Strain Energy Density as a Gaussian Process and Its Utilization in Stochastic Finite Element Analysis: Application to Planar Soft Tissues

Planar soft tissue mechanics were modeled using a data-driven constitutive framework in which strain energy density was represented with a Gaussian process. The formulation was developed to work directly with heart valve biaxial testing data, allowing mechanical response and associated uncertainty to be captured without assuming a predefined material model. The approach was evaluated using synthetic datasets and experimental biaxial measurements from porcine aortic valve leaflet tissue. Model behaviour was compared with conventional hyperelastic formulations commonly used in valve constitutive modeling, with differences observed in predictive response under multiaxial loading. The resulting constitutive descriptions were incorporated into finite element simulations, where stochastic methods were used to propagate experimental uncertainty through tissue-level mechanical predictions.