<p>Predicting full-field mechanical responses such as stress and strain distributions in heterogeneous material systems is of fundamental importance to assess materials failure and has a variety of applications in design optimizations, uncertainty quantification, and structural health monitoring. Physics-based simulations such as the finite element method (FEM) provide high-fidelity predictions but can be computationally expensive and challenging in scenarios of real-time interactive design evaluations and decision-making. On the other hand, data-driven approaches encoded with physical constraints have the promise to rapidly predicting reliable results to meet real-time application requirements. In this study, different data-driven methods based on deep learning frameworks or model order reduction techniques are applied and evaluated in predicting the high-dimensional stress field responses of heterogeneous media.</p><p>The first framework employs a combination of model order reduction and artificial neural networks (ANN). The stress fields are first projected to a low-dimensional representation using a model order reduction technique of proper orthogonal decomposition (POD). POD is a posteriori method based on the snapshot matrix of field results. After that, ANN is used to predict full-field responses based on POD reduced modes. The second framework is based on a deep Resnet-based Convolutional Neural Network (CNN), while the third framework is based on a conditional Generative Adversarial Network (GAN) (cGAN). Two numerical examples were analyzed to evaluate the above frameworks. The first is a panel containing a variety of heterogeneous material inclusions that vary in terms of position and size. The reconstructed POD fields using ANN provide accurate predictions overall but more deviations appear when the inclusion is small or close to the boundary. On the other hand, CNN and cGAN approaches give more accurate and robust predictions. In the second example, a plate with holes of varying positions and sizes is considered. Both CNN and cGAN models accurately captured stress concentrations as well as the full stress fields, while cGAN gives more accurate predictions in test validations of unseen datasets. Finally, the proper generalized decomposition (PGD) method is utilized to derive the full-field response as a function of both spatial and extra-coordinates of material variations. PGD builds on a priori separated representation of the objective field to counter the curse of dimensionality. In the PGD framework, kernel principal component analysis (kPCA) was used to solve the nonlinear parametric problems with extra-coordinates of material variations. Reduced modes in the PGD separated expression were then used to reconstruct the field solutions. The above data-driven frameworks show remarkable potentials in predicting full-field responses for a variety of heterogeneous materials.</p>

Data-Driven Methods to Predict Full-Field Responses in Heterogeneous Materials

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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