MAT-34

Shear modulus G=E/2(1+ν)

G = E / [2(1+ν)]. The isotropic relation between E, G and ν.

Reading speed

ElasticityIsotropic elasticity

Governing equation

G=\dfrac{E}{2(1+\nu)}

where

E: Young modulus (GPa)
\nu: Poisson ratio (—)
G: Shear modulus (GPa)

Lecture brief

Historical brief

Hooke (1678), Hall–Petch grain size, Arrhenius activation and Paris fatigue-crack growth are the spine of materials selection. The sheets relate stress, microstructure and life. This sheet (MAT-34 — Shear modulus G=E/2(1+ν)) is the form associated with Isotropic elasticity. Working symbols: $E$ , $\nu$ $\rightarrow$ $G$ . Simple shear and uniaxial tension share the same stiffness tensor. Eliminating λ between the Lamé pair yields G = E/2(1+ν).

Purpose

Purpose: compute

G

from

E

\nu

in Materials via

G=\dfrac{E}{2(1+\nu)}

G = E / [2(1+ν)]. The isotropic relation between E, G and ν. Use it when a real materials question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

E = 200.000\,\mathrm{GPa}

\nu = 0.300\,\mathrm{—}

, the governing relation

G=\dfrac{E}{2(1+\nu)}

yields

G = 76.92\,\mathrm{GPa}

. A shear rectangle, an E bar, a G bar. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Young modulus E200 GPaPoisson ratio \nu0.3 —

Outputs

Shear modulus G76.92 GPa

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

A shear rectangle, an E bar, a G bar.

Simple shear and uniaxial tension share the same stiffness tensor. Eliminating λ between the Lamé pair yields G = E/2(1+ν).

Reading speed

Watch on YouTube