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Discrete-to-Continuum Limits of Multibody Systems with Bulk and Surface Long-Range Interactions
Annika Bach, Andrea Braides and Marco Cicalese SIAM Journal on Mathematical Analysis 52(4) 3600 (2020) https://doi.org/10.1137/19M1289212
Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices
Malena I. Español, Dmitry Golovaty and J. Patrick Wilber Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474(2209) 20170612 (2018) https://doi.org/10.1098/rspa.2017.0612
An Integral-Representation Result for Continuum Limits of Discrete Energies with MultiBody Interactions
Nonlocal continuum analysis of a nonlinear uniaxial elastic lattice system under non-uniform axial load
Benjamin Hérisson, Noël Challamel, Vincent Picandet and Arnaud Perrot Physica E: Low-dimensional Systems and Nanostructures 83 378 (2016) https://doi.org/10.1016/j.physe.2016.03.044
Analysis of an optimization-based atomistic-to-continuum coupling method for point defects
Derek Olson, Alexander V. Shapeev, Pavel B. Bochev and Mitchell Luskin ESAIM: Mathematical Modelling and Numerical Analysis 50(1) 1 (2016) https://doi.org/10.1051/m2an/2015023
On a $\Gamma$-Convergence Analysis of a Quasicontinuum Method
Assyr Abdulle, Ping Lin and Alexander V. Shapeev Multiscale Modeling & Simulation 10(3) 696 (2012) https://doi.org/10.1137/110841163
A new adaptive modeling strategy based on optimal control for atomic-to-continuum coupling simulations
H. Ben Dhia, Ludovic Chamoin, J. Tinsley Oden and Serge Prudhomme Computer Methods in Applied Mechanics and Engineering 200(37-40) 2675 (2011) https://doi.org/10.1016/j.cma.2010.12.011
The Cauchy problem for a class of two-dimensional nonlocal nonlinear wave equations governing anti-plane shear motions in elastic materials
I. V. Andrianov, J. Awrejcewicz, D. Weichert and Yuri Vladimirovich Mikhlin Mathematical Problems in Engineering 2010(1) (2010) https://doi.org/10.1155/2010/986242
Global Energy Matching Method for Atomistic-to-Continuum Modeling of Self-Assembling Biopolymer Aggregates
Lei Zhang, Leonid Berlyand, Maxim V. Fedorov and Houman Owhadi Multiscale Modeling & Simulation 8(5) 1958 (2010) https://doi.org/10.1137/090781619
A note on the regularity of reduced models obtained by nonlocal quasi-continuum-like approaches