Deterministic Interrelation Between Elastic Moduli in Critically Elastic Materials

TL;DR

This paper reveals a universal relationship between elastic moduli in critically elastic materials derived from parent systems, enabling deterministic tuning of mechanical properties through constraint removal.

Contribution

It introduces a universal functional form linking elastic moduli in critically elastic materials and demonstrates how to select properties via constraint removal in simulations.

Findings

Elastic moduli are interrelated by a universal functional form.

Simulations show tunable Poisson's ratios and moduli through bond removal.

Framework enables deterministic design of mechanical properties.

Abstract

Critically elastic materials - those that are rigid with a single state of self-stress - can be generated from parent systems with two states of self-stress by the removal of one of many constraints. We show that the elastic moduli of the resulting homogeneous and isotropic daughter systems are interrelated by a universal functional form parametrized by properties of the parent. In simulations of both spring networks and packings of soft spheres, judicious choice of parent systems and bond removal allows for the selection of a wide variety of moduli and Poisson's ratios in the critically elastic systems, providing a framework for versatile deterministic selection of mechanical properties.