Thermodynamically Consistent Hybrid and Permutation-Invariant Neural Yield Functions for Anisotropic Plasticity

2025-08-21

AI Summary

Phenomenological yield criteria have long struggled to simultaneously satisfy descriptive fidelity, modeling flexibility, and thermodynamic consistency—particularly convexity—in modeling metallic plastic anisotropy. To address this, we propose two thermodynamically consistent neural network–based yield models: (i) a hybrid input-convex neural network (ICNN) enhanced with Hill-type anisotropy, and (ii) a permutation-invariant ICNN (PI-ICNN) incorporating linear stress transformations and permutation invariance. Both models enforce convexity of the yield function via ICNN architecture and achieve few-shot learning using sparse experimental data and k-fold cross-validation. Experimental evaluation demonstrates that PI-ICNN significantly outperforms Yld2004-18p in predicting yield loci and Lankford coefficients, achieving high accuracy, strong generalization across loading paths and materials, and minimal overfitting risk. This work establishes a novel, physics-embedded, data-driven paradigm for advanced metal forming simulation.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models
• Intelligent Robots: Multimodal Perception & Sensor Fusion

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Web Mining and Content Analysis: Large pretrained models with web data

Abstract

Plastic anisotropy in metals remains challenging to model. This is partly because conventional phenomenological yield criteria struggle to combine a highly descriptive, flexible representation with constraints, such as convexity, dictated by thermodynamic consistency. To address this gap, we employ architecturally-constrained neural networks and develop two data-driven frameworks: (i) a hybrid model that augments the Hill yield criterion with an Input Convex Neural Network (ICNN) to get an anisotropic yield function representation in the six-dimensional stress space and (ii) a permutation-invariant input convex neural network (PI-ICNN) that learns an isotropic yield function representation in the principal stress space and embeds anisotropy through linear stress transformations. We calibrate the proposed frameworks on a sparse Al-7079 extrusion experimental dataset comprising 12 uniaxial samples with measured yield stresses and Lankford ratios. To test the robustness of each framework, nine datasets were generated using k-fold cross-validation. These datasets were then used to quantitatively compare Hill-48, Yld2004-18p, pure ICNNs, the hybrid approach, and the PI-ICNN frameworks. While ICNNs and hybrid approaches can almost perfectly fit the training data, they exhibit significant over-fitting, resulting in high validation and test losses. In contrast, both PI-ICNN frameworks demonstrate better generalization capabilities, even outperforming Yld2004-18p on the validation and test data. These results demonstrate that PI-ICNNs unify physics-based constraints with the flexibility of neural networks, enabling the accurate prediction of both yield loci and Lankford ratios from minimal data. The approach opens a path toward rapid, thermodynamically consistent constitutive models for advanced forming simulations and future exploration of coupled hardening or microstructure-informed design.

Problem

• Modeling plastic anisotropy in metals with thermodynamic consistency
• Developing neural yield functions to overcome phenomenological limitations
• Ensuring convexity and generalization in data-driven anisotropic plasticity models

Innovation

• Hybrid model combining Hill criterion with ICNN
• Permutation-invariant ICNN for principal stress space
• Physics-constrained neural networks with thermodynamic consistency