Identification of transient heat sources using the reciprocity gap

The deformation of solid materials is nearly always accompanied with temperature variations, induced by intrinsic dissipation and thermomechanical coupling. Heat sources give precious information on the thermomechanical behaviour of materials. They can be indirectly observed from thermal measurements on the specimen boundary, obtained, e.g., via infrared thermography. To solve the inverse problem of identifying heat sources from such observations, a non-iterative algebraical method based on the reciprocity gap method is proposed. This approach, used elsewhere mainly for time-independent identification, is applied here to transient measurements. Under appropriate modelling assumptions the number of heat sources, their spatial locations and energies are retrieved, as demonstrated on numerical experiments where the robustness of the method to measurement noise is also studied.