Fhcnnbio: a fiber-reinforced hyperelastic constitutive neural network model for biological tissues with prior physical information

Accurate constitutive model for biological soft tissue deformation poses significant challenges, particularly under large deformations, crucial for applications in computer-assisted surgical intervention and biomedical engineering. Expert-constructed models are are typically developed with a specific material in mind, rendering them challenging to transfer to other materials. Meanwhile, existing neural network-based approaches are primarily focused on modeling the behavior of isotropic materials, with a notable scarcity of approaches being specifically designed and optimized for the complex behavior of biological soft tissues. This study introduces FHCNNBio, a data-driven hyperelastic constitutive neural network model specifically designed for biological tissues. FHCNNBio incorporates fiber-reinforced invariants to characterize the anisotropic properties of biological tissues, while also proposing a weight-adaptive factor to represent the probabilistic dependencies between fiber orientations and invariant measures. By leveraging invariant-based theory from continuum mechanics and input convex neural networks, FHCNNBio ensures physical symmetry, objectivity, and numerical stability. Extensive evaluations on real-world benchmarks, finite element simulations, and analytical models demonstrate FHCNNBio’s superior performance, adapting flexibly to various material parameters without requiring retraining. FHCNNBio’s generalizability and applicability enable precise material property characterization, facilitating advancements in engineering practice and virtual reality simulations. The developed source code and accompanying example data sets are available at https://github.com/ReFantasy/FHCNNBio .