A deep neural network surrogate for fast mechanical parameter identification using the ring tensile test

This study presents a two-stage inverse-characterization framework that combines deep learning with finite-element modeling to accelerate material parameter identification for small-artery mechanics using the ring tensile test. Because ring tensile loading produces highly nonuniform stress/strain fields (combined flexural, uniaxial, and wire contact effects) and arteries exhibit residual stress in the unloaded tubular state, simplified analytic stress–strain reductions can bias constitutive fits. The authors trained a deep neural network (DNN) surrogate on a large dataset of FEBio ring-tensile simulations using an anisotropic hyperelastic Gasser–Ogden–Holzapfel-type constitutive model, with inputs spanning both material parameters and ring geometry (thickness and inner diameter). Simulation outputs (force–displacement curves) were resampled and compressed with PCA, enabling the DNN to predict curve coefficients efficiently. The DNN is then used to generate near-optimal initial parameter guesses via global optimization, followed by a final FEM-based calibration stage that incorporates residual stresses reconstructed from a ring-opening test. Validation on experimental abdominal aorta samples from Wistar rats showed the DNN surrogate provides strong initial estimates (initial R² ≥ ~0.73 across identified parameters) and enables rapid convergence of the FEM inverse problem in only a few iterations, while sensitivity and extrapolation analyses clarified which parameters most strongly affect ring-test response and where surrogate accuracy degrades outside training bounds. Overall, the work establishes a practical, high-throughput pathway for batch arterial characterization when specimen size/availability constrains conventional multi-axial testing and when full FEM inverse analyses are too computationally expensive to run at scale.