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Encyclopedia of Nanotechnology pp 2147–2154Cite as

Plasticity Theory at Small Scales

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Synonyms

Higher-order plasticity theory; Strain gradient plasticity theory

Definition

Plasticity theory is the mathematical formalism that describes the constitutive model of a material undergoing permanent deformation upon loading. For polycrystalline metals at low temperature and strain rate, the J 2 theory is the simplest adequate model. Classic plasticity theory does not include any explicit length scale, and as a result, the constitutive behavior is independent of the sample dimensions. As the characteristic length of a sample is reduced to the micro (and nano) scale, careful experimental observations clearly reveal the presence of a size effect that is not accounted for by the classical theory. Strain gradient plasticity is a formalism devised to extend plasticity theory to these smaller scales. For most metals, strain gradient plasticity is intended to apply to objects in the range from roughly 100 nm to 100 μm. Above 100 μm, the theory converges with the classical theory and...

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Plasticity Theory at Small Scales, Fig. 1
Plasticity Theory at Small Scales, Fig. 2
Plasticity Theory at Small Scales, Fig. 3
Plasticity Theory at Small Scales, Fig. 4
Plasticity Theory at Small Scales, Fig. 5
Plasticity Theory at Small Scales, Fig. 6

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Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of California, 4227 Engineering Gateway, Irvine, CA, 92697-3975, USA

    Prof. Lorenzo Valdevit

  2. School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, MA, 02138, USA

    Prof. John W. Hutchinson

Authors
  1. Prof. Lorenzo Valdevit
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  2. Prof. John W. Hutchinson
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Corresponding author

Correspondence to Lorenzo Valdevit .

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Editors and Affiliations

  1. Ohio Eminent Scholar and The Howard D. Winbigler Professor, Director, Nanoprobe Laboratory for Bio- & Nanotechnology and Biomimetics (NLB2), Ohio State University, 201 W. 19th Avenue, Columbus, Ohio, 43210-1142, USA

    Professor Bharat Bhushan

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Valdevit, L., Hutchinson, J.W. (2012). Plasticity Theory at Small Scales. In: Bhushan, B. (eds) Encyclopedia of Nanotechnology. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9751-4_272

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