Chen, Y., Lee, J.D. and Eskandarian, A. (2002) “Connecting Discrete Atomic Model to Microcontinuum Field Theories”, 39th Annual Conference of the Society of Engineering Science, October 13-16, Pennsylvania.

Abstract: This work aims to connect atomistic model to continuum theories. The effort includes three parts: the instantaneous mechanical variables, balance laws and constitutive relations. A physical picture of micromorphic theory is introduced. The fundamentals of micromorphic continuum theory, as well as its relation with various continuum theories including Microstructure Theory, Micropolar Theory, Cosserat Theory, and Couple Stress Theory are introduced. A geometric model of an atomic system is presented. The microscopic expressions of the instantaneous mechanical variables, including mass, momentum, microinertia, generalized spin, body force, body couple, temperature, internal energy, stresses and heat flux, are derived in terms of atomic variables. The corresponding field quantities in continuum theory are obtained through ensemble average. The balance laws of micromorphic theory are obtained and verified from the viewpoint of molecular motion. The constitutive relations are discussed, and the approach to determine the material moduli through the molecular dynamics simulations is proposed and presented.