Fractional calculus & machine learning methods based rubber stress-strain relationship prediction

Molecular dynamics simulation can be used to simulate the rubber stretching process and calculate the tensile strength of elastomer materials. However, molecular dynamics simulation process with low stretching rate that is comparable with the experimental case is time-consuming. A fractional long short-term memory (F-LSTM) neural network prediction model is proposed to obtain the tensile stress values under experimental strain rate in a short time and experiments show that the model can extrapolate the results of MD simulations well. Both long short-term memory (LSTM) neural network and fractional calculus have certain memory characteristics suitable for describing the stretching process of rubber. First, fractional calculus transformation is performed on four different tensile strain data sets corresponding to four different strain rates. Then, an LSTM network is established based on the transformed stress–strain data. Experiment results show that the introduction of fractional calculus improves the prediction accuracy of the LSTM model. The established F-LSTM model is further applied to the prediction of the stress value under the experimental strain rate of 1 × 10⁶ s⁻¹.