Towards a New Framework for the Mechanics of Nonequilibrium Continua

Continuum mechanics has been the major theoretical tool for the description and understanding of the mechanics of materials. As science and engineering advance, however, classical continuum mechanics has been shown to be insufficient, e.g., for physical processes involving multiple length/time scales or for dynamic phenomena with unknown thermal transport mechanisms.

This research aims to overcome these limitations by developing a new formalism that will enhance the applicability of continuum mechanics to describe multiscale mechanical deformation and thermal transport processes from the atomic to the macroscopic. A simulation tool will be developed based on the formulation and will be freely and broadly disseminated to benefit mechanics and materials communities.

In addition, the project will be designed to serve as a scientific training ground for graduate and undergraduate students. The PI will also reach out to students from underrepresented groups as well as students with physical disabilities to provide them with hands-on research experiences from which they may launch their careers.

Different from the top-down formulation of classical continuum mechanics, this research will employ a bottom-up formalism to rederive the field representation of balance laws. The formulation will build on a concurrent atomistic and continuum description of materials by including the atomic degrees of freedom embedded within each material point; this will allow atomic-scale discontinuities and thermal fluctuations to be explicitly included in the formulation.

The Theory of Distributions will be used as the mathematical tool for the formulation, which will provide a rigorous solution to the mathematical difficulties in linking particle and field descriptions of physical behavior involving discontinuous or singular functions. The research will also redefine temperature as a derived quantity, thus enabling the descriptions of all the field quantities in continuum mechanics to be fully consistent with those measured in experiments or calculated from atomistic simulations.

In addition, a simulation tool will be developed, demonstrated, and validated by reproducing two highly nonequilibrium processes that are both temperature- and size-dependent: heteroepitaxial growth and thermally activated dislocation motion. It is expected that this research will lead to a new framework for the mechanics of continua that can predict highly non-equilibrium deformation processes and phenomena, as well as reveal the underlying mechanisms, with no empirical rules or parameters other than an interatomic potential.

This project is co-funded by the Mechanics of Materials and Structures (MOMS) program in the Division of Civil, Mechanical and Industrial Innovation (CMMI) and the Thermal Transport Processes (TTP) program in the Division of Chemical, Bioengineering, Environmental and Transport Systems (CBET).

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.