| This dissertation addresses the problem of evaluating plastic damages by using the residual surface displacement data. The plastic damages are caused by a series of unknown loadings and accumulated in an unknown sub-domain of the material.;An important application is found in composite materials, where damages are primarily accumulated along the interface between the fiber and matrix. All the characteristic quantities along the interface, such as displacement jumps and tractions, are uniquely determined by the residual surface displacements. It follows that the traction free parts of the interface correspond to cracks, the normal displacement jumps indicate debonding, and the tangential displacement jumps measure the interfacial sliding.;The problem addressed in the dissertation is an inverse problem of continuum mechanics, which is different substantially from the conventional forward analyses. Satisfactory numerical results can be obtained only if a suitable algorithm is employed. The nature of the ill-posed problem is discussed and a very powerful method is presented to convert an ill-posed problem into a well-posed one.;The surface displacements serve as sensors for the damages inside the materials. The inversion of the characteristic damage quantities requires no knowledge of the loading history. Coordinating with appropriate damage models, we can determine the mechanical effects of the material deterioration, and elucidate the process leading to the final failure.;The general problem of the damage evaluation from the residual surface displacement data is an ill-posed nonlinear problem. The residual surface displacements are not sufficient to recover the shape of the damage domain and the exact distribution of the residual plastic strains. However, some important characteristic quantities associated with the damages of the material can be obtained. These quantities include stresses in the vicinity of the damage domain, lower bounds of the strain energy and any quadratic functions of the plastic strains. Furthermore, some specific problems, which involve restrictive assumptions on the nature of damages or on the amount of information to be recovered, may lead to well-posed problems. |
