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Technical Brief

Algebraic Convexity Conditions for Gotoh's Non-Quadratic Yield Function

[+] Author and Article Information
Wei Tong

Department of Mechanical Engineering Lyle School of Engineering Southern Methodist University Dallas, Texas 75275-0337
wtong@smu.edu

1Corresponding author.

ASME doi:10.1115/1.4039880 History: Received November 12, 2017; Revised March 31, 2018

Abstract

A necessary and sufficient condition in terms of explicit algebraic inequalities on its five on-axis material constants and a similarly formulated sufficient condition on its entire set of nine material constants are given for the first time to guarantee a calibrated Gotoh's fourth-order yield function to be convex. When considering the Gotoh's yield function to model a sheet metal with planar isotropy, a single algebraic inequality has also been obtained on the admissible upper and lower bound values of the ratio of uniaxial tensile yield stress over equal-biaxial tensile yield stress at a given plastic thinning ratio. The convexity domain of yield stress ratio and plastic thinning ratio defined by these two bounds may be used to quickly assess the applicability of Gotoh's yield function for a particular sheet metal. The algebraic convexity conditions presented in this study for Gotoh's non-quadratic yield function complement the convexity certification based on a fully numerical minimization method and should facilitate its wider acceptance in modeling sheet metal anisotropic plasticity.

Copyright (c) 2018 by ASME
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