Overcoming the problem of locking in linear elasticity and poroelasticity: an heuristic approach

By P. Phillips, Mary F. Wheeler. 2009

170 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/8564c7a4d4e3704ca7ef7ecfbdb7bace938e7cfb

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Citations in the corpus

Convergence analysis of a new mixed finite element method for Biot's consolidation model (2014, background): “Cantilever Bracket Problem Phillips and Wheeler [9] heuristically examined the reasons for locking in poroelasticity and postulated that the solution to the problem of locking is to use a space for displacement that contains nonconstant divergence-free vectors.”
Stability and monotonicity for some discretizations of the Biot’s consolidation model (2015, unknown): “It is well-known that approximations by standard finite difference and finite element methods of the poroelasticity equations often exhibit strong nonphysical oscillations in the fluid pressure, see for instance [20, 21, 22, 23, 24].”
On the causes of pressure oscillations in low‐permeable and low‐compressible porous media (2012, background): “It is well known that spurious fluid pressure oscillations may occur in low‐permeable regions in finite element calculations of the poroelastic equations [10, 13, 14].”
A nonlinear, transient finite element method for coupled solvent diffusion and large deformation of hydrogels (2015, methodology): “This issue may be resolved by pressure stabilization schemes or use of discontinuous approximations (for chemical potential) as proposed by others for similar problems in poroelasticity (Hughes et al., 1986; Wan, 2002; Phillips, 2005; Phillips and Wheeler, 2009).”
Analysis of a multiphysics finite element method for a poroelasticity model (2018, methodology): “…by Adam Ellsworth, Adam Ellsworth on 27 January 2018 We remark that the ‘locking phenomenon’ was observed in the simulation of Phillips & Wheeler (2009) at T = 0.001 for this problem, namely, the computed pressure exhibits some oscillation at T = 0.001.”
A coupling of nonconforming and mixed finite element methods for Biot's consolidation model (2013, background): “Phillips and Wheeler [18–20] developed and analyzed methods that couple continuous and discontinuous Galerkin (DG) methods for the displacement with a mixed finite element method for the flow variables, and Tchonkova et al. [21] developed a mixed finite element method which seeks a solution via mini”
A coupling of mixed and discontinuous Galerkin finite-element methods for poroelasticity (2008, methodology): “Some success has been shown for particular examples in Phillips [16 ]a nd Phillips and Wheeler [ 19 ].”