Calculator for Exploring Relations Among the Elastic Constants
engineering fundamentals Elastic Constant Converter
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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 - -

 
For the case of {E, l} input, the factor R is defined as,

The 2nd Law of Thermodynamics requires that the following limits hold on the elastic constants,

E, G, and K > 0

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