Machine-learning-based virtual fields method: Application to anisotropic hyperelasticity

Thanks to advances of techniques like digital image correlation (DIC), the virtual fields method (VFM) has become a common approach to identifying mechanical parameters of materials when full-field displacement data are available. However, it is limited to a priori selected classical material models. Recently, machine learning and model discovery has become a promising alternative for non-parametric material identification. This paper proposes an approach using a machine learning framework (NN-EUCLID) combined with the VFM. This framework has already demonstrated its good performance for hyperelasticity using 2D simulated displacement fields and a loss function formulated with the local equilibrium gap. Our study focuses on training a similar NN-EUCLID framework with 3D displacement fields obtained in a bulge inflation test to discover mechanical models of arteries. Instead of using the local equilibrium gap, we employ the VFM to formulate loss functions. This novelty allows us to address issues such as unknown boundary conditions. We present numerical examples showcasing the ability to train hyperelastic models for isotropic and anisotropic materials. Results obtained with experimental data demonstrate the method’s effectiveness in training neural-network constitutive models for biological tissues using accessible full-field measurements. • A new VFM-based loss function for identifying constitutive laws via machine learning. • VFM-based constitutive modeling addresses challenges such as unknown reaction forces. • A new method for identifying anisotropic tissue properties via bulge-inflation tests. • Different virtual fields used to investigate their effects on identification process.