2014
DOI: 10.3934/nhm.2014.9.599
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Homogenization of a poro-elasticity model coupled with diffusive transport and a first order reaction for concrete

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Cited by 5 publications
(14 citation statements)
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“…Now, we choose a particular scaling (of some coefficients) with respect to the ϵ ‐parameter that leads to a distributed microstructure model in the homogenization limit: For i ∈{ A ; B }, we assume that there are constants scriptCidouble-struckR3×3×3×3, Kidouble-struckR3×3, α i , γ i > 0 such that scriptCAϵ=scriptCA,1emKAϵ=KA,1emαAϵ=αA,1emγAϵ=γA,scriptCBϵ=ϵ2scriptCB,1emKBϵ=ϵ2KB,1emαBϵ=ϵαB,1emγBϵ=ϵγB. These specific ϵ ‐scalings are quite common in the modeling of two‐phase media (e.g., ) and are usually justified (albeit only heuristically) by assuming different orders of magnitude of the characteristic time scales of the involved physical processes in the respective domains. In our case, this means that the effect of heat conduction, the dissipation, the stresses, and the thermal expansion are assumed to be smaller/slower in the inclusions when compared with what happens in the matrix.…”
Section: Setting and Transformation To Fixed Domainmentioning
confidence: 99%
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“…Now, we choose a particular scaling (of some coefficients) with respect to the ϵ ‐parameter that leads to a distributed microstructure model in the homogenization limit: For i ∈{ A ; B }, we assume that there are constants scriptCidouble-struckR3×3×3×3, Kidouble-struckR3×3, α i , γ i > 0 such that scriptCAϵ=scriptCA,1emKAϵ=KA,1emαAϵ=αA,1emγAϵ=γA,scriptCBϵ=ϵ2scriptCB,1emKBϵ=ϵ2KB,1emαBϵ=ϵαB,1emγBϵ=ϵγB. These specific ϵ ‐scalings are quite common in the modeling of two‐phase media (e.g., ) and are usually justified (albeit only heuristically) by assuming different orders of magnitude of the characteristic time scales of the involved physical processes in the respective domains. In our case, this means that the effect of heat conduction, the dissipation, the stresses, and the thermal expansion are assumed to be smaller/slower in the inclusions when compared with what happens in the matrix.…”
Section: Setting and Transformation To Fixed Domainmentioning
confidence: 99%
“…Without the scalings in the bulk equations (i.e., for scriptCBϵ, KBϵ, αBϵ, and γBϵ)), for example, we would expect to get a purely macroscopical limit problem, where only some of the information of the microstructure (and their changes) are coded into the averaged coefficients, similar to the results in . Related problems with no scaling of scriptCBϵ but otherwise the same scaling for similar scenarios (in the context of double poroelasticity) were investigated in . For a more holistic approach to different sets of scalings and their effect on the homogenization procedure, we refer to .…”
Section: Setting and Transformation To Fixed Domainmentioning
confidence: 99%
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