A novel deep operator network (DeepONet) with a residual U-Net (ResUNet) as the trunk network is devised to predict full-field highly nonlinear elastic–plastic stress response for complex geometries obtained from topology optimization under variable loads. The proposed DeepONet uses a ResUNet in the trunk to encode complex input geometries, and a fully-connected branch network encodes the parametric loads. Additional information fusion is introduced via an element-wise multiplication of the encoded latent space to improve prediction accuracy further. The performance of the proposed DeepONet was compared to two baseline models, a standalone ResUNet and a DeepONet with fully connected networks as the branch and trunk. The results show that ResUNet and the proposed DeepONet share comparable accuracy; both can predict the stress field and accurately identify stress concentration points. However, the novel DeepONet is more memory efficient and allows greater flexibility with framework architecture modifications. The DeepONet with fully connected networks suffers from high prediction error due to its inability to effectively encode the complex, varying geometry. Once trained, all three networks can predict the full stress distribution orders of magnitude faster than finite element simulations. The proposed network can quickly guide preliminary optimization, designs, sensitivity analysis, uncertainty quantification, and many other nonlinear analyses that require extensive forward evaluations with variable geometries, loads, and other parameters. This work marks the first time a ResUNet is used as the trunk network in the DeepONet architecture and the first time that DeepONet solves problems with complex, varying input geometries under parametric loads and elasto-plastic material behavior.

Original languageEnglish (US)
Article number116277
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Oct 1 2023


  • Deep operator network (DeepONet)
  • Machine/deep learning
  • Parametric geometry
  • Plastic deformation
  • Stress prediction

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications


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