General Lattice Model of Gradient Elasticity
arXiv:1501.01435 · doi:10.1142/S0217984914500547
Abstract
New lattice model for the gradient elasticity is suggested. This lattice model gives a microstructural basis for second-order strain-gradient elasticity of continuum that is described by the linear elastic constitutive relation with the negative sign in front of the gradient. Moreover the suggested lattice model allows us to have a unified description of gradient models with positive and negative signs of the strain gradient terms. Possible generalizations of this model for the high-order gradient elasticity and three-dimensional case are also suggested.
arXiv comment18 pages, LaTeX
References in corpus (7)
- Continuous Limit of Discrete Systems with Long-Range Interaction
- Fractional dynamics of coupled oscillators with long-range interaction
- On Dislocations in a Special Class of Generalized Elasticity
- The fundamentals of non-singular dislocations in the theory of gradient elasticity: dislocation loops and straight dislocations
- Map of Discrete System into Continuous
- Lattice Model of Fractional Gradient and Integral Elasticity: Long-Range Interaction of Grunwald-Letnikov-Riesz Type
- Non-singular dislocation loops in gradient elasticity