Physics-Informed Discovery of Yield Functions in Plasticity via Convex Neural Representations

2026-06-12

AI Summary

This work addresses the challenge of identifying anisotropic yield functions directly from experimental data, which is hindered by their unobservability, the need for multi-axial loading calibration, and uncertainty in their analytical form. The authors propose a physics-informed framework that identifies the yield function solely from full-field displacement and reaction force measurements within an elastoplastic stress integration architecture, without assuming a predefined functional form or relying on stress or plastic strain data. By innovatively embedding a convex neural network into the constitutive update procedure and training it through differentiable stress integration and multi-scenario force-balance losses, the method automatically enforces essential mathematical properties—convexity, positive first-order homogeneity, and tension–compression symmetry. Benchmark tests on von Mises, Hill 1948, and Yld2000-2d yield surfaces demonstrate accurate reconstruction, robustness to noise, state identifiability, and suitability for surrogate model deployment.

Abstract

Identifying anisotropic yield functions remains challenging since yielding is not directly observed in full-field mechanical measurements, directional calibration can require many loading directions, and selecting an appropriate analytical form is nontrivial. This study proposes a physics-informed framework for discovering yield functions from full-field displacement data and reaction force data, without stress observations, plastic strain measurements, direct yield surface data, or a prescribed parametric yield function. The framework identifies the yield function as a mechanically constrained constitutive component inside elastoplastic stress integration, rather than through direct stress-space supervision. The yield function is represented by a convex neural network that enforces convexity and positive homogeneity of degree one while imposing the assumed tension-compression symmetry, and this neural yield function is trained with a differentiable stress update and a physics-informed force equilibrium loss across multiple loading cases. The proposed framework is validated using finite element (FE) benchmark studies with von Mises, Hill 1948, and Yld2000-2d yield functions, assessing yield contour agreement, displacement-noise sensitivity, identifiability through plastically active stress states, epistemic uncertainty, and polynomial-surrogate deployment. This study provides a mechanics-constrained pathway for discovering anisotropic yield functions from displacement and force data while keeping the identified component within the structure of elastoplastic stress integration.

Problem

• yield function
• anisotropy
• plasticity
• constitutive modeling
• full-field data

Innovation

• Physics-informed learning
• Convex neural networks
• Yield function discovery
• Elastoplasticity
• Constitutive modeling