stress-over-strain-defines-young-modulus - Elasticity: Stress, Strain, and Material Response Step by Step

Young modulus is accepted only from checked stress and strain sources. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Young modulus starts from stress and strain sources

The modulus step cites two prior ledgers. The stress value and strain value must both be source-bound.

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

Only the matching quotient is accepted

Hold strain fixed and compare three claimed moduli. Only the row whose quotient equals the claim is accepted.

\begin{array}{c|c|c|c}\sigma&\epsilon&E&\text{accepted}\\2\ \text{Pa}&\frac{1}{4}&16\ \text{Pa}&0\\4\ \text{Pa}&\frac{1}{4}&16\ \text{Pa}&1\\8\ \text{Pa}&\frac{1}{4}&16\ \text{Pa}&0\\\end{array}

Young modulus cites checked stress and checked strain

The modulus accepts because the stress source and strain source are both pinned to the ledger.

E=\frac{\sigma}{\epsilon}=\frac{4\ \text{Pa}}{\frac{1}{4}}=16\ \text{Pa};\quad \text{accepted}=1