rigidity

Rigidity is the property of resisting deformation under applied forces or constraints. In physics and engineering, a rigid body is an ideal object whose internal distances remain constant during motion. Real materials are not perfectly rigid; their rigidity is finite and often modeled by stiffness or elastic moduli.

In geometry and kinematics, rigid motions are transformations that preserve distances between all pairs of points, such as rotations and translations. A structure built from joints connected by fixed-length bars is called rigid if its overall shape cannot be flexed without changing bar lengths; if it can flex, it is said to be flexible.

Rigidity theory studies conditions under which a framework is rigid. Local rigidity concerns small deformations; global rigidity means the entire shape is determined up to rigid motion by the bar lengths. In the plane, Laman's theorem gives a combinatorial criterion for minimal rigidity.

Material rigidity relates to stiffness, typically quantified by moduli such as Young's or shear modulus. Designers seek adequate rigidity for load-bearing components while avoiding excessive weight, and anisotropy can cause direction-dependent rigidity.

Beyond engineering, the concept appears in robotics, computer vision, and mathematics, including rigidity in topology and distance geometry. Social or organizational rigidity describes resistance to change in norms or rules.