Stiffness

Lore & Background

Stiffness is defined for an elastic body with a single degree of freedom as the ratio of applied force to the resulting displacement, k = F/δ. For bodies with multiple degrees of freedom, a matrix of stiffness coefficients is used, including direct-related stiffnesses on the diagonal and coupling stiffnesses off the diagonal. The inverse of stiffness is compliance, measured in meters per newton. Rotational stiffness is defined as the ratio of applied moment to rotation angle, k = M/θ, with units of newton-metres per radian in SI.

Reader's Guide

Stiffness is a critical property in engineering design, as it determines how much a structure deflects under load. It is distinct from the elastic modulus of a material; stiffness is an extensive property dependent on the material, shape, and boundary conditions, while elastic modulus is an intensive material property. For example, axial stiffness of a rod is 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—related to stiffness—is assessed using devices like the Cutometer to distinguish healthy skin from pathological scarring. The concept is applied in clinical and industrial settings to monitor treatments and pathophysiological changes.

Did You Know?

• Stiffness is typically measured in newtons per meter in SI units and pounds per inch in Imperial units.
• For a body with multiple degrees of freedom, a matrix of stiffness coefficients is used, with off-diagonal terms called coupling stiffnesses.
• The elastic modulus of a material is an intensive property, while stiffness is an extensive property dependent on shape and boundary conditions.
• In biology, the stiffness of the extracellular matrix is important for guiding cell migration in a phenomenon called durotaxis.