Acquiring the constitutive relationship for a thermal viscoplastic material using an artificial neural network

In conventional constitutive theories, a kind of mathematical model is formulated to represent the plastic behavior of a material. Once the model is set, the behavior of the material can only be expressed approximately by adjusting the parameters in the model. Under conditions of high strain rate and high temperature, to secure more accurate results the model has to be more complicated in mathematical formulation, but then problems related to material parameter identification, numerical stability, etc., arise. An artificial neural network may simulate a biological nervous system and is referred to as parallel distributed processing. It cannot only make decisions based on incomplete and disorderly information, but can also generalize rules from those cases on which it was trained and apply these rules to new stimuli. In back-propagation neural networks, the information contained in the input is recoded into an internal representation by hidden units that perform the mapping from input to output. It has been proven mathematically that a three-layer network can map any function to any required accuracy. A neural network can directly map the behavior for a thermal viscoplastic material. Using a neural network, it is not necessary to postulate a mathematical model and identify its parameters. In this paper, a four-layer back-propagation neural network is built to acquire the constitutive relationship of 12Cr2Ni4A. Temperature, effective strain, and effective strain rate are used as the input vectors of the neural network, the output of the neural network being the flow stress. After the network has been trained with experimental data, it can correctly reproduce the flow stress in the sampled data. Furthermore, when the network is presented with non-sampled data, it also can predict well. The results acquired from the neural network are very encouraging.