In this paper, we develop a mixed isogeometric analysis approach based on subdivision stabilization to study strongly coupled diffusion in solids in both small and large deformation ranges. Coupling the fluid pressure and the solid deformation, the mixed formulation suffers from numerical instabilities in the incompressible and the nearly incompressible limit due to the violation of the inf-sup condition. We investigate this issue using subdivision-stabilized nonuniform rational B-spline (NURBS) elements, as well as different families of mixed isogeometric analysis techniques, and assess their stability through a numerical inf-sup test. Furthermore, the validity of the inf-sup stability test in poromechanics is supported by a mathematical proof concerning the corresponding stability estimate. Finally, two numerical examples involving a rigid strip foundation on saturated soil and a swelling hydrogel structure are presented to validate the stability and to demonstrate the robustness of the proposed approach.
Dortdivanlioglu, B., Krischok, A., Beirão da veiga, L., Linder, C. (2018). Mixed isogeometric analysis of strongly coupled diffusion in porous materials. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 114(1), 28-46 [10.1002/nme.5731].
Mixed isogeometric analysis of strongly coupled diffusion in porous materials
Beirão da Veiga, L.;
2018
Abstract
In this paper, we develop a mixed isogeometric analysis approach based on subdivision stabilization to study strongly coupled diffusion in solids in both small and large deformation ranges. Coupling the fluid pressure and the solid deformation, the mixed formulation suffers from numerical instabilities in the incompressible and the nearly incompressible limit due to the violation of the inf-sup condition. We investigate this issue using subdivision-stabilized nonuniform rational B-spline (NURBS) elements, as well as different families of mixed isogeometric analysis techniques, and assess their stability through a numerical inf-sup test. Furthermore, the validity of the inf-sup stability test in poromechanics is supported by a mathematical proof concerning the corresponding stability estimate. Finally, two numerical examples involving a rigid strip foundation on saturated soil and a swelling hydrogel structure are presented to validate the stability and to demonstrate the robustness of the proposed approach.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.