A Theoretical and Computational Basis for Micro-Continuum Field Theories: From Atomic Model to Continuum Theory

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A Theoretical and Computational Basis for Micro-continuum Field Theories:From Atomic Model to Continuum TheoryJames D. LeeDepartment of Mechanical and Aerospace EngineeringThe George Washington UniversityAbstractThe objective of this proposed research is to enhance the scientific understanding of and to establish a profound theoretical foundation for mechanics of materials with micro-structure and micromotion. It includes: (1) the construction of a unified theory for micro-continuum based on statistical mechanics, molecular dynamics, nonlocal theory, polar theory and thermodynamics. It will be capable of explaining and predicting a large class of microscopic phenomena in which the ratios of the external to internal characteristic length and time approach unity; (2) the development of a computational basis, including finite element method and molecular dynamics method, for the above-mentioned theory; (3) the applications of the theory through the computer simulations to the fields where the effect of length scale is predominant to the material response.