Reciprocal theorem for the elastic-damage problem of mechanics and its application in the damage distribution estimation from displacement measurements

The reciprocal theorem of mechanical problems for an elastic and brittle damaged medium is formulated under the assumption that the damage evolution may be described by the scalar parameter. Because of the physical non-linearity of problem the theorem is introduced in an incremental version. Next, a way of the damage detection in bar systems from displacement measurements is proposed on the basis of the theorem. Finally, possibilities of the approach presented are illustrated by the computational example and laboratory experiment.