Data-Driven Anisotropic Biomembrane Simulation Based on the Laplace Stretch

Data-driven simulations are gaining popularity in mechanics of biomaterials since they do not require explicit form of constitutive relations. Data-driven modeling based on neural networks lacks interpretability. In this study, we propose an interpretable data-driven finite element modeling for hyperelastic materials. This approach employs the Laplace stretch as the strain measure and utilizes response functions to define constitutive equations. To validate the proposed method, we apply it to inflation of anisotropic membranes on the basis of synthetic data for porcine skin represented by Holzapfel-Gasser-Ogden model. Our results demonstrate applicability of the method and show good agreement with reference displacements, although some discrepancies are observed in the stress calculations. Despite these discrepancies, the proposed method demonstrates its potential usefulness for simulation of hyperelastic biomaterials.