Non‐parametric stress field estimation for history‐dependent materials: Application to ductile material exhibiting Piobert–Lüders localization bands

Estimating stress in statically undetermined tests remains an issue in experimental mechanics. Most estimation methods rely on the a priori choice of a behaviour equation leading to an unavoidable model bias. Recently, efforts have been made to propose methods circumventing the parametric description of constitutive behaviours. In particular, Leygue et al. (2018) proposed a new paradigm called data‐driven identification (DDI). An extension of Leygue's method to history‐dependent materials is proposed in this paper. The formulation of the problem and its resolution are presented with emphasis on boundary conditions. The method is tested on real experimental data where the elasto‐plastic material is subjected to the formation of Piobert–Lüders bands. We finally show that the DDI allows to obtain balanced fields that are closer (more consistent) to the field measurements than the fields obtained by parametric identification strategies, even more in the presence of strain localization bands whose kinematics are usually not described by a standard constitutive model.