Abstract
Catastrophic failure in brittle materials is often due to the rapid growth and coalescence of cracks aided by high internal stresses. Hence, accurate prediction of maximum internal stress is critical to predicting time to failure and improving the fracture resistance and reliability of materials. Existing high-fidelity methods, such as the Finite-Discrete Element Model (FDEM), are limited by their high computational cost. Therefore, to reduce computational cost while preserving accuracy, a deep learning model, StressNet, is proposed to predict the entire sequence of maximum internal stress based on fracture propagation and the initial stress data. More specifically, the Temporal Independent Convolutional Neural Network (TI-CNN) is designed to capture the spatial features of fractures like fracture path and spall regions, and the Bidirectional Long Short-term Memory (Bi-LSTM) Network is adapted to capture the temporal features. By fusing these features, the evolution in time of the maximum internal stress can be accurately predicted. Moreover, an adaptive loss function is designed by dynamically integrating the Mean Squared Error (MSE) and the Mean Absolute Percentage Error (MAPE), to reflect the fluctuations in maximum internal stress. After training, the proposed model is able to compute accurate multi-step predictions of maximum internal stress in approximately 20 seconds, as compared to the FDEM run time of 4 h, with an average MAPE of 2% relative to test data.
Highlights
Brittle materials, such as glass, ceramics, concrete, some metals, and composite materials, are widely used in many applications that involve complex dynamics, impulse, or shock loadings
The results show that StressNet significantly outperforms these time series models even though the Long Short-term Memory (LSTM) and Bidirectional LSTM (Bi-LSTM) took advantage of using more initial data for model training
Among all the variants of the loss function, the results show that the fused loss function achieves the best performance, with an error of 2%
Summary
Brittle materials, such as glass, ceramics, concrete, some metals, and composite materials, are widely used in many applications that involve complex dynamics, impulse, or shock loadings. Nie et al.[14] used Encoder-Decoder Structure based on Convolutional Neural Network (CNN) to generate the stress field in cantilevered structures These methods do not consider temporal dynamics of the stress field or fracture within the material. This work proposes a deep learning model, StressNet, to predict the maximum internal stress in the fracture propagation process. Instead of deterministically calculating the entire stress field at each time step as HOSS does, StressNet focuses on predicting only the maximum internal stress, which is the key factor influencing material failure. Spatial features of fractures, which are extracted by a Temporal Independent Convolutional Neural Network (TICNN), are incorporated to help with the multi-step prediction of the maximum internal stress. StressNet uses the Bi-directional LSTM (Bi-LSTM)[29] to capture the temporal features of fracture propagation and historical maximum internal stress. Inspired by physic knowledge and existing works in other domains, the StressNet is designed to incorporate features from fracture propagation into prediction and fuse spatial and temporal features from multiple data formats
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