Crystal plasticity simulations help to understand the local deformation behavior of multi-phase materials based on the microstructural attributes. The results of such simulations are mainly dependent on the Representative Volume Element (RVE) size and composition. The effect of RVE thickness on the changing global and local stress and strain is analyzed in this work for a test case of dual-phase steels in order to identify the minimal RVE thickness for obtaining consistent results. 100×100×100 voxel representative volume elements are constructed by varying grain size and random orientation distribution in DREAM-3D. The constructed RVEs are sliced in depth up to 1, 5, 10, 15, 20, 25, 30, 40, and 50 layers to construct different geometries with increasing thickness. Crystal plasticity model parameters for ferrite and martensite are taken from already published data and assigned to respective phases. Although the global stress/strain behavior of different RVEs is similar (<5 % divergence), the local stress/strain partitioning in RVEs with varying thickness and grain size shows a considerable variation when statistically compared. It is concluded that two-dimensional (2D) RVEs can be used for crystal plasticity simulations when global deformation behavior is of interest. Whereas, it is necessary to consider three-dimensional (3D) RVEs, which have a specific thickness and number of grains for determining stabilized and more accurate local deformation behavior. This estimation will help researchers in optimizing the computation time for accurate mesoscale simulations.
<p>Coupled thermo-hydro-mechanical (THM) models are used for the assessment of nuclear waste disposal, reservoir engineering, and other branches of geo-environmental engineering. Model-based decision-making and design optimization in these domains require sensitivity analyses (SA) and uncertainty quantification (UQ) methods that are suitable for coupled THM problems on an engineering scale. Due to different coupling levels, non-linearities, and large spatial and temporal extents, these analyses can often be challenging both conceptually and computationally.</p><p>For an initial evaluation in a setting relevant to nuclear waste disposal we start by employing an analytical solution for thermal consolidation around a point heat source which encompasses the most relevant primary couplings and allows us to cover the entire parameter space robustly and efficiently. For uncertainty quantification, we applied an experimental design (DoE-) based history-matching approach. This approach uses DoE methods to construct a proxy model, which is used later for efficient Monte Carlo sampling and subsequent filtering of the uncertainty space of the history-match error. As a result, we obtain a family of curves that is compatible with the prior parameter set and experimental data to match, which then enables further uncertainty quantification. In our work, we demonstrate the applicability of the workflow and discuss its particular suitability to this problem class, including its (in-)sensitivity to prior parameter distribution assumptions.</p><p>For SA, we contrast the conclusions drawn via two different approaches: local one variable at a time (OVAT) and global sensitivity analysis (GSA) based on Sobol indices for different spatio-temporal settings to observe near and far-field effects as well as early- and late-stage system response. The conducted studies can serve as a benchmark for UQ and SA software designed around numerical THM simulators.</p>
<p>The presented work investigates aspects of uncertainty quantification in thermal design calculations of deep geological repositories for nuclear waste. The expected evolution of thermal conditions is a key element in the design process of the repository layout. Due to the radioactive decay and the associated emission of heat, temperatures increase in the repository system, potentially affecting processes relevant to the repository negatively. In order to quantify the temperature evolution and assess its effects on the various barriers, such as the host rock, models are set up and thermal calculations are conducted. Often specific distributions are assigned to model parameters, which are not known precisely.</p><p>To achieve a robust understanding and design despite this limited knowledge, it is necessary to assess the uncertainties associated with both parameters and models as part of these calculations. However, an uncertainty quantification, which includes calculations based on full distributions is expensive. To compare different uncertainty quantification methods applied to thermal design calculations, a benchmark is created. This benchmark is based on an analytical solution for a 1-D, thermal heat conduction problem using Python. Results of uncertainty quantification calculations based on full distributions, utilizing statistical moments or employing series expansion such as the first-order-second-moment method are compared.</p><p>This benchmark can help assess methods of uncertainty quantification in context of thermal design calculations.</p>
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