2022-Sustainable Industrial Processing Summit
SIPS2022 Volume 3
Horstemeyer Intl.Symp.
Multiscale Materials Mechanics & Applications
| Editors: | F. Kongoli,E. Aifantis, A, Konstantinidis, D, Bammann, J. Boumgardner, K, Johnson, N, Morgan, R. Prabhu, A. Rajendran |
| Publisher: | Flogen Star OUTREACH |
| Publication date: | 22 December 2022 |
| Pages: | 382 pages |
| ISBN: | 978-1-989820-38-4(CD) |
| ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |
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Atomistic-based strain gradient elasticity theory, in the framework of finite deformations
Luca Placidi1;1INT. TELEMATIC U, Rome, Italy;
Type of Paper: Keynote
Id Paper: 294
Topic: 1
Abstract:
Atomistic-based strain gradient elasticity theory, in the framework of finite deformations, is proposed.
As a fundamental quantity of this approach, an objective relative displacement between atomic-pairs is considered. Besides, a deformation energy of an atomic-pair is defined in terms of such a measure in the form of a Lennard-Jones type potential.
Thus, the objective relative displacement between atomic-pairs has been Taylor's series expanded up to second order in order to obtain the deformation energy of atomic-pairs in terms of (i) non-linear strain (the Green-Saint-Venant tensor), (ii) its gradient, (iii) the orientation of the atomic-pair and (iv) Lennard-Jones coefficients, including the inter-atomic distance.
The strain energy of the continuum is assumed to be the integral over the unit sphere of the previous Lennard-Jones potential and the isotropic case will be obtained by assuming the independence of the Lennard-Jones coefficients with respect to the inter-atomic orientation.