Intrinsic methods in elasticity: a mathematical survey

In the classical approach to elasticity problems, the components of the displacement field are the primary unknowns. In an "intrinsic" approach, new unknowns with more physical or geometrical meanings, such as a strain tensor field or a rotation field for instance, are instead taken as the primary unknowns. We survey here recent progress about the mathematical analysis of such methods applied to linear and nonlinear three-dimensional elasticity and shell problems.