Description of deformations in the elastic strain engineering of nanostructure

In the present investigation we elaborate on the development of a second-order elastic deformation gradient in discrete/atomistic system. Whereas deformation kinematics is typically characterized by the Cauchy–Born rule that enforces homogeneous deformation, the second-order deformation gradient allows capturing highly non-homogeneous deformations. This is particularly important in nanosystems with strain engineered functionalities. The local inhomogeneity measure has been derived from the deformation mapping to determine variability of the deformation field of nanostructures under loading. It is shown that the knowledge about the non-homogeneous deformation pattern is necessary to provide a quantitative connection to functional properties of nanostructures.