Extraction of hyper-elastic material parameters using BLSTM neural network from instrumented indentation

Instrumented indentation is a versatile method of extracting hyper-elastic material parameters, particularly useful for applications where stress-strain data are difficult to be in-situ measured. Because the analytical force-displacement relation is still unavailable for the indentation of hyper-elastic materials, identifying hyper-elastic parameters often requires an iterative optimization strategy that fits finite element simulations with experimental data. However, the optimization strategy is burdened by heavy computation and its prediction accuracy is greatly influenced by the choice of optimization algorithm. To address these challenges in this study, a bidirectional long short-term memory (BLSTM) neural network is presented that directly predicts hyper-elastic material parameters from indentation load-displacement data, focusing on Mooney-Rivlin hyper-elasticity as an example. To improve the predication accuracy, the condition numbers for the inverse identification of the hyper-elastic parameters are investigated. And, a normalization procedure is proposed to treat the input data, which can guarantee the BLSTM network is well-conditioned. During evaluation, the trained BLSTM network significantly outperforms the iterative optimization strategy using a genetic algorithm. Furthermore, the effect of the normalization procedure is demonstrated.