Question

True strain (\( \varepsilon \)) and engineering strain (\( e \)) are related by

• A. \( \varepsilon = 1 + e \)
• B. \( \varepsilon = \ln(1 + e) \)
• C. \( e = \ln(1 + \varepsilon) \)
• D. \( \varepsilon = \dfrac{1}{1 + e} \)

Hint:

Use true strain for large deformation problems as it provides more accurate results. Engineering strain is linear and suitable only for small deformations.

Answer 1

The Correct Option is B

Step 1: Definitions - Engineering strain (\( e \)) is defined as: \[ e = \frac{\Delta L}{L_0} \] where \( \Delta L \) is the change in length and \( L_0 \) is the original length. - True strain (\( \varepsilon \)) accounts for the continuous change in length during deformation, and is defined as: \[ \varepsilon = \int_{L_0}^{L} \frac{dL}{L} = \ln\left( \frac{L}{L_0} \right) \] Step 2: Relationship Between \( \varepsilon \) and \( e \) Since: \[ \frac{L}{L_0} = 1 + e \] Substituting into the true strain formula: \[ \varepsilon = \ln(1 + e) \]