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Research Papers

Modified Maximum Mechanical Dissipation Principle for Rate-Independent Metal Plasticity

[+] Author and Article Information
Jun Chen

e-mail: jun_chen@sjtu.edu.cnDepartment of Plasticity Technology,
Shanghai Jiao Tong University,
Shanghai 200030, China

Xinhai Zhu

Livermore Software Technology Corporation,
Livermore, CA 94551

Jian Cao

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208

1Corresponding author.

Manuscript received November 30, 2012; final manuscript received January 4, 2013; accepted manuscript posted February 14, 2013; published online August 21, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(6), 061020 (Aug 21, 2013) (9 pages) Paper No: JAM-12-1536; doi: 10.1115/1.4023685 History: Received November 30, 2012; Revised January 04, 2013; Accepted February 14, 2013

The approach regarding the plastic process as a constrained optimization problem (Simo, J. C., and Hughes, T. J. R., 1998, Computational Inelasticity, Springer, New York) is discussed and found to be limited in considering nonlinear kinematic hardening and mechanical dissipation. These limitations are virtually common in elastoplastic modeling in both theoretical studies and industrial applications. A modified maximum mechanical dissipation principle is proposed to overcome the limitations and form an energy-based framework of nonlinear hardening laws. With the control functions introduced into the framework, not only are the relationships between existing hardening models clarified against their ad hoc origins, but modeling nonsaturating kinematic hardening behavior is also achieved. Numerical examples are presented to illustrate the capability of the nonsaturating kinematic hardening model to describe the phenomena of the permanent softening as well as the cyclic loading. These applications indicate the concept of the control function can be nontrivial in material modeling. Finally, the methodology is also extended to incorporate the multiterm approach.

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Figures

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Fig. 1

Comparing the behaviors of the NSK-I model, the Swift isotropic hardening model and the Armstrong–Frederick model under tension loading

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Fig. 4

The schematic curve of the NSK-II model under tension-compression loading

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Fig. 2

Comparing the behaviors of the NSK-I model, the Swift isotropic hardening model and the Armstrong–Frederick model under tension-compression (T-C) loading

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Fig. 3

Modeling the cyclic behavior of DP590 with NSK-I model

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