Young's modulus

The slope of the elastic stress-strain curve#

In a uniaxial test, stress is force divided by cross-sectional area and strain is extension divided by original length. MIT's stress-strain notes define Young's modulus, usually written E, as the proportionality constant where stress and strain have a linear relationship. Its units are pascals because strain is dimensionless.

Material selection for a robot's structural or elastic components needs this relationship to estimate deformation under load.

Material modulus and part stiffness differ#

Combining the notes' stress and strain definitions gives the axial stiffness of a uniform, linearly elastic bar as k = E A / L, where A is area and L is length. Geometry therefore matters as well as material: a longer bar stretches more under the same force if its material and area stay unchanged.

For a series elastic actuator, the complete spring geometry determines the effective stiffness used to relate deflection to force or torque.

Stiffness does not establish strength#

The MIT notes distinguish elastic slope, yield stress, and ultimate tensile strength. A high modulus does not by itself establish a high failure load. The linear relation also stops describing the whole response when the material enters nonlinear deformation or plastic flow. Use the relevant stress-strain range rather than extrapolating one modulus to every load.