elasticity-audit-cites-every-source - Elasticity: Stress, Strain, and Material Response Step by Step

The final material-response ledger accepts only a coherent source chain. 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 audit starts as a source map

The final claim is only accepted when every source role is present: stress, strain, Young modulus, bar force, shear, and bulk.

\text{sources}=6\qquad \text{accepted}=1

The audit inventory lists checked source values

These are not new calculations. The table collects values already bound by the earlier stress, modulus, bar, shear, and bulk checks.

\begin{array}{c|c|c}\text{source}&\text{value}&\text{unit}\\\text{stress}&4\ \text{Pa}&\text{Pa}\\\text{strain}&\frac{1}{4}&\text{ratio}\\\text{young}&16\ \text{Pa}&\text{Pa}\\\text{bar}&4\ \text{N}&\text{N}\\\text{shear}&9\ \text{Pa}&\text{Pa}\\\text{bulk}&2\ \text{Pa}&\text{Pa}\\\end{array}

The accepted elasticity claim cites every source

The audit accepts only the pinned chain of stress, strain, Young modulus, bar force, shear modulus, and bulk pressure.

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