Measuring stress field without constitutive equation

The present paper proposes a coupled experimental-numerical protocol to measure heterogeneous stress fields in a model-free framework. This work contributes to developing the emerging realm of mechanics without constitutive equation. In fact, until now these types of simulations have been missing database of real and rich material behaviour. The technique consists in coupling Digital Image Correlation (DIC) measurements and the Data Driven Identification (DDI) algorithm, recently developed by Leygue et al. (Data–based derivation of material response. Computer Methods in Applied Mechanics and Engineering, 331, 184–196 (2018)). This algorithm identifies the mechanical response of a material, i.e. stress–strain data, without postulating any constitutive equation, but with the help of a large database of displacement fields and loading conditions. The only governing equation used in this algorithm is the mechanical equilibrium. The bias induced by the choice and the calibration of a constitutive model is thus removed. In the above-mentioned paper, the relevance of the method has been demonstrated with synthetic data issued from finite element computations. Here, its efficiency is assessed with "real" experimental data. A multi-perforated elastomer membrane is uniaxially stretched in large strain. Practical challenges are addressed when using the DDI algorithm, especially those due to unmeasured data during experiments. Easy-to-implement solutions are proposed and the DDI technique is successfully applied: heterogeneous stress fields are computed from real data. Considering that the material is elastic, its strain energy density is then measured. Good agreement with standard uniaxial tensile experimental results validates the approach on real data.