Coupled diffusion and stress by the finite element method

Shanati, S.; Ellis, Naoko; Randall, T. J.; Marshall, John M.

doi:10.1016/0307-904x(94)00019-3

Cited by 13 publications

(7 citation statements)

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“…It would be of great interest to extend the proposed model to consider solid deformation (e.g., thermal expansion, hygroscopic swelling, and vapor pressure‐induced void growth). Coupling of conventional diffusion models with stress analysis has been studied in the literature . Similar approaches can be applied to the convection–diffusion model, except that vapor pressure must be included in the calculation of solid deformation.…”

Section: Discussionmentioning

confidence: 99%

“…Coupling of conventional diffusion models with stress analysis has been studied in the literature. 17,[76][77][78][79] Similar approaches can be applied to the convection-diffusion model, except that vapor pressure must be included in the calculation of solid deformation. Vapor pressure is crucial because it could result in large deformation and instability of soft thin films.…”

Section: Discussionmentioning

confidence: 99%

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A convection–diffusion porous media model for moisture transport in polymer composites: Model development and validation

Chen

Chu

Fan

2015

J Polym Sci B Polym Phys

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Moisture may cause many detrimental effects to polymers and their composites, thus inhibiting the applications of polymeric materials in hot and humid environments. In this article, a convection–diffusion porous media model is derived to better characterize rapid moisture transport in polymer composites at high temperatures. The model considers both continuum diffusion in solid and high‐pressure convection taking place in the pore network. Coupling of convection and diffusion is achieved by combining the law of conservation of mass, Darcy's law, the liquid–vapor chemical equilibrium, and the ideal gas law. The presented model is validated by conducting experimental tests on an epoxy compound. It is found that the proposed convection–diffusion model is more effective than diffusion‐only and convection‐only models for interpreting rapid desorption tests at high temperatures. A numerical study is also performed to predict maximum vapor pressure during a rapid heating process. Vapor pressure is found to be as high as 6.5 MPa at a heating rate of 10 K/s. It is concluded that the convection–diffusion model is able to capture both vapor dynamics and diffusion mechanism in porous polymeric materials, and can be potentially used to further investigate polymer‐moisture interactions. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015, 53, 1440–1449

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

A convection–diffusion porous media model for moisture transport in polymer composites: Model development and validation

Chen

Chu

Fan

2015

J Polym Sci B Polym Phys

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“…To date, a body of models tentatively describes the existence of strong couplings between mechanical, thermal and diffusive phenomena occurring in polymeric materials in fluid transport, with the additional difficulty in modeling the state of the fluid within the polymer. Theoretical descriptions of these coupling phenomena are based on empirical or thermodynamic interpretations, as given in the selected open literature [25][26][27][28][29][30][31][32][33][34][35][36][37].…”

Section: ¼ àDrc ð1þmentioning

confidence: 99%

Diffuso-Kinetics and Diffuso-Mechanics of Carbon Dioxide / Polyvinylidene Fluoride System under Explosive Gas Decompression: Identification of Key Diffuso-Elastic Couplings by Numerical and Experimental Confrontation

Grandidier

Baudet

Boyer

et al. 2014

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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-The work aims at identifying the key diffuso-elastic couplings which characterize a numerical tool developed to simulate the irreversible 'Explosive Decompression Failure' (XDF) in semi-crystalline polymer. The model proposes to predict the evolution of the gas concentration and of the stress field in the polymer during the gas desorption [DOI: 10.10161j.compositesa.2005.05.021]. Main difficulty is to couple thermal, mechanical and diffusive effects that occur simultaneously during the gas desorption. The couplings are splitting into two families: -indirect coupling (i.e., phenomenology) that is state variables (gas concentration, temperature, and pressure) dependent; -direct coupling, (i.e., diffuso-elastic coupling) as polymer volume changes because of gas diffusion. The numerical prediction of the diffusion kinetics and of the volume strain (swelling) of PVF 2 (polyvinylidene fluoride) under CO 2 (carbon dioxide) environment is concerned. The prediction is carried out by studying selected combinations of couplings for a broad range of CO 2 pressures. The modeling relevance is evaluated by a comparison with experimental transport parameters analytically identify from solubility tests. A pertinent result of the present study is to have demonstrated the non-uniqueness of the coefficients of diffusion (D) and solubility (S g ) between the diffuso-elastic coupling (direct coupling) and indirect coupling. Main conclusion is that it is necessary to consider concomitantly the two types of couplings, the indirect and the direct couplings.Re´sume´-Cine´tique de diffusion et comportement diffuso-me´canique du syste`me dioxide de carbone / polyfluorure de vinylide`ne sous de´compression explosive de gaz : identification des couplages diffuso-e´lastiques majeurs par confrontation nume´rique et expe´rimentale -Cette e´tude a pour objectif d'identifier les couplages diffuso-e´lastiques majeurs qui entrent en jeu dans une Oil & Gas Science and Technology -Rev. IFP Energies nouvelles, Vol. 70 (2015), No. 2, pp. 251-266 Ó J.-C. Grandidier et al., published by IFP Energies nouvelles, 2014 DOI: 10.2516 This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. La pertinence du mode`le est e´value´e par confrontation avec les parame`tres de transport qui ont e´te´e´value´s selon la proce´dure 'analytique conventionnelle' a`partir des mesures expe´rimentales de solubilite´s. Le re´sultat pertinent est d'avoir de´montre´la non-e´quivalence des coefficients de diffusion (D) et de solubilite´(S g ) entre le couplage diffuso-e´lastique (couplage direct) et le couplage indirect. Une bonne mode´lisation du comportement diffuso-e´lastique du polyme`re ne´cessite la conside´ration concomitante des deux familles de couplages, direct et indirect.

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“…Indeed the coupling between deformation and diffusion plays an important role also in many other applications and technological processes, such as metal forming, integrated circuit fabrication (doping of semi-conductors), curing of certain ceramics, etc. (see for example [6][7][8]). Often, in these applications, the complete two-way interaction between the diffusing species and the solid into which it diffuses is neglected.…”

mentioning

confidence: 99%

“…Often, in these applications, the complete two-way interaction between the diffusing species and the solid into which it diffuses is neglected. The mechanical equations of equilibrium, together with the equations of elasticity and compatibility of the solid matrix, are solved to determine the stress distribution, which, in turn, is used in the diffusion equations, formulated in terms of concentration and stress [7,8], or, on the contrary, Fick's law based on a constant diffusivity is employed to derive the concentration field, which is then introduced in the mechanical equations as an initial strain [5]. In the first case, the diffusion equations are coupled to stress, but the effect of concentration variation on the mechanical response is not included, while, in the second case, the mechanical equations are coupled to concentration, but the effect of stress on the diffusive process is not included.…”

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confidence: 99%

A simple solution strategy for coupled piezo-diffusion in elastic solids

et al. 2009

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In this work, a simple solution strategy for the fully coupled problem of the diffusion of a mobile constituent into an elastic solid is proposed. The key features of the proposed solution strategy are a superconvergent strain recovery and a final stress filtering, suitably arranged with a standard recursive staggering scheme. The strategy is devised to overcome some shortcomings arising when solving the problem within the standard finite element framework and can be easily implemented by using existing finite element packages for uncoupled elasticity and diffusion problems. Numerical applications show the effectiveness of the proposed solution strategy.

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Coupled diffusion and stress by the finite element method

Cited by 13 publications

References 5 publications

A convection–diffusion porous media model for moisture transport in polymer composites: Model development and validation

A convection–diffusion porous media model for moisture transport in polymer composites: Model development and validation

Diffuso-Kinetics and Diffuso-Mechanics of Carbon Dioxide / Polyvinylidene Fluoride System under Explosive Gas Decompression: Identification of Key Diffuso-Elastic Couplings by Numerical and Experimental Confrontation

A simple solution strategy for coupled piezo-diffusion in elastic solids

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