<p> Multiscale simulation is a long standing dream in computational physics and materials. The motivation is natural: each single-scale model has its deficiencies. For example, microscale models such as Molecular Dynamics are limited to size in space and time; macroscale models such as Finite Element Method find difficulty recovering some fundamental physical phenomena such as materials defects. Simulations across scales are challenging because quantities in different scales have distinct properties. Mechanism needs to be harnessed to translate the information. Cross-scale communication is a typical two-way message passing: bottom-up and top down. Bottom-up approach is relatively straightforward, where statistical theory or homogenization is used to collect lower-scale information and interpret it in higher levels. On the other hand, top-down approach requires physical insights. Specifically, in a mechanical system, top-down message passing can be the response of the molecular system when macroscale boundary conditions such as distributed load are enforced. </p><p> In this work, we reveal an intrinsic multiscale structure in solid materials. A “supercell” is introduced as a cluster of particles. Compare with “material point” in continuum mechanics, the “supercell” has internal degrees of freedom, which makes it equivalent to molecular systems. By introducing different force fields, we derive the dynamical equations for the different scales in the structure. The systematic multiscale framework solves the issue of top-down message passing by including quantities from different scales and connecting them in a uniform dynamical framework. We discuss the technical aspects in implementing the theory, i.e. constraints of the variables, integrators and temperature control. Numerical example of phase transition are presented to validate the theory, including bulk Nickel lattice under displacement and traction boundary conditions and Nickel nanowire with traction. Furthermore, based on the developed multiscale theory, we establish a computational model to achieve efficiency in realistic multiscale simulations. The model includes three parts: atomistic region, macro region and transition zone. Atomistic region is where physical details are desired and is simulated by Molecular Dynamics. Macro region only concerns macroscale deformable behaviors of solid materials, which can be calculated by various models depending on the problem of interests. We choose state-based peridynamics in this work as a demonstration. The essential part is the transition zone which is responsible for translating messages across different domains. The “supercell” developed in the previous theory is employed as a transition element to carry those different messages. With solid theoretic foundation, the cross-scale message translation is clearly characterized. We also construct a filter to solve the issue of high-frequency wave reflection. Examples of 1-D and 2-D wave propagations are presented to demonstrate the procedure of cross-scale transition and the effect of the filter.</p>
| Identifer | oai:union.ndltd.org:PROQUEST/oai:pqdtoai.proquest.com:10150814 |
| Date | 02 September 2016 |
| Creators | Tong, Qi |
| Publisher | University of California, Berkeley |
| Source Sets | ProQuest.com |
| Language | English |
| Detected Language | English |
| Type | thesis |
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