A Multiscale Modeling Technique for Bridging Molecular Dynamics with Finite Element Method

PhD Student: Yongchang Lee

Publication Date: 2013

Advisor: Cemal Basaran

Abstract: The recent dramatic increase in computational power, which is available for mathematical modeling and simulation, plays the significant role of modern numerical methods in the analysis of various structures. In the numerical methods, molecular dynamics (MD) and finite element (FE) analysis are well developed and most popular on nanoscale and macroscale analysis, respectively. This dissertation studied a new multiscale modeling technique to couple MD with FE for a concurrent multiscale method and molecular dynamics simulations to characterize the materials properties and the atomistic behaviors of materials for a sequential multiscale method.

The previous concurrent multiscale modeling techniques have shown their own limitations, such as spurious wave reflection, short timestep in FE region, expensive computational cost, and complex mathematical framework. In order to resolve the limitations, we proposed a Weighted Averaging Momentum Method (WAMM). The key idea of WAMM is to couple momentum of both domains on the basis of weighted averaging momentum in the handshake region instead of the additional pseudo-force to reduce the spurious wave reflection. A wave propagation example has been used to illustrate the challenges in coupling MD with FE and to verify the proposed technique. Furthermore, 2-Dimensional problem has also been used to demonstrate how this method would translate into real world applications.

As a complement to experimental work and possessing the ability to fill in the limitations of experiments, molecular simulation serves to reinforce experimental predictions and provide insight into the atomistic processes that govern studied phenomena. In the sequential multiscale method, molecular dynamics simulations are employed in order to estimate materials properties and atomistic behaviors of materials. In this study, MD simulations for β-Sn microstructures are performed over a temperature range of 300K to 450K for investigating thermodynamics properties, thermo-mechanical materials properties and shear deformation mechanism in Sn-based solder alloys.

The effect of Ni impurity on the self-diffusivity of β-Sn in the (101) symmetric tilt grain boundary is investigated. Using molecular dynamics simulations, it is shown that Ni solute decreases the grain boundary self-diffusivity of β-Sn as the amount of solute in grain boundary increases. We also study the solute effect on the diffusive width of grain boundary and observe that low concentrations of Ni solute lead to shrinking of the grain boundary width relative to the pure β-Sn grain boundary.

In order to study viscoplasticity in β-Sn lattice and grain boundaries, two kinds of β-Sn lattice structure are considered in the atomistic level: Model I is the perfect β-Sn lattice structure in [001] orientation, and Model II is β-Sn lattice structure with several symmetric tilt grain boundaries. Through the study of the different strain-rate on β-Sn, MD simulation results show that higher strain rate leads not only increased shear stress but also wider grain boundary width. The results also agree with the strain rate and thermal dependency of experimental data about viscoplastic behaviors of bulk β-Sn.

Finally, shear deformation of β-Sn along five different lattice orientations is studied at the atomistic level. Simulated models are perfect β-Sn lattice without defects. In order to obtain the constitutive relationship of β-Sn in shear, the shear stress is computed by using virial stress. The MD results showed the shear deformation mechanism and shear stress-strain relationship are different along each crystal orientation. The computed thermal dependency in shear modulus agrees with experimental data. (Abstract shortened by UMI.)