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| ife-ps [2024/09/12 15:43] – paulo | ife-ps [2024/09/12 20:15] (current) – paulo |
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| In this project, we propose a new decomposition formulation for the dynamic analysis of poroelastic problems called //**y**//<sup>s</sup>//**v**//<sup>f</sup>//p//<sup>f</sup> considering geometric nonlinearity and allowing large displacements, where the superindex denotes the respective phase {//f,s//}. These guarantees full modularity of the calculation code and is particularly suitable when displacements are large. In developing this formulation, several assumptions are made to reduce the complexity of the poroelastic problem. A poroelastic solid is considered saturated with fluid, and both the liquid and solid phases are considered materially incompressible within the particle, ignoring the effects of thermal and chemical reactions. Furthermore, porosity is assumed to remain constant during the deformation process, and although large displacements are well represented, the scope is limited to small deformation problems (see e.g [1]). | In this project, we propose a new decomposition formulation for the dynamic analysis of poroelastic problems called //**y**//<sup>s</sup>//**v**//<sup>f</sup>//p//<sup>f</sup> considering geometric nonlinearity and allowing large displacements, where the superindex denotes the respective phase {//f,s//}. These guarantees full modularity of the calculation code and is particularly suitable when displacements are large. In developing this formulation, several assumptions are made to reduce the complexity of the poroelastic problem. A poroelastic solid is considered saturated with fluid, and both the liquid and solid phases are considered materially incompressible within the particle, ignoring the effects of thermal and chemical reactions. Furthermore, porosity is assumed to remain constant during the deformation process, and although large displacements are well represented, the scope is limited to small deformation problems (see e.g [1]). |
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| The solution process for the porous solid phase is based on the positional Finite Element Method (FEM) in Lagrangian description with the Neo-Hookean constitutive model, while for the interstitial incompressible fluid flow the Pressure-Stabilized/Petrov–Galerkin method is used (PSPG) [2] using the ALE description. The generalized alpha method was used for temporal integration for both phases. | The solution process for the porous solid phase is based on the positional Finite Element Method (FEM) in Lagrangian description with the Neo-Hookean constitutive model, while for the interstitial incompressible fluid flow the Pressure-Stabilized/Petrov–Galerkin method is used (PSPG) [2] using the Arbitrary Lagrangian-Eulerian (ALE) description. The generalized alpha method was used for temporal integration for both phases. |
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| In summary, the strong coupling between the two problems occurs through the transfer of forces between the phases, in which the fluid in the following partitioned scheme transfers pressure (//p//<sup>f </sup>) and the resistance force generated due to the microscale effect, also called the Darcy force (//**f**//<sup> f </sup>), which can be seen in Figure.1. | In summary, the strong coupling between the two problems occurs through the transfer of forces between the phases, in which the fluid in the following partitioned scheme transfers pressure (//p//<sup>f </sup>) and the resistance force generated due to the microscale effect, also called the Darcy force (//**f**//<sup> f </sup>), which can be seen in Figure.1. |
