Work

An evolving non-associated Hill-Barlat yield criterion for anisotropic hardening with closed-form analytical calibration and guaranteed convexity

Year: 2026

Type: article

Abstract: Accurate description of anisotropic hardening is critical for the predictive simulation of sheet metal forming. Within a non-associated flow rule framework, the evolving Hill48 family of models provides an attractive analytical route, in which the anisotropy parameters are obtained directly from the directional flow curves without optimization-based recalibration. Their quadratic structure, however, limits the curvature of the yield surface between the uniaxial and equibiaxial tension states. Higher curvature flexibility has been introduced through the coupled quadratic and non-quadratic (CQN) family, but the resulting yield functions require strain- and material-dependent verification of convexity, which can fail for realistic materials. This work proposes an evolving non-associated Hill48-Yld91 yield criterion that resolves both limitations. The Yld91 yield function controls the curvature through its non-quadratic exponent, while the quadratic Hill48 plastic potential captures the r -value anisotropy. Convexity is inherited intrinsically from the Yld91 structure, with no subsequent verification. The mathematical core of the work is an explicit closed-form analytical solution for the four Yld91 anisotropy parameters at exponent n =2, derived directly in terms of the Hill48 calibration coefficients, which reduces the evolving calibration to a single algebraic step without numerical iteration. By construction, the anisotropy parameters and the curvature-controlling exponent are obtained independently, so the deployment exponent can be chosen separately from the calibration. The proposed model is validated against the directional anisotropic hardening of two steels (718AT and MP980) and two aluminum alloys (AA5182-O and AA6022-T43), and is further tested for convexity against cases (QP1180 and an artificial material) for which CQN-type formulations have been reported to lose convexity. The framework provides a simple, analytically calibrated, and convexity-guaranteed route to evolving anisotropic hardening.

Source: International Journal of Plasticity

DOI: 10.1016/j.ijplas.2026.104762

Authors: Guijia Li, Junhe Lian, Jeong Whan Yoon

Institutions: Aalto University, RWTH Aachen University, Deakin University, Korea Advanced Institute of Science and Technology

Language: English

Topic: Metal Forming Simulation Techniques

Subfield: Mechanical Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,740