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

• Published in: Computer methods in applied mechanics and engineering Vol. 372; p. 113402
• Main Authors: Liu, Minliang, Liang, Liang, Sun, Wei
• Format: Journal Article
• Language: English
• Published: Netherlands Elsevier B.V 01.12.2020; Elsevier BV
• Subjects: Aorta; Biaxial tests; Constitutive modeling; Constitutive models; Convexity; Elastic properties; Hyperelastic material; Machine learning; Neural network; Neural networks; Parameters; Soft tissues; Stress analysis; Test procedures; Neural network; Hyperelastic material; Constitutive modeling; Machine learning
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2020.113402

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.