Neural Network-Based Distortional Hardening Inferred from Experiments via FE-Coupled Backpropagation: Application to Ti-6Al-4V and Third-Generation AHSS

Abstract

To learn the elasto-plastic constitutive response of metals from experiments with heterogeneous mechanical fields, we developed a finite element-coupled backpropagation algorithm that trains neural network-based plasticity models using force-displacement curves from notched tension and central-hole tension specimens. This approach enables training deep into the post-necking regime, well beyond the strain ranges accessible to standard uniaxial tests. Building on this framework, a neural network-based distortional hardening model is proposed in which a single network simultaneously predicts the flow resistance, anisotropic yield parameters, and yield function exponent of the YLD2000-3D yield locus as functions of equivalent plastic strain. This unified formulation enables continuous transition of the yield locus between sharp-cornered shapes and smooth shapes with high flexibility during deformation. The model is first pre-trained using uniaxial tension stress-strain data, after which the finite element-coupled training substantially improves predictions at large deformations. Ti-6Al-4V exhibits strong plastic anisotropy together with an unusual reversal in the orientation ranking of force-displacement responses between notched and central-hole tension specimens. The investigated third-generation advanced high-strength steel (AHSS) exhibits a hardening response that transitions from convex to concave curvature. For both materials, the proposed model accurately reproduces the large-deformation and post-necking behavior of all training experiments and successfully predicts unseen validation experiment results, including local strains and the evolution of Lankford coefficients. The proposed framework is computationally stable, efficient, and readily implementable in commercial finite element software. Moreover, the methodology is general and can be extended to arbitrary phenomenological yield functions and experimental training configurations.