Data-driven continuum damage mechanics with built-in physics.

Area of Science:

• Continuum mechanics
• Materials science
• Computational mechanics

Background:

• Soft materials like rubbers and tissues undergo large deformations and damage, affecting their function.
• Continuum damage mechanics provides a thermodynamically consistent framework for understanding energy dissipation.
• Deep learning offers high accuracy for complex material behaviors, but modeling inelasticity with physics constraints remains challenging.

Purpose of the Study:

• To extend neural ordinary differential equations (NODEs) for modeling energy dissipation in soft materials.
• To incorporate thermodynamically consistent frameworks into deep learning for material modeling.
• To address the challenge of modeling inelastic behavior with built-in physics in neural networks.

Main Methods:

• Utilizing neural ordinary differential equations (NODEs) with an inelastic potential and a monotonic yield function.
• Introducing a novel network architecture capable of modeling arbitrary hyperelastic materials with automatic polyconvexity.
• Demonstrating the flexibility of the network architecture across various damage models.

Main Results:

• The developed NODEs successfully model energy dissipation in a thermodynamically consistent manner.
• The network architecture inherently satisfies physics constraints like polyconvexity.
• The NODEs accurately re-discover damage functions from synthetic data and characterize experimental soft tissue data.

Conclusions:

• Neural ordinary differential equations (NODEs) offer a powerful and flexible approach for modeling complex material behaviors, including inelasticity and damage.
• This data-driven method provides a thermodynamically consistent framework for understanding energy dissipation in soft materials.
• The approach shows significant potential for characterizing both synthetic and experimental data for soft tissues.