Non-parametric material state field extraction from full field measurements

Data-driven computations propose a completely new paradigm to the computational mechanics research community and to experimentalists. Classically, admissible material states can only be obtained experimentally for homogeneous stress/strain configurations or using a parametric optimization of material laws based on heterogeneous tests. Data-driven algorithms aim at circumventing these limitations. However, data-driven algorithms require a large database of admissible material states, otherwise extrapolation is required and some limitations of the classical constitutive equation based approach remain. In this paper, an inverse data-driven approach based on full field measurements is presented. The main idea is to extract, with no assumption on the constitutive equations, rich (i.e. heterogeneous and multiaxial) material state fields from displacement fields and external load measurements. The capability of the proposed method to extract databases of admissible material states and to evaluate stress fields without parametric constitutive equations is illustrated through three examples dedicated to non-linear elasticity, plasticity and dynamics.