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Metals 2018, 8(9), 708; https://doi.org/10.3390/met8090708

A Brief Note on the Nix–Gao Strain Gradient Plasticity Theory

1
Distance Learning Institute, University of Lagos, Lagos State PMB 0001, Nigeria
2
Department of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, China
3
Hubei Key Laboratory of Engineering Structural Analysis and Safety Assessment, Wuhan 430074, China
4
Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China
*
Author to whom correspondence should be addressed.
Received: 25 August 2018 / Revised: 2 September 2018 / Accepted: 6 September 2018 / Published: 10 September 2018
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Abstract

The mathematical nature of the flow rule for the strain gradient plasticity theory proposed by Nix and Gao (W.D. Nix and H. Gao, J Mech Phys Solids 46(3), 411(1998)) is discussed based on the paradigm developed by Gurtin and Anand (M.E. Gurtin and L. Anand, J Mech Phys Solids 57 (3), 405 (2009)). It is shown that, when investigated on the basis of Gurtin–Anand theory, the Nix–Gao flow rule is a combination of constitutive equations for microstresses, balance law, and a constraint. As an accessory, we demonstrate that the strain gradient term introduced in the model is energetic. The results are obtained by combining a virtual-power principle of Fleck and Hutchinson, and the free-energy imbalance under isothermal conditions. View Full-Text
Keywords: strain gradient plasticity; principle of virtual power; defect energy; flow rule; material length scale strain gradient plasticity; principle of virtual power; defect energy; flow rule; material length scale
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Borokinni, A.S.; Liu, D. A Brief Note on the Nix–Gao Strain Gradient Plasticity Theory. Metals 2018, 8, 708.

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