A 2D novel non-local lattice bond model for initiation and propagation of cracks in rock materials

2021 ◽  
Vol 126 ◽  
pp. 181-199
Author(s):  
Xiao-Ping Zhou ◽  
Liang Fu ◽  
Qi-Hu Qian
Keyword(s):  
Rock Materials ◽  
Bond Model ◽  
Initiation And Propagation ◽  
Local Lattice ◽  
Non Local

A generalized 2D non-local lattice spring model for fracture simulation

2014 ◽  
Vol 54 (6) ◽  
pp. 1541-1558 ◽  
Author(s):  
Hailong Chen ◽  
Enqiang Lin ◽  
Yang Jiao ◽  
Yongming Liu
Keyword(s):  
Spring Model ◽  
Lattice Spring Model ◽  
Fracture Simulation ◽  
Local Lattice ◽  
Non Local

scholarly journals Exit manifolds for lattice differential equations

2011 ◽  
Vol 141 (1) ◽  
pp. 77-92 ◽  
Author(s):  
Aaron Hoffman ◽  
J. Douglas Wright
Keyword(s):  
Differential Equations ◽  
Travelling Waves ◽  
Linear Part ◽  
Original System ◽  
Travelling Wave ◽  
Asymptotically Stable ◽  
Linear Superposition ◽  
Lattice Differential Equations ◽  
Local Lattice ◽  
Non Local

We study the weak interaction between a pair of well-separated coherent structures in possibly non-local lattice differential equations. In particular, we prove that if a lattice differential equation in one space dimension has asymptotically stable (in the sense of a paper by Chow et al.) travelling-wave solutions whose profiles approach limiting equilibria exponentially fast, then the system admits solutions which are nearly the linear superposition of two such travelling waves moving in opposite directions away from one another. Moreover, such solutions are themselves asymptotically stable. This result is meant to complement analytic or numeric studies into interactions of such pulses over finite times which might result in the scenario treated here. Since the travelling waves are moving in opposite directions, these solutions are not shift-periodic and hence the framework of Chow et al. does not apply. We overcome this difficulty by embedding the original system in a larger one wherein the linear part can be written as a shift-periodic piece plus another piece which, although it is non-autonomous and large, has certain properties which allow us to treat it as if it were a small perturbation.

Can a non-local lattice fermion formulation avoid the doubling problem?

1987 ◽  
Vol 193 (2-3) ◽  
pp. 279-282 ◽  
Author(s):  
M. Campostrini ◽  
G. Curci ◽  
A. Pelissetto
Keyword(s):  
Lattice Fermion ◽  
Local Lattice ◽  
Non Local

New non-local lattice models for the description of wave dispersion in concrete

2015 ◽  
Author(s):  
Sokratis N. Iliopoulos ◽  
Demosthenes Polyzos ◽  
Dimitrios G. Aggelis
Keyword(s):  
Lattice Models ◽  
Wave Dispersion ◽  
Local Lattice ◽  
Non Local
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