2016-Sustainable Industrial Processing Summit
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) |
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Peridynamic Green¡¯s Functions for Elasticity and Diffusion
Jianxiang Wang1;1PEKING UNIVERSITY, Beijing, China;
Type of Paper: Regular
Id Paper: 480
Topic: 1
Abstract:
The peridynamic theory replaces the conventional differential equation of motion of continuum mechanics with an integral formula, leading to a strongly non-local theory that accounts for long range interactions among material points. It also facilitates treatment of discontinuities, initiation and evolution of damage in continua. We will present the solutions of the Green¡¯s functions for point forces in one-, two- and three-dimensional domains, as well as the Green¡¯s functions for general diffusion problems within the formalism of peridynamics. We show that these peridynamic Green¡¯s functions can be uniformly expressed as classical solutions plus Dirac functions, and convergent non-local integrals. They have different values close to the source of loading, but approach the classical theory when the non-local length tends to zero or the considered material point is far away from the loading point. The Green¡¯s functions can be used to develop methods to solve elastic and diffusion problems in infinite, semi-infinite and finite domains.
Keywords: Peridynamic theory, Green¡¯s functions, Elasticity, Diffusion