# What is Poisson's ratio and how does it relate to stress and strain?

• Engineering
• joemte
In summary, Poisson's ratio is a measure of a material's response to stress in different directions, calculated by dividing lateral strain by axial strain. It affects the stress-strain relationship by indicating how a material will deform when under stress. In materials science, it is significant in predicting behavior and aiding in material selection. It can be negative for certain anisotropic materials, and is directly related to stress in a material.
joemte
Homework Statement
A tensile test is performed on a 10mm thick sample of nylon with a width of 20mm. The sample was tested to fracture and had a total length of 94mm (original 90mm) at 33kN. Calculate the stress at the point of failure.
Relevant Equations
none.
I'm working through the equations and I have a lot of information missing. I have calculated the longitudinal strain to be 0.4mm (4/90)

is the lateral strain directly proportional to the longitudinal strain? As I need to work out poisson's ratio in order to calculate Bulk modulus, then youngs modulus, then finally stress (stress= E * stain)

I have calculated Shear modulus to be 0.37

Strain is dimensionless (change in length) ÷ (original length). If it is Engineering Stress, the original cross-sectional area is used.

## 1. What is Poisson's ratio?

Poisson's ratio is a material property that describes the ratio of the lateral strain (perpendicular to the applied force) to the axial strain (parallel to the applied force) when a material is subjected to stress. It is denoted by the Greek letter ν (nu) and is typically represented as a decimal or fraction.

## 2. How is Poisson's ratio calculated?

Poisson's ratio can be calculated by dividing the lateral strain by the axial strain, or by using the Young's modulus (a measure of a material's stiffness) and the shear modulus (a measure of a material's resistance to deformation). The formula is ν = (lateral strain/axial strain) = E/(2G), where E is the Young's modulus and G is the shear modulus.

## 3. What is the range of values for Poisson's ratio?

Poisson's ratio can range from -1 to 0.5, with most materials falling between 0 and 0.5. Negative values indicate a material that expands laterally when stretched, while positive values indicate a material that contracts laterally when stretched. A value of 0.5 represents a perfectly incompressible material.

## 4. How does Poisson's ratio relate to stress and strain?

Poisson's ratio is a measure of a material's response to stress and strain. It describes the relationship between the forces applied to a material and the resulting deformation or change in shape. Materials with a low Poisson's ratio are more resistant to deformation, while those with a high Poisson's ratio are more easily deformed.

## 5. How does Poisson's ratio affect the behavior of materials?

Poisson's ratio affects the mechanical properties of materials, such as their stiffness, strength, and ductility. Materials with a lower Poisson's ratio tend to be stiffer and stronger, while those with a higher Poisson's ratio tend to be more flexible and ductile. Poisson's ratio also plays a role in determining the stability and failure modes of materials under different types of stress.

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