  An adjoint-based procedure to determine weaknesses, or, more generally the
material properties of structures is developed and tested. Given a series of
force and deformation/strain measurements, the material properties are obtained
by minimizing the weighted differences between the measured and computed
values. Several examples with truss, plain strain and volume elements show the
viability, accuracy and efficiency of the proposed methodology using both
displacement and strain measurements. An important finding was that in order to
obtain reliable, convergent results the gradient of the cost function has to be
smoothed.
