Recent developments in imaging techniques now facilitate local field measurements (e.g. strain, temperature, etc.). In this study, we identify the spatial distribution of material properties and local stress fields using an inverse identification method based on the constitutive equation gap (CEG). The CEG concept is based both on minimization of a cost function equal to the sum of the potential and complementary energies, and on the deviation between the measured and computed strain fields. We propose a new approach for identifying heterogeneous property fields (mechanical parameters and stress) using a secant elastoplastic tensor and a measured strain field obtained by full-field measurement. The reliability of the method is checked using finite element simulation data as reference full-field measurements. The method is then applied on noisy displacement fields to assess its robustness. Finally, the developed inverse method is tested on real measured data.