How is the modulus of resilience defined?

• A. Energy per unit volume stored up to the yield point
• B. Energy per unit volume stored up to the ultimate tensile strength
• C. Area under the entire stress–strain curve
• D. Stress at yield

Answer: (A)

Modulus of resilience is the energy per unit volume a material can store elastically, up to the yield point. It represents the recoverable energy contained in the elastic portion of the stress–strain curve from zero strain to the yield strain. Beyond yield, deformation becomes plastic and that energy is no longer recoverable, so it doesn’t contribute to resilience. The energy up to the ultimate tensile strength or the entire area under the curve relates to other concepts (toughness), and the stress at yield is just a strength value, not an energy measure. For linear elastic materials, resilience can be expressed as sigma_y^2/(2E), but the core idea is the elastic energy up to yielding.