Mechanical Strain: Measures, Deformation Regimes, and the Strain Tensor

All flashcards

Why is strain dimensionless?

Strain compares lengths, so the units in its numerator and denominator cancel.

What is engineering strain?

The change in length divided by the original length: $e = \frac{l-L}{L}$.

What does engineering shear strain measure?

The tangent of the angular change between material lines initially perpendicular to each other.

When is infinitesimal-strain theory appropriate?

When both strains and rotations are small enough for the configurations to be treated as nearly identical.

What does a metric tensor determine?

The squared length of a vector, providing a geometric way to describe lengths and angles.

Quiz questions

1. A line has original length $L$ and final length $l$. Which expression gives its engineering strain?Answer: $e = \frac{l-L}{L}$
2. What is the stretch ratio of a material line that undergoes no change in length?Answer: $\lambda = 1$
3. Which expression defines logarithmic strain in terms of stretch ratio $\lambda$?Answer: $\varepsilon = \ln(\lambda)$
4. In the infinitesimal strain tensor, how is the tensor component $\varepsilon_{xy}$ related to engineering shear strain $\gamma_{xy}$?Answer: $\varepsilon_{xy} = \frac{\gamma_{xy}}{2}$
5. Which deformation theory accommodates both large strains and large rotations?Answer: Finite-strain theory