标题： 具有最近邻和次近邻相互作用的梯度弹性晶格模型 显示英文标题

标题： Lattice Model with Nearest-Neighbor and Next-Nearest-Neighbor Interactions for Gradient Elasticity

摘要： 讨论了弹性理论中二阶应变梯度模型的格子模型。 为了结合两类二阶梯度模型的优点，我们提出了一种新的格子模型，该模型可以被视为梯度连续介质模型的离散微观结构基础。 证明了两类二阶梯度模型（梯度前有正号和负号）可以有一个通用的格子模型作为其微观结构基础。 为了获得二阶梯度连续介质模型，我们考虑了一个具有最近邻和次近邻相互作用的格子模型，其中有两个不同的耦合常数。 所提出的格子模型统一描述了具有应变梯度项正负号的二阶梯度模型。 梯度前的符号由最近邻和次近邻相互作用的耦合常数之间的关系决定。 显示英文摘要

摘要： Lattice models for the second-order strain-gradient models of elasticity theory are discussed. To combine the advantageous properties of two classes of second-gradient 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 second-gradient models (with positive and negative sign in front the gradient) can have a general lattice model as a microstructural basis. To obtain the second-gradient continuum models we consider a lattice model with the nearest-neighbor and next-nearest-neighbor interactions with two different coupling constants. The suggested lattice model gives unified description of the second-gradient 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 nearest-neighbor and next-nearest-neighbor interactions.