A generic physics-informed neural network-based constitutive model for soft biological tissues

Minliang Liu, Liang Liang, Wei Sun

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


Constitutive modeling is a cornerstone for stress analysis of mechanical behaviors of biological soft tissues. Recently, it has been shown that machine learning (ML) techniques, trained by supervised learning, are powerful in building a direct linkage between input and output, which can be the strain and stress relation in constitutive modeling. In this study, we developed a novel generic physics-informed neural network material (NNMat) model which employs a hierarchical learning strategy by following the steps: (1) establishing constitutive laws to describe general characteristic behaviors of a class of materials; (2) determining constitutive parameters for an individual subject. A novel neural network structure was proposed which has two sets of parameters: (1) a class parameter set for characterizing the general elastic properties; and (2) a subject parameter set (three parameters) for describing individual material response. The trained NNMat model may be directly adopted for a different subject without re-training the class parameters, and only the subject parameters are considered as constitutive parameters. Skip connections are utilized in the neural network to facilitate hierarchical learning. A convexity constraint was imposed to the NNMat model to ensure that the constitutive model is physically relevant. The NNMat model was trained, cross-validated and tested using biaxial testing data of 63 ascending thoracic aortic aneurysm tissue samples, which was compared to expert-constructed models (Holzapfel-Gasser-Ogden, Gasser–Ogden–Holzapfel, and four-fiber families) using the same fitting and testing procedure. Our results demonstrated that the NNMat model has a significantly better performance in both fitting (R2 value of 0.9632 vs 0.9019, p=0.0053) and testing (R2 value of 0.9471 vs 0.8556, p=0.0203) than the Holzapfel–Gasser–Ogden model. The proposed NNMat model provides a convenient and general methodology for constitutive modeling.

Original languageEnglish (US)
Article number113402
JournalComputer Methods in Applied Mechanics and Engineering
StatePublished - Dec 1 2020


  • Constitutive modeling
  • Hyperelastic material
  • Machine learning
  • Neural network

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)
  • Computer Science Applications


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