Elasto-plasticity with convex model-data-driven yield functions
Résumé
The formulation of history-dependent material laws has been a significant challenge in solid mechanics for over a century. Recently, data-driven techniques have generated accurate and reliable surrogates for elasto-plastic constitutive laws. However, most of these methods are deeply rooted in the big data domain and fail when only a few physically obtained experimental data points are available. To combat this, we propose a plasticity formulation with model-data-driven yield functions that is designed to work in the small data regime. This is done by locally improving a phenomenological yield function (model component) with a data-driven correction term (data component) which only utilizes uniaxial and biaxial experimental data describing the shape of the initial yield surface. This allows seamless merging of conventional material models with their data-driven counterparts enabling the derivation of hybrid models that significantly improve the accuracy and robustness of traditional approaches. In order to obtain convex yield functions in this framework, it is sufficient for the data-driven correction to be convex. Strategies based on convex extensions to Support Vector Regression (SVR), Gaussian Process Regression (GPR), and Neural Networks (NN) are analysed. The proposed approach is tested on synthetic data of anisotropic yield functions commonly used for rolled metal sheets.
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