M.Sc Student | Trapper Pavel |
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Subject | A Simple Theory of Gradient Plasticity with Two Characteristic Lengths |

Department | Department of Civil and Environmental Engineering |

Supervisors | Professor Konstantin Volokh |

Mr. Dimitry Val | |

Full Thesis text |

A new strain
gradient plasticity theory is formulated to accommodate more than one material
length parameter. The theory is an extension of the classical *J*_{2}
flow theory of metal plasticity to the micron scale. Distinctive features of
the proposed theory as compared to other existing theories are the simplicities
of mathematical formulation, numerical implementation and physical
interpretation. The proposed theory is based on the physical idea that the
effective plastic strain is a measure of the defect density. (Point, line
dislocations, and surface defects underlying plastic flow are considered. These
defects should not be confused with microcracks, voids etc underlying damage
accumulation. The latter is out of the scope of the present work.) The latter
allows interpreting the yield/hardening condition as an equation describing
(quasi-static) evolution of defects. At the macroscopic scale, the defect
diffusion is negligible and the yield condition is a purely algebraic equation.
At the scale of microns, however, the defect diffusion is sound and it can be
included in the yield condition through the divergence of the vector of the
defect flux. We propose that the defect flux is linearly proportional to the
gradient of the defect density, i.e. the accumulated plastic strain. This
proportionality is provided by a second-order tensor of the defect conductivity.
Such tensor is the main source of the material characteristic lengths. If, for
example, this tensor is equivalent to the length-scaled identity tensor then we
arrive at the earlier Aifantis theory of strain-gradient plasticity where the
defect diffusion is isotropic. It is reasonable, however, to assume that the
defect diffusion is not purely isotropic and stresses induce anisotropy. The
latter means that the defect conductivity tensor should depend on the scaled
stress tensor. The corresponding formulation of strain gradient plasticity is
developed in the present work. It appears that the proposed theory is,
probably, the simplest one among the theories, which include more than one
characteristic length. It is also important that in contrast to the majority of
strain gradient theories no direct use of higher-order stresses, which can
hardly be interpreted in simple physical terms, has been made in the present
work.