Effect of architecture disorder on the elastic response of two-dimensional lattice materials

TL;DR

This study investigates how disorder in joint positions affects the elastic properties of two-dimensional lattice materials, revealing that disorder can tune isotropy and stiffness depending on lattice connectivity.

Contribution

It introduces a numerical analysis of disorder effects on elastic behavior in 2D lattice materials, challenging classical views on connectivity and scaling laws.

Findings

Disorder increases isotropy in initially anisotropic lattices.

High connectivity lattices soften with disorder, low connectivity lattices stiffen.

Disorder influences the crossover density between different elastic scaling regimes.

Abstract

We examine how disordering joint position influences the linear elastic behavior of lattice materials via numerical simulations in two-dimensional beam networks. Three distinct initial crystalline geometries are selected as representative of mechanically isotropic materials low connectivity, mechanically isotropic materials with high connectivity, and mechanically anisotropic materials with intermediate connectivity. Introducing disorder generates spatial fluctuations in the elasticity tensor at the local (joint) scale. Proper coarse-graining reveals a well-defined continuum-level scale elasticity tensor. Increasing disorder aids in making initially anisotropic materials more isotropic. The disorder impact on the material stiffness depends on the lattice connectivity: Increasing the disorder softens lattices with high connectivity and stiffens those with low connectivity, without modifying the scaling between elastic modulus and density (linear scaling for high connectivity and cubic scaling for low connectivity). Introducing disorder in lattices with intermediate fixed connectivity reveals both scaling: the linear scaling occurs for low density, the cubic one at high density, and the crossover density increases with disorder. Contrary to classical formulations, this work demonstrates that connectivity is not the sole parameter governing elastic modulus scaling. It offers a promising route to access novel mechanical properties in lattice materials via disordering the architectures.