%0 Journal Article %1 ArmitiJuber.2021 %A Armiti-Juber, Alaa %A Ricken, Tim %D 2021 %J Archive of Applied Mechanics %K FOR5151 SPP1886 exc2075 from:timricken isd myown pn2 theory_of_porous_media %R 10.1007/s00419-021-01907-3 %T Model order reduction for deformable porous materials in thin domains via asymptotic analysis %X We study fluid-saturated porous materials that undergo poro-elastic deformations in thin domains. The mechanics in such materials are described using a biphasic model based on the theory of porous media (TPM) and consisting of a system of differential equations for material’s displacement and fluid’s pressure. These equations are in general strongly coupled and nonlinear, such that exact solutions are hard to obtain and numerical solutions are computationally expensive. This paper reduces the complexity of the biphasic model in thin domains with a scale separation between domain’s width and length. Based on standard asymptotic analysis, we derive a reduced model that combines two sub-models. Firstly, a limit model consists of averaged equations that describe the fluid pore pressure and displacement in the longitudinal direction of the domain. Secondly, a corrector model re-captures the mechanics in the transverse direction. The validity of the reduced model is finally tested using a set of numerical examples. These demonstrate the computational efficiency of the reduced model, while maintaining reliable solutions in comparison with original biphasic TPM model in thin domain.

@article{ArmitiJuber.2021, abstract = {We study fluid-saturated porous materials that undergo poro-elastic deformations in thin domains. The mechanics in such materials are described using a biphasic model based on the theory of porous media (TPM) and consisting of a system of differential equations for material’s displacement and fluid’s pressure. These equations are in general strongly coupled and nonlinear, such that exact solutions are hard to obtain and numerical solutions are computationally expensive. This paper reduces the complexity of the biphasic model in thin domains with a scale separation between domain’s width and length. Based on standard asymptotic analysis, we derive a reduced model that combines two sub-models. Firstly, a limit model consists of averaged equations that describe the fluid pore pressure and displacement in the longitudinal direction of the domain. Secondly, a corrector model re-captures the mechanics in the transverse direction. The validity of the reduced model is finally tested using a set of numerical examples. These demonstrate the computational efficiency of the reduced model, while maintaining reliable solutions in comparison with original biphasic TPM model in thin domain. }, added-at = {2021-12-08T13:23:29.000+0100}, author = {Armiti-Juber, Alaa and Ricken, Tim}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/29011bdca6bf8365b024eaba43c848946/isd}, doi = {10.1007/s00419-021-01907-3}, file = {848c2012-85ab-49a4-81c6-b2f50fa94646:C\:\\Users\\ac130180\\AppData\\Local\\Swiss Academic Software\\Citavi 6\\ProjectCache\\bkyd3fzxdr3rziq0dosvpq10u8ycyepwckx0sx\\Citavi Attachments\\848c2012-85ab-49a4-81c6-b2f50fa94646.pdf:pdf}, interhash = {3a01daa2ebb5357740c473c64a9dd240}, intrahash = {9011bdca6bf8365b024eaba43c848946}, issn = {1432-0681}, journal = {Archive of Applied Mechanics}, keywords = {FOR5151 SPP1886 exc2075 from:timricken isd myown pn2 theory_of_porous_media}, timestamp = {2023-12-06T22:49:55.000+0100}, title = {Model order reduction for deformable porous materials in thin domains via asymptotic analysis}, year = 2021 }