This dissertation presents the formulation and implementation of the variational multiscale enrichment computational framework for scale inseparable multiscale modeling of structures subjected to extreme environments. In the presence of structures with elasto-viscoplastically behaved heterogeneous materials, the framework includes the variational multiscale enrichment (VME) method, the reduced order variational multiscale enrichment (ROVME) method for mechanical and thermo-mechanical problems, and the hybrid integration for reduced order variational multiscale enrichment (HROVME) method.
First, the variational multiscale enrichment method for elasto-viscoplastic problems is developed for the scale inseparable multiscale modeling. VME is a global-local approach that allows accurate fine scale representation at small subdomains whereas the response within far-fields is idealized using a coarse scale representation. The scale inseparable character is represented by the relatively insignificant scale size difference and strong coupling effect between the scales. A one-parameter family of mixed boundary conditions that range from Dirichlet to Neumann is employed to study the effect of the choice of boundary conditions at the fine scale on accuracy. Second, the reduced order variational multiscale enrichment method for elasto-viscoplastic problems is developed to improve the computational efficiency of the VME method. By eliminating the requirement of direct fine scale discretization and repetitive evaluation of the microscale equilibrium state, the computational effort associated with the VME method is significantly reduced. Third, the reduced order variational multiscale enrichment method for coupled thermo-mechanical problems is presented which extends the ROVME method to model structures with temperature sensitive constituent properties. The temperature-dependent coefficient tensors of the reduced order approach are approximated in an efficient manner, retaining the computational efficiency of the reduced order model in the presence of spatial/temporal temperature variations. Last, the hybrid integration for reduced order variational multiscale enrichment method is developed to further improve the computational efficiency of the proposed framework. Considering the coupled transport-thermo-mechanical effects, it employs the key ideas of the ROVME and the computational homogenization approaches to directionally consider scale separation within the structures. The HROVME method also extends the ROVME approach to microstructures with periodic boundary conditions and improves the stability of the ROVME method by avoiding the potential hourglass modes. Numerical verifications are performed to demonstrate the high accuracy, computational efficiency and capability of the proposed computational framework.
| Identifer | oai:union.ndltd.org:VANDERBILT/oai:VANDERBILTETD:etd-06282017-213422 |
| Date | 29 June 2017 |
| Creators | Zhang, Shuhai |
| Contributors | Caglar Oskay, Prodyot K. Basu,, Ravindra Duddu, Haoxiang Luo, Ravi Penmetsa |
| Publisher | VANDERBILT |
| Source Sets | Vanderbilt University Theses |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.library.vanderbilt.edu/available/etd-06282017-213422/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Vanderbilt University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
Page generated in 0.0023 seconds