Highlight Seminar by Professor Bill Curtin

Multiscale Modeling in Metals: from Quantum to Continuum
Professor Bill Curtin (Director of the Institute of Mechanical Engineering, EPFL)

Phenomena governing the plastic deformation and fracture in metals are controlled by phenomena over a wide range of scales, from atomistic features in the core of a dislocation or tip of a crack at the Angstrom scale up to plastic zone sizes of 10-1000 microns filled with dislocations. Moreover, these phenomena are interacting, and simultaneously operative, so that attention to only one scale is insufficient for obtaining quantitative and predictive understanding. These aspects of the problem motivate the development of "concurrent" multiscale methods wherein different spatial domains of a material are treated at different scales simultaneously within one integrated computational framework. The challenge in developing such methods is in developing the seamless coupling that intimately connects different scales, so that small scales are unaware that other regions of the material are not being treated at the same small scale level of fidelity. Here, we present our efforts over the last decade to link together quantum (via density functional theory), atomistic (via molecular dynamics using interatomic potentials), discrete-dislocation models, and continuum crystal plasticity models, with the main application being aimed at fracture. We first discuss the Coupled Atomistic/Discrete-Dislocation (CADD) model, with emphasis on the mechanical coupling and the handling of dislocations as they move between atomistic and continuum domains. We then move down in scale and show how the CADD coupling is used with DFT quantum mechanics replacing the atomistic domain, and why such an approach has significant benefits. We then move up in scale and present a method to couple discrete-dislocation plasticity to continuum plasticity, again emphasizing the developments that overcome the difficulty of direct coupling of discrete and continuum theories. In each case, we show applications to problems in fracture and demonstrate how the use of the multiscale method enables us to tackle problems that could not be approached using brute-force, single-scale methods. The methods we have developed preserve important fundamental physics and mechanics with demonstrated high and controllable accuracy. But, putting such methods on a firmer mathematical foundation or finding new methods that are derived from a more-formal structure both remain huge challenges for the Mechanics field.