Materials are highly complex mechanical systems; visible material behavior is the macroscopic manifestation of innumerable mechanical processes taking place at multiple length and time scales. The vast number of degrees of freedom make it impossible to simulate every atom for a material of any appreciable size. Thus a different approach is required for large-scale models. Although many macroscopic models exist and are sufficient for many applications, their range of validity is inherently limited to those cases for which experimental data is available. Therefore to truly understand and predict the broad range of complex material behavior, it is necessary to model large scale responses based on small-scale phenomena.

Accurate physics-based material models are in high demand in the modern technological and scientific communities, as materials research drives innovation in applications ranging from from microchips to airplanes. A multidisciplinary approach is needed to develop new models based on methods in mechanics, mathematics, materials science, and engineering. The overarching goal is to understand the mechanics of materials, to model the behavior mathematically, and to use these models to predict and simulate material behavior for scientific and engineering purposes.