Benchmarking physics-informed frameworks for data-driven hyperelasticity.

Area of Science:

• Materials Science
• Computational Mechanics
• Artificial Intelligence

Background:

• Data-driven methods offer flexibility in materials modeling but suffer from extrapolation issues and physics violations.
• Existing methods struggle with overfitting and ensuring predictions align with physical constraints.

Purpose of the Study:

• To review, extend, and compare three physics-informed data-driven methods: Constitutive Artificial Neural Networks (CANN), Input Convex Neural Networks (ICNN), and Neural Ordinary Differential Equations (NODE).
• To ensure automatic satisfaction of objectivity, material symmetries, and polyconvexity in hyperelasticity modeling.

Main Methods:

• A shared formulation for strain energy potentials was developed, expanding them into sums of convex non-decreasing functions of invariants.
• The three methods (CANN, ICNN, NODE) were trained using stress-strain data from rubber and skin.
• Performance was benchmarked against traditional neural networks and evaluated for accuracy, overfitting, and extrapolation.

Main Results:

• All three physics-informed methods (CANN, ICNN, NODE) accurately captured training data with minimal overfitting and demonstrated extrapolation capabilities.
• Unlike unconstrained networks, these methods produced physically meaningful predictions outside the training range.
• While stress predictions were similar, the identified energy functions differed, particularly in second derivatives, potentially impacting numerical solvers.

Conclusions:

• CANN, ICNN, and NODE successfully combine data-driven flexibility with physics-based constraints for hyperelastic material modeling.
• These methods offer a robust alternative to traditional approaches, overcoming limitations in extrapolation and physical consistency.
• The choice between CANN, ICNN, and NODE may depend on specific application needs and desired trade-offs between model complexity and accuracy.