Predicting tensile behavior from nanoindentation using gradient plasticity model with neural network and genetic algorithm

The conventional J₂-flow theory of plasticity fails to account for size-dependent behavior, limiting its ability to describe the mechanical properties of materials at the microscale accurately. In contrast, the strain gradient plasticity theory incorporates strain gradient effect, making it more suitable for capturing the indentation size effect observed in the nanoindentation of materials. This study employs the conventional theory of mechanism-based strain gradient (CMSG) model with a small strain assumption to approximate the indentation problem involving finite deformation. To extract material parameters from nanoindentation experiments, specifically focusing on the CMSG plasticity model, this study introduces an inversion method that integrates a Long Short-Term Memory (LSTM) neural network model with a genetic algorithm. Finite element simulations using the CMSG plasticity model were employed to generate training and validation data for the neural network model, which was then combined with a genetic algorithm for material parameters determination. The method was validated through comparing the simulations with the experimental results from nanoindentation and uniaxial tensile tests on pure copper. The results demonstrate a strong correlation between the experimental data and the simulations, thereby affirming the accuracy of the inversion approach in retrieving strain gradient parameters of the CMSG plasticity model. The study also highlights the critical role of the indentation size effect in microscale material behavior, offering deeper insights into mechanical properties at small scales. Moreover, the results of material parameters of annealed copper films determined by this method further illustrate the universality of the proposed approach.