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

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.

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.