Question

The true strain ($\epsilon$) and engineering strain (e) are related by

• A. $\epsilon=\ln(e)$
• B. $e=\ln(\epsilon)$
• C. $\epsilon=\ln(1+e)$
• D. $e=\ln(1+\epsilon)$

Hint:

True strain is always more accurate at large deformation.

Answer 1

The Correct Option is C

Concept: Strain measures deformation. Engineering strain assumes constant original length, while true strain accounts for continuous change in length.

Step 1: Definition of engineering strain.
\[ e = \frac{L - L_0}{L_0} \]

Step 2: Definition of true strain.
True strain is incremental: \[ d\epsilon = \frac{dL}{L} \] Integrating: \[ \epsilon = \int_{L_0}^{L} \frac{dL}{L} \] \[ \epsilon = \ln\left(\frac{L}{L_0}\right) \]

Step 3: Relating both strains.
Since: \[ \frac{L}{L_0} = 1 + e \] Thus: \[ \epsilon = \ln(1+e) \] Final Answer: \[ \boxed{\epsilon = \ln(1+e)} \]