General Lattice Model of Gradient Elasticity

TL;DR

This paper introduces a new lattice model for gradient elasticity that provides a microstructural foundation for second-order strain-gradient theories, accommodating both positive and negative gradient signs and suggesting extensions to higher orders and 3D cases.

Contribution

A novel lattice-based framework for gradient elasticity that unifies models with different gradient signs and extends to higher-order and three-dimensional elasticity.

Findings

Provides a microstructural basis for second-order strain-gradient elasticity.

Unifies gradient models with positive and negative signs.

Suggests extensions to high-order and 3D gradient elasticity.

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.