Generative Hyperelasticity with Physics-Informed Probabilistic Diffusion Fields.

Area of Science:

• Computational mechanics
• Materials science
• Applied mathematics

Background:

• Natural materials possess complex, nonlinear, anisotropic, and heterogeneous mechanical properties.
• Data-driven strain energy functions can model these behaviors but often neglect uncertainty and spatial heterogeneity.
• Existing methods lack the flexibility to capture the full complexity of material responses.

Purpose of the Study:

• To develop a data-driven approach for modeling hyperelastic materials that incorporates uncertainty and spatial heterogeneity.
• To create flexible and physics-constrained strain energy functions.
• To advance predictive modeling for complex materials like biological tissues.

Main Methods:

• Utilized neural ordinary equations (NODE) to construct polyconvex strain energy functions.
• Employed probabilistic diffusion models to generate diverse strain energy functions from noise.
• Extended the diffusion model for spatially correlated outputs to represent heterogeneous material properties.

Main Results:

• Successfully generated plausible strain energy functions with inherent uncertainty.
• Demonstrated the capability to model spatially heterogeneous material properties for arbitrary geometries.
• Validated the approach using synthetic and experimental data from biological tissues.

Conclusions:

• This generative model approach significantly enhances data-driven hyperelasticity models by including uncertainty.
• The method provides a robust framework for predicting the mechanical behavior of complex, heterogeneous materials.
• Represents a significant advancement in the field of computational materials science and predictive modeling.