Implementation of a Neural Network into a User-Material Subroutine for Finite Element Simulation of Material Viscoplasticity

In this study, a neural network is trained to predict the response of a viscoplastic solder alloy based on a reduced data set. The model is shown to accurately describe the behavior of the material for the temperature range from 298 °K to 398 °K and the strain rate range from 2 × 10⁻⁵ s⁻¹ to 2 × 10⁻² s⁻¹. The model is then implemented in the form of a user subroutine in the finite element code Abaqus to be used for simulations of the material behavior. The implementation requires that the weights and biases of the network are extracted and that its gradients (derivatives of the output with respect to the inputs) are calculated to be passed on to the user subroutine. Finite element (FE) simulations based on the implemented neural network are compared with those based on the physical viscoplastic model of Anand, showing an overall good agreement between both approaches. However, some limitations concerning the neural network ability to predict the transient effects during a strain rate jump or a temperature change are identified and discussed.