2015-Sustainable Industrial Processing Summit
SIPS 2015 Volume 1: Aifantis Intl. Symp. / Multiscale Material Mechanics
| Editors: | Kongoli F, Bordas S, Estrin Y |
| Publisher: | Flogen Star OUTREACH |
| Publication Year: | 2015 |
| Pages: | 300 pages |
| ISBN: | 978-1-987820-24-9 |
| ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |
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Determination of Nanoscopic Parameters in Second Strain Gradient Elasticity
Farzaneh Ojaghnezhad1; Hossein Shodja2;1, Karaj, Iran (Islamic Republic of Iran); 2SHARIF UNIVERSITY OF TECHNOLOGY, Tehran, Iran (Islamic Republic of Iran);
Type of Paper: Regular
Id Paper: 434
Topic: 1
Abstract:
Mindlin's second strain gradient theory, due to its competency in capturing the surface effects, is of particular interest. For a homogeneous, centrosymmetric and isotropic material, formulation in this framework introduces sixteen additional constants. Fifteen parameters bring up four characteristic lengths associated with bulk and another one associated with surface. Bulk characteristic lengths and Lame constants appear in equilibrium equations, while surface characteristic length enters the formulation through boundary conditions. The remaining parameter is modulus of cohesion characterizing the surface effect. To date, there are no successful experimentations measuring these internal length scales. Due to the lack of experimental and computational data, quantitative analyses based on these enriched theories have been impossible. The present work gives an accurate remedy for the calculation of these parameters by utilizing an analytical formulation in lattice dynamics combined with the first principles. From the equivalency between the atomistic crystal lattice dynamics of bulk and its counterpart in second strain gradient elasticity, bulk characteristic lengths are expressed in terms of atomic force constants. Additionally, considering a free standing film that brings the surface effect into account, analytical expressions for surface energy and change in film thickness are obtained in terms of modulus of cohesion, Lame constants, surface and bulk characteristic lengths and film thickness. The numerical values of atomic force constants, surface energy and change in film thickness are calculated using ab initio simulations and subsequently bulk and surface characteristic lengths and modulus of cohesion are evaluated from the developed analytical expressions.
Keywords:
Characterization; Crystal; Mechanics; Nanoscale; Surface;References:
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