A lattice model describing scale effects in nonlinear elasticity of nano-inhomogeneities

TL;DR

This paper develops a lattice model to analyze how atomistic effects influence the nonlinear elastic behavior of nano-inhomogeneities, revealing a universal scaling law at the nanoscale.

Contribution

It introduces a method to map continuum elasticity laws onto a discrete lattice to study nanoscale elastic behavior, highlighting atomistic effects and universal scaling.

Findings

Atomistic effects significantly influence nanoscale elastic properties.

Linear and nonlinear elastic behaviors share the same scaling exponent.

Elastic behaviors at the nanoscale belong to the same universality class.

Abstract

We present a procedure to map the constitutive laws of elasticity (both in the linear and nonlinear regime) onto a discrete atomic lattice and we apply the resulting elastic lattice model to investigate the strain field within an embedded nano-inhomogeneity. We prove that its elastic behavior at the nanoscale is governed by relevant atomistic effects. In particular, we demonstrate that such effects on the linear and nonlinear elastic properties are described by the same scaling exponent, in a large range of elastic contrast between the matrix and the nano-inhomogeneity. This suggests that the linear and nonlinear elastic behaviors of the composite system belong to the same universality class (at least within the nanometer length scale here investigated).