Continuum-based and cluster models for nanomaterials

As a result of the rapid advances in the synthesis of nanomaterials, developing robust modeling methods for evaluating the physical properties of nanomaterials is becoming increasingly important. Nanomaterials are distinguished by their near-perfect molecular structures at the nanometer scale and outstanding mechanical properties defined at the macroscopic level. Correspondingly, hierarchical modeling approach has the unique advantage in its ability to describe the structure-property relations. In this work, two different hierarchical approaches for describing the mechanics of nanomaterials are presented. The first model is a continuum-based model derived from the theory of crystal elasticity. The second is the virtual atom cluster (VAC) model recently proposed in [1, 2]. In the proposed continuum-based model, it is shown that the deformation measures introduced in the model strongly depend on the underlying atomistic model. As a result, the significances of these measures are fundamentally different from those in the classical continuum theory. The VAC model, on the other hand, is a discrete model that is extracted directly from the atomistic model. Following the presentation of the two models, a systematic comparison is presented in terms of the accuracy and range of applicability. Finally, the robustness of both models and their link to the atomistic model are discussed and shown through benchmark problems.