Uncertainty quantification in damage mechanics models
| Author(s) | Troy, Jerome | |
| Date Accessioned | 2023-10-09T17:42:51Z | |
| Date Available | 2023-10-09T17:42:51Z | |
| Publication Date | 2023 | |
| SWORD Update | 2023-09-20T19:10:35Z | |
| Abstract | Computational modeling of material response, at the macroscopic scale, under external stimuli, is paramount to predicting material failure in various structural applications. Material properties often vary within a given sample of material, and these distributions will vary from one sample to another. Various methods can be employed to understand these variations and gain insight into how a material will behave when put under external stresses. These responses can be quantified in specific properties such as stress-strain curves, times of failure, and other quantities of interest (QoIs). These QoIs are random variables, and their distributions can be understood using Monte Carlo techniques. This thesis primarily focuses on using these techniques to analyze the results from a specific damage mechanics model. Damage mechanics simulations can be very expensive computationally, and thus we discuss techniques to reduce the required computational costs while maintaining the same level of accuracy and uncertainty as more traditional methods. We investigate these ideas in multiple settings and for various QoIs. Each scenario presents a new challenge depending on the problem geometry and various properties of the QoIs. We present methods to employ uncertainty quantification (UQ), which are generally agnostic to the underlying model and only require knowledge of the model outputs. The presented results are a survey of techniques and potential experiments which can be employed in multiple fields. To aid with the computational complexity involved in the simulations, we apply Multilevel Monte Carlo methods, which combine results from multiple model resolutions. We extend the application of these Multilevel techniques to building confidence intervals and probability distributions. Similarly, the results can be used in UQ techniques to bound modeling errors between the nominal and potential alternative models. | |
| Advisor | Plechac, Petr | |
| Degree | Ph.D. | |
| Department | University of Delaware, Department of Mathematical Sciences | |
| DOI | https://doi.org/10.58088/10ax-bz35 | |
| Unique Identifier | 1410119765 | |
| URL | https://udspace.udel.edu/handle/19716/33468 | |
| Language | en | |
| Publisher | University of Delaware | |
| URI | https://login.udel.idm.oclc.org/login?url=https://www.proquest.com/dissertations-theses/uncertainty-quantification-damage-mechanics/docview/2866706604/se-2?accountid=10457 | |
| Keywords | Damage mechanics | |
| Keywords | Uncertainty quantification | |
| Keywords | Quantities of interest | |
| Keywords | Computational modeling | |
| Title | Uncertainty quantification in damage mechanics models | |
| Type | Thesis |