Stiffness

Lore & Background

Stiffness is defined for an elastic body with a single degree of freedom as the ratio of applied force to displacement (k = F/δ). For multiple degrees of freedom, an M×M matrix is used, with diagonal terms representing direct stiffness and off-diagonal terms representing coupling stiffness. The International System of Units measures stiffness in newtons per meter, while Imperial units use pounds per inch.

Reader's Guide

Stiffness is a property of a structure or component, distinct from the elastic modulus of the material. For a rod in tension or compression, axial stiffness is given by k = E·A/L, where E is Young's modulus, A is cross-sectional area, and L is length. Torsional stiffness is k = G·J/L, with G as the rigidity modulus and J as the torsion constant. In biology, stiffness of the extracellular matrix guides cell migration (durotaxis), and skin pliability—encompassing elasticity, stiffness, and adherence—is evaluated using devices like the Cutometer to distinguish healthy skin from pathological scarring. Stiffness is crucial in engineering for selecting materials based on desired deflection or flexibility.

Did You Know?

• Stiffness is typically measured in newtons per meter in SI units and pounds per inch in Imperial units.
• The inverse of stiffness is flexibility, elasticity, or compliance, measured in meters per newton.
• Rotational stiffness is defined as the ratio of applied moment to rotation angle, measured in newton-metres per radian.
• The elastic modulus is an intensive property of a material, while stiffness is an extensive property dependent on shape and boundary conditions.