Multiscale modeling from atoms to genuine continuum

Basically, there exist two fundamental physical models that provide foundations for almost all material behavioral simulations: microscopic discrete atomistic models and macroscopic continuum models. In the range of nanometer or below, the material body is viewed as a collection of discrete particles moving under the influence of their mutual interaction forces. On the other hand, the results of centuries of experimental work at larger length scale are usually formalized into well-structured continuum theories (Chen et al., 2006; Eringen, 1980; Liu, 2002; Truesdell and Noll, 2004; Truesdell and Toupin, 1960) with the purpose to inscribe all objects of our perception into the familiar framework of a four-dimensional space-time. Although the underlying physical concept may be the same, the descriptions by the two distinct models are as different as day and night, whereas the success of both models has been demonstrated and tested throughout the history of science in explaining and predicting various physical phenomena.