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 nonquadratic yield function complement the convexity certification based on a fully numerical minimization algorithm and should facilitate its wider acceptance in modeling sheet metal anisotropic plasticity.
Skip Nav Destination
Article navigation
July 2018
Technical Briefs
Algebraic Convexity Conditions for Gotoh's Nonquadratic Yield Function
Wei Tong
Wei Tong
Professor
Mem. ASME
Department of Mechanical Engineering,
Lyle School of Engineering,
Southern Methodist University,
Dallas, TX 75275-0337
e-mail: wtong@smu.edu
Mem. ASME
Department of Mechanical Engineering,
Lyle School of Engineering,
Southern Methodist University,
Dallas, TX 75275-0337
e-mail: wtong@smu.edu
Search for other works by this author on:
Wei Tong
Professor
Mem. ASME
Department of Mechanical Engineering,
Lyle School of Engineering,
Southern Methodist University,
Dallas, TX 75275-0337
e-mail: wtong@smu.edu
Mem. ASME
Department of Mechanical Engineering,
Lyle School of Engineering,
Southern Methodist University,
Dallas, TX 75275-0337
e-mail: wtong@smu.edu
Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received November 12, 2017; final manuscript received March 31, 2018; published online May 8, 2018. Assoc. Editor: A. Amine Benzerga.
J. Appl. Mech. Jul 2018, 85(7): 074501 (7 pages)
Published Online: May 8, 2018
Article history
Received:
November 12, 2017
Revised:
March 31, 2018
Citation
Tong, W. (May 8, 2018). "Algebraic Convexity Conditions for Gotoh's Nonquadratic Yield Function." ASME. J. Appl. Mech. July 2018; 85(7): 074501. https://doi.org/10.1115/1.4039880
Download citation file:
Get Email Alerts
Cited By
Enhancement of Synchronization in Nonlinear MEMS Oscillator Based on Electrothermal Adjustment
J. Appl. Mech (April 2025)
Dynamics of an Electric Field Vulnerable Morpho-Elastic Biological Membranes
J. Appl. Mech (April 2025)
Related Articles
Scaling Laws in the Ductile Fracture of Metallic Crystals
J. Appl. Mech (July,2015)
On Void Coalescence Under Combined Tension and Shear
J. Appl. Mech (July,2015)
A Simple Physically Based Phenomenological Model for the Strengthening/Softening Behavior of Nanotwinned Copper
J. Appl. Mech (December,2015)
Extraction of Anisotropic Mechanical Properties From Nanoindentation of SiC-6H Single Crystals
J. Appl. Mech (September,2016)
Related Proceedings Papers
Related Chapters
Introductory Information
The Stress Analysis of Cracks Handbook, Third Edition
Recent Developments in J Ic Testing
Developments in Fracture Mechanics Test Methods Standardization
Conclusions
Introduction to Finite Element, Boundary Element, and Meshless Methods: With Applications to Heat Transfer and Fluid Flow