An investigation on the validity of Cauchy–Born hypothesis using Sutton-Chen many-body potential

The Cauchy–Born hypothesis has been used to concurrently bridge atomistic information to continuum model. It has been a prevalent assumption in computational nano-mechanics during the past decade. This kinematic assumption relates the deformation of the continuum to the deformation of its underlying crystalline structure. The main objective of this paper is to investigate the validity of this hypothesis by means of direct atomistic simulations and the continuum mechanic calculations. In fact, we intend to determine under which strain or stress state the crystalline structure undergoes inhomogeneous deformation due to a small perturbation of the homogeneously deformed system. Two failure criteria are produced in principal strain and stress domains using different deformation paths, to illustrate the validity of Cauchy–Born hypothesis. It has been shown that the continuum model essentially obeys the hyperelastic model in the inner area of the produced curves. Obviously, the validity of Cauchy–Born hypothesis is analogous to the yield surface used in the theory of plasticity.