A strategy for identifying the shape and the parameters of elastoplastic laws in heterogeneous material is proposed here. It allows the local characterization of both mechanical properties and stress fields. This method relies on the constitutive equation gap principles and on the measurement of overall loads and strain fields. These fields are obtained by the numerical differentiation of displacement fields measured by Digital Image Correlation. The identification method is based on the iterative minimization of an energy norm involving the secant elastoplastic tensor. We propose here to characterize the robustness of the method and its stability (to noise, initial parameters and mesh) on numerical data sets obtained on numerically-deformed images. Finally, we illustrate the ability of the method to identify the local material properties of a heterogeneous material on real experimental data.