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Modeling soft, permeable matter with the Proper Generalized Decomposition (PGD) approach, and verification by means of nanoindentation

Abstract

Understanding sliding and load-bearing mechanisms of biphasic soft matter is crucial for designing synthetic replacements of cartilage, contact-lens materials or for coating medical instruments. Interstitial fluid pressurization is believed to be the intrinsic load-carrying phenomenon governing the frictional properties. In this study, we have characterized permeability and identified the fluid contribution to the support of load during nanoindentation of soft polymer brushes in aqueous environments, by means of the Proper Generalized Decomposition (PGD) approach. First, rate-dependent nanoindentation was performed on a poly(acrylamide) (PAAm) brush in an aqueous environment, to probe purely elastic as well as poro-viscoelastic properties. Second, a biphasic model decoupling the fluid and solid load contributions was proposed, using Darcy's equation for liquid flow in porous media. Using realistic time-dependent simulations requires many direct solutions of the 3D partial differential equation. To efficiently alleviate the time-consumption of multi-dimensional modeling, we used PGD to solve a Darcy model defined in a 7D domain, considering all the unknowns and material properties as extra coordinates of the problem. The obtained 7D simulation was compared to experimental results by using a direct Newton algorithm. Thus, a simulation-based solution for depth- and rate-dependent permeability can be obtained. From the PGD-based model the permeability is calculated, and the velocity- and pressure-fields in the material can be obtained in real-time in 3D by adjusting the parameters to the experimental values. The result is a step forward in understanding the fluid flow, permeability and fluid contribution to the load support of biphasic soft matter.

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Publication details

The article was received on 04 Feb 2017, accepted on 16 May 2017 and first published on 18 May 2017


Article type: Paper
DOI: 10.1039/C7SM00246G
Citation: Soft Matter, 2017, Accepted Manuscript
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    Modeling soft, permeable matter with the Proper Generalized Decomposition (PGD) approach, and verification by means of nanoindentation

    C. S. Ghnatios, C. S. Mathis, R. Simic, N. D. Spencer and F. Chinesta, Soft Matter, 2017, Accepted Manuscript , DOI: 10.1039/C7SM00246G

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