A parameter identification scheme for the orthotropic Poly6 yield function satisfying the convexity condition

• Published in: European journal of mechanics, A, Solids Vol. 92; p. 104467
• Main Author: Soare, Stefan C.
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Masson SAS 01.03.2022; Elsevier BV
• Subjects: Algorithms; Convexity; Decoupling; Functions (mathematics); Identification algorithm; Mathematical models; Metals; Optimization; Parameter identification; Plastic deformation; Plasticity; Polynomials; Strain rate; Uniaxial tests; Yield function; Identification algorithm; Polynomials; Convexity; Yield function; Metals; Plasticity
• ISSN: 0997-7538; 1873-7285
• DOI: 10.1016/j.euromechsol.2021.104467

The yield surface is the boundary of the elastic domain of a material and determines, via the normality rule, the direction of plastic deformation. Therefore, an accurate model of the yield surface of a material is crucial for the numerical simulation of its deformation processes. In addition, the yield surface must be convex in order to ensure a one-to-one relationship between the plastic strain rate and a corresponding stress state. In this context, homogeneous polynomial functions, in their most general form, have been shown to have a wide modeling range. However, it is also well known that these functions are not convex by default and hence the material parameters (the polynomial coefficients) must be subject to additional convexity constraints. Here we show that Poly6, the sixth order polynomial, features complete decoupling between pure shear and uniaxial traction. This allows us to devise a simple least squares optimization scheme based on biaxial and uniaxial test data, and an additional set of convexity control points which leads to a fast and explicit identification algorithm (Supporting code at https://github.com/stefanSCS/Poly6). [Display omitted] •A rigorous and robust, with emphasis on convexity, identification procedure for Poly6 is proposed.•Minimal input data: the three mechanical traction tests at 0°, 45°and 90°from the metal sheet rolling direction.•Supporting Python code is provided.