  We consider solutions to the Lam\'e system in two dimensions. By using
systematic way, based on layer potential techniques and the field expansion
(FE) method (formal derivation), we establish a rigorous asymptotic expansion
for the perturbations of the displacement field caused by small perturbations
of the shape of an elastic inclusion with C2-boundary. We extend these
techniques to determine a relationship between traction-displacement
measurements and the shape of the object and derive an asymptotic expansion for
the perturbation in the elastic moments tensors (EMTs) due to the presence of
small changes in the interface of the inclusion.
