Locking effects in the finite element approximation of elasticity problems

The P and H-P Versions of the Finite Element Method: Basic Principles and Properties

“…As v -* 0.5, we see that the incompressibility constraint, certain general conditions (see [BS4]) which are shown in [BS5] to be satisfied for our model problem. This reduces the whole question of locking to one of approximability alone.…”

“…and let the exact As shown in [BS5], HB correspond to precisely the correct weighted spaces k,v that characterize the regularity of the solution when the data is appropriately bounded.…”

On volumetric locking‐free behaviour of p‐version finite elements under finite deformations

“…The p-version of the finite element method ( p-FEM) based on the displacement formulation is known to be locking free beyond a moderate polynomial order for nearly incompressible problems in linear elasticity (see [1][2][3] and references therein). Recently, p-FEMs have been shown to be efficient for finite-deformation problems [4,5], and we demonstrate herein that of compressibility and isotropy.…”

A Locking-Free MHM Method for Elasticity

“…It is well-known that the most common (and used) low order finite element methods show poor performance in such a case, a phenomena called locking (c.f. [2]). A way to overcome such a numerical drawback consists of introducing the scalar "pressure" field and rewriting the second-order isotropic elasticity model (1) in the following equivalent form:…”

“…It is well known that standard low order finite element schemes suffer from the "locking" phenomena when they are applied to nearly incompressible material problems (Poisson ratio close to 1/2) [2]. One way to circumvent this difficulty is to rewrite the elasticity model in its mixed counterpart making resorting the stress tensor as an independent variable.…”