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Modeling of Multi-Scale Continuum-Atomistic System Using Homogenization Theory

Oral Defense by: Karthikeyan Chockalingam, Ph.D. Candidate, USC, Astani Department of Civil and Environmental EngineeringThe main objective of the dissertation is to develop multi-scale algorithms for continuum-atomistic problems. The focus is on sequential multi-scale simulations. In sequential multi-scale methods, the computations at the various scales are, in a sense, decoupled. This means, for example, that, for a continuum/atomistic simulation, large scale macroscopic continuum calculations rely on the results of fine scale computations and information obtained on an atomistic cell. While the procedures developed in this thesis could be used in conjunction with a number of sequential multi-scale methods, the focus here is on the homogenization technique. As has been the case in traditional finite element applications of homogenization, one of the principal focuses in this thesis will be on the computation of macro scale constitutive parameters; but, in this case, these constitutive representations come from the atomistic calculations.The thesis has four parts that develop various aspects of the theme of the work. The dissertation focuses on the following applications:1. Problems involving mechanical loading of solids and structures under static load at zero temperature.The focus is on creating multi-scale continuum/atomistic simulation methods which use the atomistic model to provide an improved material representation including the effects of material defects. This topic could be useful in modeling fracture and failure.2. Computation of thermo-mechanical constitutive parameters at finite temperature conditions.This procedure focuses on using the atomistic scale calculation to define constitutive parameters. It assumes that equilibrium conditions exist at the atomistic scale. It does not attempt to track, in a time history sense, the dynamics at the atomistic scale. It does require the solution of an atomistic free vibration problem with natural frequencies dependent on temperature. The procedure defines macroscopic thermo-mechanical constitutive parameters, like the specific heat and the coefficient of thermal expansion, as a function of temperature. These properties could be used directly in a macroscopic continuum finite element model which would be valid at the full range of temperatures.3. Dynamic problems involving the simulation of the thermo-mechanical behavior of systems at finite temperature, with and without heat transfer.This procedure focuses on using the atomistic scale calculation to define multi-scale, thermo-mechanical momentum and energy equations. It does attempt to track, in a time history sense, the dynamics at the atomistic scale. Energy equations are derived for both the scales based on first law of thermo-dynamics. Two types of application problems are used to demonstrate the theory. The first involves thermal stress analysis simulation in which the temperature has no time variability and, thus, no heat transfer occurs. The second involves simulations with time varying temperatures and include heat transfer effects. 4. Implicit time integrations algorithms for atomistic momentum equations that can be seamlessly coupled to macro models.

Location: Kaprielian Hall (KAP) - 209

Audiences: Everyone Is Invited

Contact: Evangeline Reyes