  Data-based approaches are promising alternatives to the traditional
analytical constitutive models for solid mechanics. Herein, we propose a
Gaussian process (GP) based constitutive modeling framework, specifically
focusing on planar, hyperelastic and incompressible soft tissues. The strain
energy density of soft tissues is modeled as a GP, which can be regressed to
experimental stress-strain data obtained from biaxial experiments. Moreover,
the GP model can be weakly constrained to be convex. A key advantage of a
GP-based model is that, in addition to the mean value, it provides a
probability density (i.e. associated uncertainty) for the strain energy
density. To simulate the effect of this uncertainty, a non-intrusive stochastic
finite element analysis (SFEA) framework is proposed. The proposed framework is
verified against an artificial dataset based on the Gasser--Ogden--Holzapfel
model and applied to a real experimental dataset of a porcine aortic valve
leaflet tissue. Results show that the proposed framework can be trained with
limited experimental data and fits the data better than several existing
models. The SFEA framework provides a straightforward way of using the
experimental data and quantifying the resulting uncertainty in simulation-based
predictions.
