Universal Law for the Elastic Moduli of Solids and Structures

TL;DR

This paper introduces a universal law linking all elastic moduli of solids to their specific volume, supported by extensive experimental data across diverse materials, enabling accurate predictions of their elastic properties.

Contribution

It generalizes a previously known law for shear moduli to all elastic moduli, providing a unified analytical and empirical framework for solids and structures.

Findings

Elastic moduli depend solely on specific volume.

The law accurately predicts bulk moduli across various materials.

Experimental validation includes metals, ceramics, foams, and metamaterials.

Abstract

A law previously found for shear moduli of crystalline materials is developed and extended to all elastic moduli in solids and structures. Shear moduli were previously shown to depend only on specific volume. The bulk moduli of many materials and structures are now predicted analytically and empirically shown with unerring accuracy by observing the elasticity as a specific volume power law. The law is supported by experimental evidence from: foams, Schneebeli 2-dimensional graphene mats, metamaterials, fully dense metals, ceramics and minerals. This new, generalized, universal, elastic moduli law always describes materials that support shear stresses i.e., solids; it is shown that all elastic moduli are directly dependent only on the specific volume.