Physics-Informed AI Discovers Material Yield Functions.

Identifying the yield functions of materials, especially those exhibiting anisotropy, poses a significant challenge in materials science and engineering. Traditional methods often require extensive directional calibration, direct observation of yielding, or the pre-selection of an appropriate analytical form, which can be difficult given that yielding is not directly observable through standard mechanical measurements. This research proposes a novel physics-informed framework that can discover these yield functions solely from full-field displacement and reaction force data, bypassing the need for stress observations, plastic strain measurements, or predefined parametric yield functions. The core of the framework is a convex neural network that represents the yield function, inherently enforcing convexity, positive homogeneity, and tension-compression symmetry. This neural yield function is trained within a differentiable stress update mechanism, using a physics-informed force equilibrium loss across various loading scenarios. The framework's efficacy has been validated through finite element benchmark studies using established yield functions like von Mises and Hill 1948, demonstrating strong agreement in yield contours and robustness to noise.