Mixed isogeometric analysis of strongly coupled diffusion in porous materials. (4th January 2018)

• Record Type: Journal Article
• Authors: Dortdivanlioglu, B.; Krischok, A.; Beirão da Veiga, L.; Linder, C.
• Is Part Of: International journal for numerical methods in engineering. Volume 114:Number 1(2018)
• Page Start: 28
• Page End: 46
• Publication Date: 2018-01-04
• Subjects: coupled diffusion -- inf‐sup condition -- isogeometric analysis -- NURBS -- porous materials -- subdivision technique; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5731
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: 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.