Discrete-Continuum Transition in Modelling Nanomaterials

In the present investigation we elaborate on the development of a second-order elastic deformation gradient in discrete/atomistic system. Whereas kinematics are typically characterized by the Cauchy-Bom rule that enforces homogeneous deformation, the second-order deformation gradient allows to capture highly nonhomogeneous deformations. This is particularly important in disordered molecular systems where nonaffine deformations are responsible for the mechanical behaviour of nanomaterials. The local inhomogeneity measure has been defined to determine variability of the deformation field of nanostructures under loading. Several application examples have been worked out comprising fullerene structures, diamond plates and nanowires.