Instrumented indentation is widely utilized as one of the most versatile and practical means of extracting mechanical properties of materials, especially when it is difficult to obtain elastic-plastic properties from testing coupon specimens. Despite significant efforts made in the past two decades, a robust method is still missing that can extract accurately the full stress-strain behavior from indentation test data.
Applying and extending the latest multi-fidelity methodology for training neural networks (NNs), deep-learning algorithms are trained to extract elastoplastic properties of metals and alloys from instrumented indentation results, using simulation and experimental datasets with different levels of fidelity/accuracy. These NNs are trained for solving inverse problems, covering the entire parameters space of engineering metals, by recourse to single, dual and multiple indentation and are shown to significantly outperform traditional function-fitting methods based on brute-force computations. The predictive capabilities and advantages of these multi-fidelity methods have been validated for different commercial alloys, including six 3D-printed titanium alloys. 
Moreover, we demonstrate several multi-fidelity approaches specifically for solving the inverse indentation problem which i) significantly reduce the number of costly high-fidelity datasets required to achieve a given level of accuracy, ii) utilize known physical and scaling laws to improve the learning efficiency and accuracy, and iii) integrate seamlessly simulation and experimental data for training with disparate datasets to learn and minimize systematic errors. These multi-fidelity deep-learning approaches are expected to be useful for solving other challenging inverse problems in science and engineering.

Multi-fidelity deep learning for extracting mechanical properties from instrumented indentation

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