New geometry-inspired numerical convex analysis method for yield functions under isotropic and anisotropic hardenings

Abstract

Convexity of a yield function must be guaranteed to ensure unique relationship between plastic strain increments and stress components. A geometry-inspired numerical convex analysis (GINCA) approach is developed to analyze the convexity of a yield function. The numerical approach is verified by the computation of convex domains for several typical yield functions of Drucker, Cazacu-Barlat2004, Hu2017, Cazacu2018 and a newly proposed function for differential-anisotropic hardening. The verified GINCA is applied to analyze the convexity of the Gao2011 yield function since it was not determined yet. The numerical approach is also used to determine the convex domain evolution with respect to plastic deformation in an anisotropic hardening function. It is also applied to investigate the convexity of polynomial yield functions for strong anisotropic metals. The result shows that the GINCA can effectively and correctly compute the convex domain for different yield functions. Besides, the numerical approach only needs to compute the effective stress from a yield function without any computation of the first- and second-order partial derivatives, compared to the complicated convex analysis by the Hessian matrix. Therefore, the proposed GINCA is user-friendly, effective and accurate to analyze the convexity of a yield function both for isotropic hardening and anisotropic/differential hardening. The Matlab codes are shared as electric attachments for scientists and engineers to check the convexity of a yield surface under biaxial loading, plane stress with shear stress and triaxial loading conditions.