan
International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, Mafikeng Campus, North-West University, Private Bag X 2046, Mmabatho 2735, South Africa
Author to whom correspondence should be addressed.
Received: 30 July 2017 / Revised: 25 August 2017 / Accepted: 4 September 2017 / Published: 9 September 2017
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Mixture theory provides a continuum framework to model a multi-phase system. The basic assumption is, at any instant of time all phases are present at every material point and momentum and mass balance equations are postulated. This paper reviews the recent developments in mixture theory and focuses on the applications of the theory in particular areas of biomechanics, composite manufacturing and infiltration into deformable porous materials. The complexity based upon different permeability and stress functions is also addressed. The review covers the literature presented in the past fifty years and summarizes applications of mixture theory in specific areas of interest, for the sake of brevity, only necessary details are provided rather than complete modeling and simulation. View Full-Text
Keywords: mixture theory; deformable porous materials; compression moulding; biomechanics; capillary rise mixture theory; deformable porous materials; compression moulding; biomechanics; capillary rise

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Siddique, J.I.; Ahmed, A.; Aziz, A.; Khalique, C.M. A Review of Mixture Theory for Deformable Porous Media and Applications. Appl. Sci. 2017, 7, 917.

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