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. It 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 currently accepted form is Max Born's refinement of Cauchy's original hypothesis which was used to derive the equations satisfied by the Cauchy stress tensor.
The Cauchy–Born rule or approximation in solid mechanics associates atomic movements within a crystal with bulk deformation. It suggests that under small strain conditions, atoms' positions mirror the medium's strain. Max Born's modification of Cauchy's original hypothesis was used to derive equations for the Cauchy stress tensor.