Numerical and analytic routes from microscales to macroscales in theories of deformation and fracture

Abstract

Numerical simulation has reached a point where it is on a par with laboratory experiment and mathematical theory as a tool for materials research. For example, molecular dynamics computations now can predict the motions of tens of millions of molecules in a solid that is undergoing deformation or fracture. The question is how to use such huge amounts of information to gain deeper understanding of the properties of real materials. I believe that it is an inefficient use of computational facilities to try to go directly from atomistic simulations to specific macroscopic phenomena. A better strategy is to use the simulations to identify dynamic variables that characterize the internal states of materials, and to use the equations of motion for these variables along with equations for stress and strain to predict macroscopic behavior. I shall illustrate this strategy by describing recent work by M. Falk and myself on plasticity in amorphous solids.