# Strain Gradient Plasticity

**DOI:**https://doi.org/10.1007/978-3-662-53605-6_110-1

## Synonyms

## Definitions

Strain gradient plasticity (SGP) is a theory of continuum solid mechanics which aims at modeling the irreversible mechanical behavior of materials, with specific focus on metals and on their response at appropriately small size, typically on the order of micrometers or less. For such small metallic components, a variation in size leads to a peculiar effect, denoted as “smaller being stronger.”

## Background

The term plasticity refers to the irreversible mechanical behavior of materials, with particular reference to metals. This behavior occurs when the stress state is large enough for the material to *yield*, thus leading to a permanent deformation, denoted as plastic deformation. Such deformation can be observed, and the inherent plastic strain measured, after removing a suitable, monotonically applied load which enables yielding. In simple tests, such as uniaxial tension, the *yield stress*is...

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