Stabilized mixed finite element formulations for materially nonlinear partially saturated two-phase media

By A. Truty, Thomas Zimmermann. 2006

88 citations recorded by the source corpus.

Standard and enhanced (BBAR or EAS) low order finite elements applied to the problem of consolidation of two-phase nonlinear continua do not satisfy the LBB condition when the same interpolation functions are used for both displacement and pore pressure fields. Strong spatial pressure oscillations are the main consequence of the LBB condition violation. The class of direct stabilized methods, widely used in the field of fluid mechanics, is a powerful tool to circumvent violation of the aforementioned condition. Three stabilized formulations, designed for the problem of consolidation of fully or partially saturated media are presented: Galerkin/least-squares (GLS) with the least-squares term construction based on the residuum of the local fluid mass conservation equation; the pressure stabilized formulation (FPL) in which the rate of the pore pressure Laplacian (residual free in the incompressibility limit) is added to the fluid mass conservation equation; and, finally, a stabilized formulation in which the stabilization term is constructed based on the rate of the residuum of the local momentum equation. An h-convergence study and test problems for the three stabilized schemes are discussed.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/228d34d8d3a2d764357d6ed5847351034d1ecd70

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Sequential methods for coupled geomechanics and multiphase flow (2010, methodology): “Stabilization techniques to deal with spurious pressure oscillations have been studied by several authors (Murad and Loula, 1992, 1994; Wan, 2002; Wan et al., 2003; Truty and Zimmermann, 2006; White and Borja, 2008).”
Performance of mixed formulations for the particle finite element method in soil mechanics problems (2016, methodology): “To avoid this problem two strategies are common: either to use more complex, but stable, finite elements [26,38], or to apply stabilization procedures to originally unstable finite elements [21,23,39].”
Stability, Accuracy, and Efficiency of Sequential Methods for Coupled Flow and Geomechanics (2011, background): “Stabilization techniques for such spurious pressure oscillations have been studied by several authors (Murad and Loula, 1992, 1994; Wan, 2002; Truty and Zimmermann, 2006; White and Borja, 2008).”
A stabilized assumed deformation gradient finite element formulation for strongly coupled poromechanical simulations at finite strain (2013, methodology): “First, we point out that the stabilization methods in [17] and [18] can both be derived from the weak inf-sup condition.”