Cauchy Strain with Length Calculator

What is Cauchy Strain?

Cauchy strain, also known as engineering strain, is a measure of deformation that represents the relative change in length of a material under stress. It is a fundamental concept in materials science and engineering, used to quantify how much a material stretches or compresses relative to its original length.

Formula

The formula for Cauchy strain is:

\[ \varepsilon = \frac{L - L_0}{L_0} \]

Where:

• \( \varepsilon \) is the Cauchy strain (dimensionless)
• \( L \) is the final length of the material
• \( L_0 \) is the initial length of the material

Calculation Steps

Let's calculate the Cauchy strain for a material that has been stretched:

1. Given:
   • Initial length (\( L_0 \)) = 100 mm
   • Final length (\( L \)) = 105 mm
2. Apply the Cauchy strain formula: \[ \varepsilon = \frac{L - L_0}{L_0} \]
3. Substitute the known values: \[ \varepsilon = \frac{105 \text{ mm} - 100 \text{ mm}}{100 \text{ mm}} \]
4. Perform the calculation: \[ \varepsilon = \frac{5 \text{ mm}}{100 \text{ mm}} = 0.05 \]
5. Express the result as a percentage: \[ \varepsilon = 0.05 = 5\% \]

Example and Visual Representation

Let's visualize the Cauchy strain in a material:

This diagram illustrates:

• The initial length (\( L_0 \)) of the material (blue line)
• The final length (\( L \)) after stretching (green line)
• The change in length (\( \Delta L \)) (red line)
• The Cauchy strain (\( \varepsilon \)) as the ratio of elongation to initial length