Speaker
Description
The Data-Driven Identification (DDI) method introduced by Leygue et al. (2018) aims to estimate the mechanical response of materials without relying on a predefined constitutive model. The main output of DDI is the stress field identified from full-field kinematic measurements and load cell measurements, with the intuition that similar strain values should yield similar stress values. It depends on the availability of heterogeneous and rich data, which are clustered to build a strain-stress database. Given the displacement and strain fields, DDI solves an inverse problem by minimizing the distance between the current mechanical state and its nearest representative in a material database, while ensuring equilibrium is satisfied.
DDI has been tested and applied to both synthetic and real data, including studies on: elasticity, hyperelasticity, viscoelasticity, elastoplasticity, and large deformation behaviors. Despite these successful applications, a comprehensive analysis of the method to confirm that DDI can accurately estimate and converge to the true mechanical stress is still missing. In addition, this method relies on algorithmic parameters that are often chosen empirically.
In this work, we investigate numerically and algorithmically the preliminary work of Leygue (2024), where a criterion for the uniqueness of the solution was introduced. We first illustrate the well-posedness of the DDI minimization problem when this criterion is verified, and then propose three methods for numerically characterizing the criterion. Additionally, we will analyze these methods and compare their computational costs. This study will help us in the selection of the parameters for DDI. As the DDI parameters are pushed to gain accuracy, the DDI becomes ill-posed. However, it is possible to detect and correct the stress estimate in this case. This can be done through additional non-invasive regularization or through the detection of the few degrees of liberty responsible for the loss of uniqueness.
