Variational Multiscale Enrichment Method for Modeling of Structures Subjected to Extreme Environments

Abstract

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.