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 Year: | 2022 |

Pages: | 382 pages |

ISBN: | 978-1-989820-38-4(CD) |

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

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.