A measure of the stiffness of an elastic material defined by stress/strain?

• A. Young's Modulus
• B. Hardness
• C. Toughness
• D. Shear Modulus

Answer: (A)

Stiffness under axial loading is captured by how much strain results from a given stress. The proportionality constant in that relationship is Young's modulus, so stress divided by strain in the elastic regime defines stiffness. In other words, when you apply a load along the length, the slope of the stress–strain curve in the elastic area equals Young's modulus, and a larger value means the material is stiffer. Hardness relates to resistance to surface indentation, not how much the material stretches under a load. Toughness measures the energy a material can absorb before fracturing, which is about resilience rather than the immediate stretch under a given stress. The shear modulus describes stiffness under shear deformations, a different mode of loading from axial tension or compression. Hence, the ratio of stress to strain for axial loading identifies Young's modulus as the measure of stiffness.