Uncertainty Quantification in Hyperelastic Materials — A Nonintrusive Spectral Stochastic Smoothed Finite Element Method

This study presents a novel nonintrusive stochastic approach to model the large deformation behavior of quasi-incompressible hyperelastic materials with inherent uncertainty in the material properties and geometric parameters. In addition, the mesh distortion parameter is also considered a random parameter. The input and output uncertainties are represented by Polynomial Chaos Expansion (PCE). The domain is discretized with three-noded triangular elements and the edge-based smoothed finite element method is used to compute the corresponding bilinear/linear forms. The robustness and the efficacy of the framework are elucidated with a few standard benchmark problems considering the bulk modulus as the uncertain parameter by comparing with the brute-force Monte Carlo simulations. For identifying critical influencing parameters, a sensitivity analysis based on Sobol’ indices is adopted.