MAT-39

True strain

Logarithmic strain.

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GoverningTrue strain

Governing equation

\varepsilon_t=\ln(1+\varepsilon)

$eps \in \left[0, 1.2\right]$

where

eps: eps (—)
et: True strain (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\varepsilon_t=\ln(1+\varepsilon)

$eps \in \left[0, 1.2\right]$

$eps = 0$ $et = 0$

Along the curve

②

Domain of the variable — blue

eps_{\min} = 0,\quad eps_{\max} = 1.2

$eps \in \left[0, 1.2\right]$

$eps = 0$ $eps = 0$

Along the curve

③

Response curve — green

\varepsilon_t=\ln(1+\varepsilon)

$eps \in \left[0, 1.2\right]$

$eps = 0$ $et = 0$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}et}{\mathrm{d}eps}

$eps \in \left[0, 1.2\right]$

$eps = 0.008$ $et^{\prime} = 0.993$

Along the curve

Lecture brief

Historical brief

Hooke (1678), Hall–Petch grain size, Arrhenius activation and Paris fatigue-crack growth are the spine of materials selection. The sheets relate stress, microstructure and life. This sheet (MAT-39 — True strain) is the form associated with True strain. Working symbols: $eps$ $\rightarrow$ $et$ . Logarithmic strain. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

et

from

eps

in Materials via

\varepsilon_t=\ln(1+\varepsilon)

Logarithmic strain. Use it when a real materials question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

eps = 0.200\,\mathrm{—}

, the governing relation

\varepsilon_t=\ln(1+\varepsilon)

yields

et = 0.182\,\mathrm{—}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

eps eps0.2 —

Outputs

True strain et0.182 —

Reading speed

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Logarithmic strain. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube