Discontinuity, Nonlinearity, and Complexity
Lattice Model with NearestNeighbor and NextNearestNeighbor Interactions for Gradient Elasticity
Discontinuity, Nonlinearity, and Complexity 4(1) (2015) 1123  DOI:10.5890/DNC.2015.03.002
Vasily E. Tarasov
Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, Russia
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Abstract
Lattice models for the secondorder straingradient models of elasticity theory are discussed. To combine the advantageous properties of two classes of secondgradient models, we suggest a new lattice model that can be considered as a discrete microstructural basis for gradient continuum models. It was proved that two classes of the secondgradient models (with positive and negative sign in front the gradient) can have a general lattice model as a microstructural basis. To obtain the secondgradient continuum models we consider a lattice model with the nearestneighbor and nextnearestneighbor interactions with two different coupling constants. The suggested lattice model gives unified description of the secondgradient models with positive and negative signs of the strain gradient terms. The sign in front the gradient is determined by the relation of the coupling constants of the nearestneighbor and nextnearestneighbor interactions.
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