PSI - Issue 71

A Shivnag Sharma et al. / Procedia Structural Integrity 71 (2025) 469–476

472

vector, the Von-Mises stress, plastic strain (PEEQ) etc. are by default saved in ABAQUS. A python script was developed to write the variables in text format for each increment, thus rendering 1000 text files for every variable which was then used for training and testing. 2.3. ConvLSTM The ConvLSTM model extends traditional LSTM networks by incorporating convolutional structures, which allows it to capture spatial and temporal dependencies in sequential data. In ConvLSTM, the cell state and hidden state are tensors rather than vectors, and convolutions are used to process these tensors. The key equations for the ConvLSTM update are

1 2 3

Table 1. Properties used in CP model.

100.17 GPa 47.14 GPa 26.515GPa 0.001 −1 0.02

Reference slip rate, γ 0α̇ Strain rate sensitivity, Initial hardening rate, ℎ 0 Ratio self/latent hardening, Initial slip resistance, 0α

180 MPa

1.4

16 MPa

=σ( ∗ + ℎ ∗ℎ −1 + ∘ −1 + ) =σ( ∗ + ℎ ∗ℎ −1 + ∘ −1 + ) ̃ = tanh( ∗ + ℎ ∗ℎ −1 + ) = ∘ −1 + ∘ ̃ =σ( ∗ + ℎ ∗ℎ −1 + ∘ + ) ℎ = ∘ tanh( )

(8) (9)

(10) (11) (12)

(13) where * denotes the convolution operation, σ is the sigmoid function, and ͦ denotes element-wise multiplication. The components W xi , W hi , W ci ,W xf , W hf , W cf, W xc , W hc ,W xo , W ho , and W co represent weights for respective variables while b i , b f , b c , and b o are the biases for each gate. This architecture is particularly effective for tasks involving spatio-temporal sequences, such as video prediction and weather forecasting. ConvLSTM forecasts the future state of a grid cell by leveraging both the current inputs and the historical states of its neighbouring cells. Implementing this is straightforward due to the use of convolution operators for state-to-state and input-to-state transitions. Padding is necessary before performing the convolution operation to ensure that the output states match the dimensions of the inputs. Padding can be thought of as setting the boundary conditions for hidden states at the edges. Typically, LSTM states are initialized to zero before processing the first input to avoid future dependency. If zero padding is used for hidden states, it assumes that the external environment is not considered, effectively setting its state to zero. The same assumption of zero padding was made to the dataset from CPFEM while training and testing using ConvLSTM. 3. Results and discussion Plane strain CPFEM simulation was performed at constant time increment of 0.001 secs, as was mentioned earlier. The total time for the simulation was set to 1, making the total number of increments to 1000 with a constant time step. The full-field evolution of CP variables- slip system resistances g α , components of displacement (u and v) vector,