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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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Correspondence to Lorenzo Valdevit .

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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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