Stochastic isotropic hyperelastic materials: constitutive calibration and model selection

Area of Science:

• Materials Science
• Solid Mechanics
• Computational Mechanics

Background:

• Biological and synthetic materials display variable elastic responses under large strains due to inhomogeneities or viscoelasticity.
• Hyperelastic models calibrated to mean data offer limited insight into material property dispersion, crucial for practical applications.

Purpose of the Study:

• To develop stochastic hyperelastic models incorporating random field parameters to represent material property variability.
• To establish a Bayesian criterion for selecting the most parsimonious model among those that fit experimental data.

Main Methods:

• Combining finite elasticity and information theories to construct homogeneous isotropic hyperelastic models.
• Calibrating models using mean values and standard deviations of stress-strain functions or nonlinear shear modulus from experimental tests.
• Applying Bayesian statistics for model selection based on Occam's razor.

Main Results:

• Demonstrated the ability of stochastic models to capture data dispersion in material responses.
• Successfully calibrated and selected models for rubber and brain tissue under various loading conditions.
• Validated the effectiveness of the Bayesian model selection criterion.

Conclusions:

• Stochastic hyperelastic models provide a more comprehensive representation of material behavior than traditional models.
• The developed Bayesian approach offers a robust method for selecting appropriate models when data variability is present.
• This framework enhances the predictive capability of hyperelastic models for inhomogeneous and variable materials.