The framework can be broadly divided into three parts:
1) Generation of the training data
For the Artificial Neural Network (ANN) to be truly predictive the first step is to train the ANN for a variety of conditions. This involves finding a hull that describes the entire space on which the ANN will be operating. The crystal plasticity computation acts as the input training data that can be used in the ANN.
To generate the initial database, crystal plasticity calculations are performed on single crystal simulations for constrained strain paths. The crystal plasticity computations can all be performed on the principal frame of reference and then converted back to the sample frame. The initial database is generated by varying the input parameters i.e. the stretch rate, the angle that defines all possible principal deformation strains, the spin tensor and the orientations.
2) Training the Artificial Neural Network (ANN)
Using this training data the ANN can be trained. The input function to the ANN will be and the output function will be i.e. the slip rate, the rigid body rotation and the deviatoric stress. A back propagation algorithm will be used to train the network. The goal of the back propagation algorithm is to minimize the sum of the squared errors of the training data by updating the weights of each connection through an iterative process.
3) Verification of the predictions obtained from ANN
Once the ANN is fully trained it will be used to verify the predictions of forming operations with experimental results. The results from the ANN can also be used to arrive at a microstructure that leads to the best formability.