For crystalline bodies of finite size, the effect of surface stress is also significant. However, the standard Cauchy–Born rule cannot deduce the surface properties. To overcome this limitation, Park et al. (2006) proposed a surface Cauchy–Born rule. Several modified forms of the Cauchy–Born rule have also been proposed to cater to crystalline bodies having special shapes. Arroyo & Belytschko (2002) proposed an exponential Cauchy Born rule for modeling of mono-layered crystalline sheets as two-dimensional continuum shells. Kumar et al. (2015) proposed a helical Cauchy–Born rule for modeling slender bodies (such as nano and continuum rods) as special Cosserat continuum rods.