A Virtual Fields Method-Genetic Algorithm (VFM-GA) calibration framework for isotropic hyperelastic constitutive models with application to an elastomeric foam material

Abstract: This work introduces a calibration framework for material parameter identification in isotropic hyperelastic constitutive models. The framework synergizes the Virtual Fields Method (VFM) to define an objective function with a Genetic Algorithm (GA) as the optimization method to facilitate automated calibration. The formulation of the objective function uses experimental displacement fields measured from Digital Image Correlation (DIC) synchronized with load cell data and can accommodate data from experiments involving homogeneous or inhomogeneous deformation fields. The framework places no restrictions on the target isotropic hyperelastic constitutive model, accommodating models with coupled dependencies on deformation invariants and specialized functional forms with a number of material parameters, and assesses material stability, eliminating sets of material parameters that potentially lead to non-physical behavior for the target hyperelastic constitutive model. To minimize the objective function, a GA is deployed as the optimization tool due to its ability to navigate the intricate landscape of material parameter space. The VFM-GA framework is evaluated by applying it to a hyperelastic constitutive model for compressible elastomeric foams. The evaluation process entails a number of tests that employ both homogeneous and inhomogeneous displacement fields collected from DIC experiments on open-cell foam specimens. The results outperform manual fitting, demonstrating the framework's robust and efficient capability to handle material parameter identification for complex hyperelastic constitutive models.