Calculator for Exploring Relations Among the Elastic Constants

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Calculators

Calculator Introduction

For isotropic materials, only two independent elastic constants are needed for describing the stress-strain relationship, i.e., Hooke's Law.

This calculator computes the inter-relations among the 5 commonly used elastic constants:

Symbol	Name	Other Names
E	Youngs modulus	Elastic modulus, tension modulus
n	Poisson ratio
G or m	Shear modulus	Rigidity modulus, 2nd Lamé constant
K	Bulk modulus	Compression modulus
l	1st Lamé constant

Select 2 constants for input, and calculate the rest.

Input

Units for modulii (E, G, K, l)

Answer

Young's Modulus E: 70.00 GPa

Poisson's Ratio n: 0.30

Shear Modulus G: 26.92 GPa

Bulk Modulus K: 58.33 GPa

Lamé's Constant l: 40.38 GPa

Table of Relations among Elastic Constants

The relationships amongst the 5 elastic constants are shown in the table below.

Input
Constants Output Relations

E = n = G = K = l =

E, n - -

E, G - -

E, K - -

E, l - -

n, G - -

n, K - -

n, l - -

G, K - -

G, l - -

K, l - -