A Physics-Informed Assembly of Feed-Forward Neural Network Engines to Predict Inelasticity in Cross-Linked Polymers

Area of Science:

• Solid mechanics
• Material modeling
• Data-driven approaches

Background:

• Traditional constitutive models in solid mechanics face limitations in accuracy and complexity.
• Implementing machine learning in material modeling is hindered by high-dimensional data, missing data, and convergence issues.

Purpose of the Study:

• To propose a framework integrating polymer science, statistical physics, and continuum mechanics for super-constrained, reduced-order machine learning.
• To address challenges in data-driven material modeling.

Main Methods:

• Sequential order-reduction to simplify 3D stress-strain tensor mapping into 1D problems.
• Utilizing an assembly of replicated neural network learning agents (L-agents) for classification.
• Employing a physics-based approach to enhance interpretability.

Main Results:

• The proposed framework significantly outperforms existing constitutive laws in training speed and accuracy.
• Successfully captures complex loading modes using simplified, dispersed experimental data.
• Demonstrates superior performance even in complicated loading scenarios.

Conclusions:

• The hybrid assembly of L-agents offers a new generation of machine-learned approaches for material modeling.
• The physics-based nature provides better interpretability compared to conventional machine learning models.
• This approach overcomes key difficulties in implementing machine learning for solid mechanics.