Area under stress-strain curve represents energy density

Steps:

• Stress (y-axis) is force per unit cross-sectional area; strain (x-axis) is fractional extension.
• The graph shows material response to loading; shaded area integrates stress over strain.
• Mathematically, area = ∫σ dε, which equals elastic strain energy stored per unit volume.
• For the whole wire, total energy = area × volume, but the graph directly gives per-unit-volume value, interpreted as strain energy capacity in the wire.

Why A is correct:

• By definition, the area under a stress-strain curve is the strain energy density (J/m³) stored in the material up to that strain.

Why the others are wrong:

• B: Cross-sectional area is a fixed geometric property, not derived from graph integration.
• C: Same as B; it's not represented by the curve's area.
• D: Original length affects strain calculation (strain = ΔL/L₀) but isn't the area under the curve.

Final answer: A