@inbook{a4df5fb008794290bb5c95c97ecbcfe7,
title = "Strain Gradient Plasticity: Theory and Implementation",
abstract = "This chapter focuses on the foundation and development of various higher-order strain gradient plasticity theories, and it also provides the basic elements for their finite element implementation. To this aim, we first refer to experiments exhibiting size-effects in metals and explain them by resorting to the concept of geometrically necessary dislocations. We then bring this concept to the continuum level by introducing Nye{\textquoteright}s dislocation density tensor and by postulating the existence of higher-order stresses associated with dislocation densities. This provides the motivation for the development of higher-order strain gradient plasticity theories. For this purpose, we adopt the generalized principle of virtual work, initially illustrated for conventional crystal plasticity and subsequently extended to both crystal and phenomenological strain gradient plasticity theories.",
keywords = "Micron-scale metal plasticity, Geometrically necessary dislocations, Dislocation density tensor, Strain gradient crystal plasticity, Strain gradient plasticity",
author = "Lorenzo Bardella and Niordson, {Christian F.}",
year = "2020",
doi = "10.1007/978-3-030-43830-2_5",
language = "English",
isbn = "978-3-030-43829-6",
volume = "600",
series = "International Centre for Mechanical Sciences. Courses and Lectures",
publisher = "Springer",
pages = "101--149",
editor = "A. Bertram and S. Forest",
booktitle = "Mechanics of Strain Gradient Materials. CISM International Centre for Mechanical Sciences (Courses and Lectures)",
}