Cauchy–Born rule

The Cauchy–Born rule or Cauchy–Born approximation is a basic hypothesis used in the mathematical formulation of solid mechanics which relates the movement of atoms in a crystal to the overall deformation of the bulk solid. A widespread simplified version states that in a crystalline solid subject to a small strain, the positions of the atoms within the crystal lattice follow the overall strain of the medium.

The rule first appears in Max Born and Huang Kun's Dynamical Theory of Crystal Lattices, a refinement of Augustin-Louis Cauchy's relations which were used to derive the equations satisfied by the Cauchy stress tensor.