A comparative numerical study on the failure evolution at different simulation scales
Abstract
[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI-COLUMBIA AT REQUEST OF AUTHOR.] In computational mechanics, different numerical approaches and simulation scales may lead to different results. It is because each approach has its own solution scheme feature, such as the governing equation, forcing function, and integration algorithm, for the specific scale including the nanoscale, mesoscale, and macroscale. Recently, a particle method that is the material point method (MPM) has become a popular research topic at macroscale due to its advantage combining the Eulerian and Lagrangian descriptions. However, the MPM has not been evaluated in a systematic manner for the fully coupled thermodynamic fluid-structure interaction (FSI) cases. Since the constitutive models and heat transfer in solid and fluid materials are quite different, a fully coupled computational scheme is designed in this dissertation for simulating the FSI with the MPM, in which the governing equations for both solid and fluid material points are related to each other. Additionally, the MPM has been upgraded to the generalized interpolation MPM (GIMP), also described in this work, for solving the problems with large deformation. At nanoscale, the object is usually divided by atoms or molecules. Therefore, another computational particle method, molecular dynamics (MD), has been widely utilized for simulating the movements of atoms or molecules. Although MD is an accurate tool at nanoscale, it would cost numerous computational resources. To obtain similar nanoscale information with less cost, a developed coarse-grained MD (CG-MD), which traverses the time and spatial scales, is introduced, verified, and validated in this dissertation. Although the MPM (or GIMP) and MD both belong to particle methods, their forcing functions are different, namely, they are continuous and discrete forcing functions for MPM and MD, respectively. With these similarity and difference, a series of mechanical simulations involving large deformation by using the GIMP, MD, and CG-MD were conducted and discussed in this dissertation to investigate the failure evolution at different simulation scales.
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