SIPS 2016 Volume 7: Yang Intl. Symp. / Multiscale Material Mechanics

Editors: | Kongoli F, Aifantis E, Wang H, Zhu T |

Publisher: | Flogen Star OUTREACH |

Publication Year: | 2016 |

Pages: | 190 pages |

ISBN: | 978-1-987820-48-5 |

ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |

The analytical shear band-type solutions are obtained at different periods for steady- state softening and hardening materials for the finite domain. For this purpose, strain gradient plasticity theory is discussed in detail and the constitutive equation for the gradient plasticity is solved using the analytic technique, i.e. homotopy analysis method (HAM), which is also constructed step by step, analyzed and implemented. The nonlinear governing partial differential equation is reduced to the non-dimensionalized nonlinear ordinary differential equation by using the appropriate similarity transformations. Convergent solutions are obtained with the help of optimal convergence-control parameter. Moreover, the error analysis has been performed to guarantee the convergence of our series solution. This present contribution addresses that HAM is a powerful tool for solving a complicated nonlinear problem and it deserves to be applied for more problems in deformation patterning phenomenon.

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