Deeper Elasticity Closure Scans

Strain Length Extension Inversion Three-Row Scan

A strain ratio and original length recover the exact extension. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Strain and original length can be inverted to recover extension

The dimensionless strain 1 over 2 acts on original length 6 m to give extension 3 m. The length vector and extension vector are checked separately.

ΔL=ϵL0=12×6 m=3 m\Delta L=\epsilon L_0=\frac{1}{2}\times6\ \text{m}=3\ \text{m}
Strain inversion rowThe extension is recovered from the checked strain ratio.original lengthextensionoriginalLength=6 mextension=3 mstrain=1/2

Strain and original length can be inverted to recover extension

The dimensionless strain 1 over 3 acts on original length 12 m to give extension 4 m. The length vector and extension vector are checked separately.

ΔL=ϵL0=13×12 m=4 m\Delta L=\epsilon L_0=\frac{1}{3}\times12\ \text{m}=4\ \text{m}
Strain inversion rowThe extension is recovered from the checked strain ratio.original lengthextensionoriginalLength=12 mextension=4 mstrain=1/3

Strain and original length can be inverted to recover extension

The dimensionless strain 1 over 5 acts on original length 15 m to give extension 3 m. The length vector and extension vector are checked separately.

ΔL=ϵL0=15×15 m=3 m\Delta L=\epsilon L_0=\frac{1}{5}\times15\ \text{m}=3\ \text{m}
Strain inversion rowThe extension is recovered from the checked strain ratio.original lengthextensionoriginalLength=15 mextension=3 mstrain=1/5