Interpretable data-driven modeling of hyperelastic membranes

We proposed an approach for interpretable data-driven modeling of an isotropic incompressible hyperelastic membrane deformation. The approach is based on the response functions in terms of the Laplace stretch and the finite element method, where response functions are partial derivatives of a hyperelastic potential with respect to the chosen strain measure. The Laplace stretch as the strain measure allows us to recover directly the response functions from experimental data and construct automatically data-driven constitutive relations. All needed formulas were obtained explicitly. We tested our approach for membrane inflation with data-driven constitutive relations based on the perforated membrane extension tests.