Incorporating uncertainty in stress‐strain data acquisition: extended model‐free data‐driven identification

Abstract

Based on the increasing ability to collect and store large amounts of data and information, data‐driven methods have recently gained importance in the context of computational mechanics. Compared to the traditional approach of defining a suitable constitutive model and fit the parameters to experimental data, these methods aim to capture complex material behavior without the assumption of a certain material formulation. Distinguished are model‐based data‐driven methods, leading to an approximation of the constitutive material description for example, by neural networks, and model‐free data‐driven methods. The approach of data‐driven computational mechanics (DDCM), introduced by Kirchdoerfer and Ortiz (2016), enables to circumvent any material modeling step by directly incorporating material data into the structural analysis. A basic prerequisite for both types of data‐driven methods is a large amount of data representing the material behavior, in solid mechanics consisting of stresses and strains. Obtaining these databases numerically by multiscale approaches is computationally expensive and requires the definition of lower scale models. In case of an experimental characterization, constitutive descriptions are generally required to compute the stress states corresponding to displacement fields, for example, identified by full‐field measurement techniques, such as digital image correlation (DIC). The method of data‐driven identification (DDI), introduced in Leygue et al. (2018) based on the principles of DDCM, enables the determination of detailed information about the constitutive behavior based on displacement fields and applied boundary conditions without a specific material model. Stresses corresponding to given strains are identified by iteratively clustering and enforcing equilibrium. The algorithm has shown to be applicable to synthetic as well as real data taking linear and non‐linear material behavior into account. Generalized polymorphic uncertainty models, resulting as a combination of aleatoric and epistemic uncertainty models, are utilized to take variability, imprecision, inaccuracy and incompleteness of data into account. The consideration of uncertain material properties by data‐driven simulation approaches leads to the requirement of data sets representing uncertain material behavior. In this contribution, different sources of uncertainty occurring within DDI of stress‐strain relations are addressed and an efficient method for the identification of data sets representing uncertain material behavior based on the concept of DDI is proposed. In order to demonstrate the developed methods, numerical examples are carried out.