Numerical investigation of theories of strain-gradient plasticity

Mhlongo, Nothando Precious

Numerical investigation of theories of strain-gradient plasticity

Master Thesis

2018

Abstract

In this work, a higher-order irrotational strain gradient plasticity theory is studied in the small strain regime. This theory is based on that originally developed by Gurtin and Anand, and includes both dissipative and energetic contributions. A detailed numerical study is based on the problem of simple shear of a homogeneous and a non-homogeneous block. Combinations of micro-hard and micro-free boundary conditions are used. The elastic gap, that is, elastic behaviour following a change in the plastic regime from micro-free to micro-hard boundary conditions, is clearly evident. A second phenomenon studied is that of strengthening and hardening with increase in dissipative and energetic length scales, respectively. For the purely dissipative theory, it has been shown that the flow relation in terms of Cauchy stress is necessarily global in terms of the dissipation function. This relation cannot be inverted in closed form to obtain a relation in terms of a global yield function. Approximations to the yield function are proposed using a maximisation relation, and these predictions of yield are compared with actual yield determined numerically.

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