Automated data-driven discovery of material models based on symbolic regression: A case study on the human brain...

Area of Science:

• Computational Mechanics
• Materials Science
• Biophysics

Background:

• Hyperelastic constitutive models are crucial for describing the mechanical behavior of soft materials.
• Traditional methods often require extensive data and complex formulations, limiting interpretability.
• Automated discovery of physically meaningful models from sparse data remains a challenge.

Purpose of the Study:

• To introduce a data-driven framework for automatically identifying interpretable and physically meaningful hyperelastic constitutive models.
• To leverage symbolic regression for generating parsimonious mathematical expressions that adhere to hyperelasticity constraints.
• To validate the approach using synthetic and experimental data, including human brain tissue.

Main Methods:

• Utilized symbolic regression to explore invariant-based, principal stretch-based, and normal strain-based hyperelastic models.
• Ensured strict adherence to hyperelasticity constraints such as polyconvexity and ellipticity.
• Validated the framework with synthetic data from established models and experimental data from the human brain cortex.

Main Results:

• The symbolic regression framework successfully discovered accurate hyperelastic models with succinct mathematical expressions.
• The strain-based model demonstrated superior accuracy, while stretch-based and strain-based models captured brain tissue's nonlinearity and asymmetry.
• Models exhibited robust interpolation capabilities and acceptable extrapolation performance, with polyconvexity/ellipticity assessments confirming physical validity.

Conclusions:

• Symbolic regression provides a powerful tool for the automated discovery of isotropic hyperelastic models from sparse data.
• The developed framework accurately models soft matter, exemplified by its application to human brain tissue.
• This approach offers broad applicability for discovering constitutive models in various soft matter systems.