Physics-informed neural networks for spherical indentation problems

A scientific deep learning (SciDL) approach was developed by integrating a regression-based spherical indentation method with an artificial neural network (ANN) to extract elastic–plastic properties from indentation load-depth curves. Different combinations of material parameters are constructed through Latin Hypercube Sampling (LHS) process to create a database of indentation parameters. An attempt is made to reversely obtain load-depth (P-h) data using a regression function for a given set of material parameters; this method is further verified by performing finite element (FE) simulations. SciDL models i.e., physics-informed artificial neural network (PI-ANN) with autoencoder (AE) are built based on PyTorch library, and the models are trained using the generated database. Transfer learning (TL) techniques are employed to achieve better training performance with the PI-ANN model. Compared with data-driven models, SciDL models produce consistent predictions with higher accuracy; the coefficient of determination R2 values are observed greater than 0.960. TL techniques allows the SciDL model to learn much faster (≈ 42 epochs) than traditional method (≈ 2400 epochs). Finally, we perform spherical indentation experiments on STS304 and SM45C, and validate the performance of the trained SciDL models; AE integrated PI-ANN model with tanh activation function predicts the material properties close to reference values of SS400 and SM45C. The proposed SciDL approach can be extended for characterizing engineering materials and structures by incorporating any priorly developed mechanical testing method with ANN.