[Paper Review] Thermodynamic Consistent Neural Networks for Learning Material Interfacial Mechanics

Jiaxin Zhang, Congjie Wei+1 more|arXiv (Cornell University)|Nov 28, 2020

Model Reduction and Neural Networks18 references4 citations

TL;DR

This paper proposes a thermodynamic consistent neural network (TCNN) to model traction-separation relations (TSR) in material interfaces using sparse experimental data. By embedding three thermodynamic principles—positive energy dissipation, steepest energy dissipation gradient, and energy-conservative loading paths—into a physics-informed loss function, TCNN accurately predicts the full TSR surface while reducing thermodynamic violations to ~5%, significantly outperforming unconstrained models.

ABSTRACT

For multilayer materials in thin substrate systems, interfacial failure is one of the most challenges. The traction-separation relations (TSR) quantitatively describe the mechanical behavior of a material interface undergoing openings, which is critical to understand and predict interfacial failures under complex loadings. However, existing theoretical models have limitations on enough complexity and flexibility to well learn the real-world TSR from experimental observations. A neural network can fit well along with the loading paths but often fails to obey the laws of physics, due to a lack of experimental data and understanding of the hidden physical mechanism. In this paper, we propose a thermodynamic consistent neural network (TCNN) approach to build a data-driven model of the TSR with sparse experimental data. The TCNN leverages recent advances in physics-informed neural networks (PINN) that encode prior physical information into the loss function and efficiently train the neural networks using automatic differentiation. We investigate three thermodynamic consistent principles, i.e., positive energy dissipation, steepest energy dissipation gradient, and energy conservative loading path. All of them are mathematically formulated and embedded into a neural network model with a novel defined loss function. A real-world experiment demonstrates the superior performance of TCNN, and we find that TCNN provides an accurate prediction of the whole TSR surface and significantly reduces the violated prediction against the laws of physics.

Motivation & Objective

• To address the challenge of learning accurate traction-separation relations (TSR) from sparse experimental data in multilayer material systems.
• To overcome the limitation of standard neural networks in violating thermodynamic laws due to data scarcity and lack of physical understanding.
• To develop a data-efficient, physics-informed deep learning framework that enforces thermodynamic consistency in interfacial fracture modeling.
• To enable robust prediction of the entire TSR surface under complex loading paths with minimal experimental coverage.

Proposed method

• The TCNN framework uses a deep neural network with inputs of separation norm |δ| and phase angle φ, and outputs of normal and tangential J-integrals (Jₙ, Jₜ).
• A novel loss function combines data fidelity (MSE loss) with three thermodynamic constraints: TC₁ (positive energy dissipation), TC₂ (steepest energy dissipation gradient), and TC₃ (energy-conservative loading path).
• TC₁ is enforced via a max function over discrete derivative differences to penalize negative dissipation; TC₂ ensures gradient alignment along fixed-phase paths.
• TC₃ is implemented as an equality constraint to maintain correct traction direction relative to the phase angle, using the ratio σₜ/σₙ = tan(φ).
• The total loss is a weighted sum of MSE and three thermodynamic constraints, with hyperparameters tuned via trust-region Bayesian optimization.
• Automatic differentiation is used to compute gradients for loss backpropagation, enabling end-to-end training with physical consistency.

Experimental results

Research questions

• RQ1 Can a data-driven neural network model accurately predict the full traction-separation relation surface using only sparse experimental data?
• RQ2 How can thermodynamic consistency principles be mathematically formulated and embedded into a deep learning model for interfacial mechanics?
• RQ3 To what extent does enforcing thermodynamic constraints reduce physical law violations in neural network predictions of interfacial fracture behavior?
• RQ4 Can physics-informed neural networks effectively model complex, non-PDE-based physical laws such as energy dissipation and path-conservative behavior in fracture mechanics?

Key findings

• The TCNN model successfully predicts the entire TSR surface with high accuracy using only 236 data points across 10 loading paths.
• Thermodynamic violations in predicted interfacial fracture toughness were reduced to approximately 5%, compared to 20–40% in unconstrained models.
• The TCNN framework effectively enforces three thermodynamic principles: positive energy dissipation, steepest energy dissipation gradient, and energy-conservative loading paths.
• The use of a physics-informed loss function with embedded physical constraints significantly improves generalization and physical plausibility of the learned TSR model.
• The model demonstrates robust performance even with limited experimental data, highlighting its data efficiency and suitability for real-world engineering applications.