indéformables

Indéformables is a term used in mechanics, derived from French, to describe bodies that do not deform when subjected to external forces. In English-language literature the closest standard concept is a rigid body. Indéformables are idealizations: while real materials deform under load, certain objects or problems can be modeled as rigid to simplify analysis.

In continuum mechanics, a rigid body is defined by the property that the distance between any two material points remains constant in time. Consequently its motion can be described as a rigid motion, consisting of a translation plus a rotation. If x represents a point in the body’s reference configuration, its current position can be written as X(t) = a(t) + R(t) x, where a is a translation vector and R is a rotation matrix. This framework implies that internal strain is zero and shape is preserved during the motion, even though the body as a whole may move and rotate.

Indéformables provide a useful approximation when material stiffness is very high or deformations are small relative to the scale of motion. They enable simpler equations of motion and straightforward kinematic descriptions. In real materials, elasticity and plasticity govern deformation, and more sophisticated models treat bodies as deformable continua or use finite-element methods to capture strains and stresses.

Applications of the indéformables concept appear in various fields, including celestial mechanics (attitude dynamics of satellites), robotics (rigid-link mechanisms), computer graphics (rigid-body simulations), and classical mechanics education. The concept contrasts with deformable bodies, where internal deformations are essential to the analysis.