How to Determine Young's Modulus and Poisson's Ratio from Elastic Stiffnesses?

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In summary, the conversation is about determining Young's modulus and Poisson's ratio from the elastic stiffnesses of a cubic crystal being stressed along the x axis. The initial dimensions are given as L*w and change to (L+delta L)*(w-delta w). The discussion also involves the relationship between stresses, strains, lengths, and elastic stiffnesses through Hooke's law and the Poisson coefficient.
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RAD17
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I need to determine Young's modulus and Poisson's ratio from the elastic stiffnesses for a cubic crystal that is being stressed along the x axis.
It is initially L *w and goes to (L+delta L)*(w - delta w). Where w is along the x-axis and L is along the y axis. How do I change stresses and strains along with lengths into elastic stiffnesses?
 
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RAD17 said:
I need to determine Young's modulus and Poisson's ratio from the elastic stiffnesses for a cubic crystal that is being stressed along the x axis.
It is initially L *w and goes to (L+delta L)*(w - delta w). Where w is along the x-axis and L is along the y axis. How do I change stresses and strains along with lengths into elastic stiffnesses?

What exactly do you mean by ' L*w '? Do you know the stresses?
 
  • #3
Looking into some elasticity book you'll find:

-The change in volume of the cube is relationed to the poisson coefficient, such that for poisson coefficients 1/2 the body is incompressible.

-The stresses, deformations, elastic modulii and poisson coefficient are relationed through the Hooke's law.
 

FAQ: How to Determine Young's Modulus and Poisson's Ratio from Elastic Stiffnesses?

What is Young's Modulus?

Young's Modulus, also known as the Elastic Modulus, is a measure of the stiffness or elasticity of a material. It is defined as the ratio of stress to strain within the elastic limit of a material.

What is the formula for calculating Young's Modulus?

The formula for Young's Modulus is E = σ / ε, where E is the Young's Modulus, σ is the stress applied to the material, and ε is the resulting strain.

What is Poisson Ratio?

Poisson Ratio is a measure of the lateral contraction or expansion of a material when it is under compression or tension. It is defined as the ratio of the transverse strain to the axial strain.

How is Poisson Ratio related to Young's Modulus?

Poisson Ratio and Young's Modulus are related through the formula ν = -ε_x / ε_y, where ν is the Poisson Ratio, ε_x is the transverse strain, and ε_y is the axial strain. In other words, Poisson Ratio is a measure of how much a material will change in width when it is stretched or compressed, and it is inversely proportional to Young's Modulus.

What are the units of Young's Modulus and Poisson Ratio?

The units of Young's Modulus are usually expressed in pascals (Pa) or newtons per square meter (N/m^2). The units of Poisson Ratio are dimensionless, as it is a ratio of two strains.

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