Errors of Scale in Discrete Element Computations

TLDR: This question is discussed from the standpoint of scale effects that infect all numerical approximations, is it reasonable to foresee a day when a continuum view is unnecessary?

Abstract: The discrete element method (DEM) is ideal for modeling many problems not accessible to traditional continuum-based methods such as finite difference and finite elements (Homer et al., 2001). DEM has the advantage of inherently capturing large non-affine deformations and the fluid--solid phase changes so commonly found in granular media. The DEM appears to derive much of its power from the kinematic freedom for the particles such that seemingly simplistic micro-scale models can replicate realistic macro-scale behavior. With the advent of large-scale computing, by which simulations of several million particles are possible, the DEM will become an important tool for geotechnical and industrial applications within the next 20 years. The advances in DEM have and will continue to mirror advances in computer hardware. Several advances in DEM technology will accompany the improvements in computer technology. The constitutive response of the DEM medium depends on micro-scale laws that define the contact mechanisms, particle size and shape, and particle distribution. The success of the method requires a correlation between the phenomenology of the DEM medium and the micro-scale laws. Most of these advances will be accomplished through numerical experiments, which at present are a popular tool for understanding granular media as a continuum. Is it reasonable to foresee a day when a continuum view is unnecessary? In this paper, this question is discussed from the standpoint of scale effects that infect all numerical approximations,