wrong-strain-rejects-the-modulus - Elasticity: Stress, Strain, and Material Response Step by Step

A same-looking modulus claim fails when its cited strain source changes. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The rejected claim still cites real sources

The stress and strain sources are valid. The rejection comes from the claimed modulus failing their exact quotient.

\sigma=4\ \text{Pa}\qquad \epsilon=\frac{1}{8}

Changing the strain source changes the required modulus

Two rows are internally consistent. The final row keeps the small strain source but claims the wrong modulus.

\begin{array}{c|c|c|c}\sigma&\epsilon&E&\text{accepted}\\4\ \text{Pa}&\frac{1}{8}&32\ \text{Pa}&1\\4\ \text{Pa}&\frac{1}{4}&16\ \text{Pa}&1\\4\ \text{Pa}&\frac{1}{8}&16\ \text{Pa}&0\\\end{array}

A wrong strain source rejects the claimed modulus

The displayed modulus is not trusted because the cited strain makes the exact quotient different.

\frac{4\ \text{Pa}}{\frac{1}{8}}=32\ \text{Pa}\ne16\ \text{Pa};\quad \text{accepted}=0