A Computational Methodology in Python for Calibrating Hyperelastic Material Models Using the Generalized Sine-Hyperbolic Formulation

Resumo

This work presents a computational methodology for calibrating hyperelastic models using the Python programming language and based on the strain energy theory, with a focus on the Generalized Hyperbolic Sine (GHS) strain measures. The objective is to provide a flexible and accessible framework for identifying material parameters from experimental stress-strain data through nonlinear optimization. The constitutive model obtained from GHS measures allows an accurate representation of the nonlinear behavior of soft materials, offering versatility in the choice of constitutive equations and suitability for various deformation modes. The strainenergy function is tailored to capture the material response under uniaxial, biaxial or shear conditions, with parameters calibrated using the scipy.optimize.minimize function from the SciPy library, using the methods: Broyden-Fletcher-Goldfarb-Shanno (BFGS), Nelder-Mead, Powell, Truncated Newton (TNC) and Sequential Least SQuares Programming (SLSQP). Analytical stress values are compared with experimental data, and the error between the two datasets is minimized iteratively until convergence is achieved, considering minimum squared error. Data are used as Excel spreadsheets or Python lists, facilitating manipulation. To validate the methodology, a soft rubber material was analyzed, i.e. a vulcanized rubber. The application shows that the method can work with different levels of strains (moderate to large, both in compression and tension), allowing precise matching of complex models to experimental data.