Lacy, Thomas E.
Bednarcyk, Brett A.
Newman, James C., Jr.
Other Advisors or Committee Members
Date of Degree
Dissertation - Open Access
Doctor of Philosophy
Multiscale analysis procedures for composites often involve coupling the macroscale (e.g., structural) and meso/microscale (e.g., ply, constituent) levels. These procedures are often computationally inefficient and thus are limited to coarse subscale discretizations. In this work, various computational strategies were employed to enhance the efficiency of multiscale analysis procedures. An ensemble averaging technique was applied to stochastic microscale simulation results based on the generalized method of cells (GMC) to assess the discretization required in multiscale models. The procedure was shown to be applicable for micromechanics analyses involving both elastic materials with damage and viscoplastic materials. A trade-off in macro/microscale discretizations was assessed. By appropriately discretizing the macro/microscale domains, similar predicted strengths were obtained at a significantly less computational cost. Further improvements in the computational efficiency were obtained by appropriately initiating multiscale analyses in a macroscale domain. A stress-based criterion was used to initiate lower length scale GMC calculations at macroscale finite element integration points without any a priori knowledge of the critical regions. Adaptive multiscale analyses were 30% more efficient than full-domain multiscale analyses. The GMC sacrifices some accuracy in calculated local fields by assuming a low-order displacement field. More accurate microscale behavior can be obtained by using the highidelity GMC (HFGMC) at a significant computational cost. Proper orthogonal decomposition (POD) order-reduction methods were applied to the ensuing HFGMC sets of simultaneous equations as a means of improving the efficiency of their solution. A Galerkin-based POD method was used to both accurately and efficiently represent the HFGMC micromechanics relations for a linearly elastic E-glass/epoxy composite for both standalone and multiscale composite analyses. The computational efficiency significantly improved as the repeating unit cell discretization increased (10-85% reduction in computational runtime). A Petrov-Galerkin-based POD method was then applied to the nonlinear HFGMC micromechanics relations for a linearly elastic E-glass/elastic-perfectly plastic Nylon-12 composite. The use of accurate order-reduced models resulted in a 4.8-6.3x speedup in the equation assembly/solution runtimes (21-38% reduction in total runtimes). By appropriately discretizing model domains and enhancing the efficiency of lower length scale calculations, the goal of performing highidelity multiscale analyses of composites can be more readily realized.
Ricks, Trenton Mitchell, "Application of Order-Reduction Techniques in the Multiscale Analysis of Composites" (2017). Theses and Dissertations MSU. 709.