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

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...

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Main Authors:	A. S. Borokinni, Dabiao Liu
Format:	Article
Language:	English
Published:	MDPI AG 2018-09-01
Series:	Metals
Subjects:	strain gradient plasticity principle of virtual power defect energy flow rule material length scale
Online Access:	http://www.mdpi.com/2075-4701/8/9/708

id	doaj-art-83d4faf83b2d44e694966f255af8d6a6
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spelling	doaj-art-83d4faf83b2d44e694966f255af8d6a62018-09-12T06:50:49ZengMDPI AGMetals2075-47012018-09-018970810.3390/met8090708met8090708A Brief Note on the Nix–Gao Strain Gradient Plasticity TheoryA. S. Borokinni0Dabiao Liu1Distance Learning Institute, University of Lagos, Lagos State PMB 0001, NigeriaDepartment of Mechanics, Huazhong University of Science and Technology, Wuhan 430074, ChinaThe 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.http://www.mdpi.com/2075-4701/8/9/708strain gradient plasticityprinciple of virtual powerdefect energyflow rulematerial length scale
institution	Open Data Bank
collection	Open Access Journals
building	Directory of Open Access Journals
language	English
format	Article
author	A. S. Borokinni Dabiao Liu
spellingShingle	A. S. Borokinni Dabiao Liu A Brief Note on the Nix–Gao Strain Gradient Plasticity Theory Metals strain gradient plasticity principle of virtual power defect energy flow rule material length scale
author_facet	A. S. Borokinni Dabiao Liu
author_sort	A. S. Borokinni
title	A Brief Note on the Nix–Gao Strain Gradient Plasticity Theory
title_short	A Brief Note on the Nix–Gao Strain Gradient Plasticity Theory
title_full	A Brief Note on the Nix–Gao Strain Gradient Plasticity Theory
title_fullStr	A Brief Note on the Nix–Gao Strain Gradient Plasticity Theory
title_full_unstemmed	A Brief Note on the Nix–Gao Strain Gradient Plasticity Theory
title_sort	brief note on the nix–gao strain gradient plasticity theory
publisher	MDPI AG
series	Metals
issn	2075-4701
publishDate	2018-09-01
description	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.
topic	strain gradient plasticity principle of virtual power defect energy flow rule material length scale
url	http://www.mdpi.com/2075-4701/8/9/708
_version_	1612603757192806400

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

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