A machine learning perspective on the inverse indentation problem: uniqueness, surrogate modeling, and learning elasto-plastic properties from pile-up

The inverse analysis of indentation curves, aimed at extracting the stress-strain curve of a material, has been under intense development for decades, with progress relying mainly on the use of analytical expressions derived from small data sets. Here, we take a fresh, data-driven perspective to this classic problem, leveraging machine learning techniques to advance indentation technology. Using a neural network (NN), we efficiently assess uniqueness and identify materials that have indistinguishable indentation responses without the need for complex, domain knowledge-based algorithms. We then demonstrate that inclusion of the residual imprint information resolves the non-uniqueness problem. We show that the elasto-plastic properties of a material can be learned directly from indentation pile-up. Notably, an accurate stress-strain curve can be derived using solely the applied indentation load and pile-up information, thereby eliminating the need for depth-sensing. We also present a systematic analysis of the machine learning model, covering important aspects such as prediction performance, sensitivity, feature selection, and permutation importance, providing insight for model development and evaluation. This study introduces and provides the groundwork of a machine-learning-based profilometry-informed indentation inversion (PI3) technique. It showcases the potential of machine learning as a transformative alternative when analytical solutions are difficult or impossible to obtain.