Net work done equals hysteresis loop area

Steps:

• Trace loading curve: work input is area under curve from origin to max extension.
• Trace unloading curve: work output is area under curve from max to zero force (permanent extension).
• Subtract unloading area from loading area: difference is enclosed hysteresis loop.
• Identify loop area as X+Y on graph.

Why B is correct:

• X+Y is hysteresis loop area, defined as net work on sample (energy dissipated as heat, per work-energy principle).

Why the others are wrong:

• A: X is partial loading area, ignores unloading recovery.
• C: Y+Z combines dissipation and recovery, overstates net input.
• D: Z is unloading recovery area, represents elastic energy returned, not net.

Final answer: B