Under some circumstances the displacements calculated by the finite element method are orders of magnitude smaller than they should be, and when this happens, the elements are said to be locking. The two most common types of locking are shear and pressure locking. Locking occurs in lower order elements because an elementes kinematics arenet rich enough to represent the correct solution. Shear locking occurs when elements are subjected to bending, and pressure locking occurs when the material is incompressible. Most of the research on reducing locking is devoted to elements with linear shape functions, with the remainder devoted to quadratic elements.
Locking in linear quadrilateral elements occurs when they are subjected to bending. For simplicity, letês examine the simplest case of a quad in bending.
A deìnitive way to determine whether locking will occur is the Babuska- Brezzi condition, but it is di cult to apply. Constraint counting, however, is an easy-to-apply, rough guide to determining whether an element formulation is likely to lock for incompressible problems.