An official website of the United States government
We propose a high-order stochastic–statistical moment closure model for efficient ensemble prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. The statistical moment equations are closed by a precise calibration of the high-order feedbacks using ensemble solutions of the consistent stochastic equations, suitable for modeling complex phenomena including non-Gaussian statistics and extreme events. To address challenges associated with closely coupled spatiotemporal scales in turbulent states and expensive large ensemble simulation for high-dimensional systems, we introduce efficient computational strategies using the random batch method (RBM). This approach significantly reduces the required ensemble size while accurately capturing essential high-order structures. Only a small batch of small-scale fluctuation modes is used for each time update of the samples, and exact convergence to the full model statistics is ensured through frequent resampling of the batches during time evolution. Furthermore, we develop a reduced-order model to handle systems with really high dimensions by linking the large number of small-scale fluctuation modes to ensemble samples of dominant leading modes. The effectiveness of the proposed models is validated by numerical experiments on the one-layer and two-layer Lorenz ‘96 systems, which exhibit representative chaotic features and various statistical regimes. The full and reduced-order RBM models demonstrate uniformly high skill in capturing the time evolution of crucial leading-order statistics, non-Gaussian probability distributions, while achieving significantly lower computational cost compared to direct Monte-Carlo approaches. The models provide effective tools for a wide range of real-world applications in prediction, uncertainty quantification, and data assimilation.
more »
« less
Data-driven statistical reduced-order modeling and quantification of polycrystal mechanics leading to porosity-based ductile damage
Predicting the process of porosity-based ductile damage in polycrystalline metallic materials is an essential practical topic. Ductile damage and its precursors are represented by extreme values in stress and material state quantities, the spatial probability density function (PDF) of which are highly non-Gaussian with strong fat tails. Traditional deterministic forecasts utilizing sophisticated continuum-based physical models generally lack in representing the statistics of structural evolution during material deformation. Computational tools which do represent complex structural evolution are typically expensive. The inevitable model error and the lack of uncertainty quantification may also induce significant forecast biases, especially in predicting the extreme events associated with ductile damage. In this paper, a data-driven statistical reduced-order modeling framework is developed to provide a probabilistic forecast of the deformation process of a polycrystal aggregate leading to porosity-based ductile damage with uncertainty quantification. The framework starts with computing the time evolution of the leading few moments of specific state variables from the spatiotemporal solution of full- field polycrystal simulations. Then a sparse model identification algorithm based on causation entropy, including essential physical constraints, is utilized to discover the governing equations of these moments. An approximate solution of the time evolution of the PDF is obtained from the predicted moments exploiting the maximum entropy principle. Numerical experiments based on polycrystal realizations of a representative body-centered cubic (BCC) tantalum illustrate a skillful reduced-order model in characterizing the time evolution of the non-Gaussian PDF of the von Mises stress and quantifying the probability of extreme events. The learning process also reveals that the mean stress is not simply an additive forcing to drive the higher-order moments and extreme events. Instead, it interacts with the latter in a strongly nonlinear and multiplicative fashion. In addition, the calibrated moment equations provide a reasonably accurate forecast when applied to the realizations outside the training data set, indicating the robustness of the model and the skill for extrapolation. Finally, an information-based measurement is employed to quantitatively justify that the leading four moments are sufficient to characterize the crucial highly non-Gaussian features throughout the entire deformation history considered.
more »
« less
- Award ID(s):
- 2118399
- PAR ID:
- 10477046
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Journal of the Mechanics and Physics of Solids
- Volume:
- 179
- Issue:
- C
- ISSN:
- 0022-5096
- Page Range / eLocation ID:
- 105386
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Understanding stress distributions at grain boundaries in polycrystalline materials is crucial for predicting damaged nucleation sites. In high-purity materials, voids often nucleate at grain boundaries due to high stress from granular interactions and weakened atomic ordering. While traditional crystal plasticity models simulate grain-level mechanics, their high computational cost often prevents systematic identification of critical microstructural features and efficient forecast of extreme damage events. This paper addresses these challenges by developing a computationally efficient physics-assisted statistical modelling framework. The method starts by leveraging physical knowledge to hypothesize a broad set of microstructural factors influencing stress conditions. Causal inference is then applied to reveal the predominant features with physical explanations, leading to a parsimonious statistical model. A conditional Gaussian mixture model (CGMM) is employed when the identified relationship is utilized as a predictive model to quantify the uncertainty not readily explained by these features. Using body-centred cubic (BCC) tantalum as a representative material, a series of synthetic microstructures from single- to octu-crystal configurations are created. Results show that high-stress states strongly correlate with the elastic and plastic deformation capabilities and the directional misalignment of grain responses near boundaries. The statistical model achieves rapid and accurate forecasts, demonstrating its potential for analysing realistic polycrystalline materials.more » « less
-
Recent advances pertaining to modeling of grain fragmentation during deformation and recrystallization of polycrystalline metals using viscoplastic self-consistent (VPSC) polycrystal plasticity are combined into a field fluctuations VPSC (FF-VPSC) model. The FF-VPSC model is a higher-order formulation calculating the second moments of lattice rotation rates based on the second moments of stress fields inside grains and resulting intragranular misorientation distributions. The misorientation distributions are used to define a grain fragmentation sub-model for improving predictions of deformation texture evolution and to formulate kinetics sub-models for nucleation as well as to influence the stored energy governing grain growth for the predictions of recrystallization texture evolution. Formation of a copper-like texture in moderately high stacking fault energy (SFE) Cu and a brass-like texture in low SFE brass during rolling to very large strains are successfully predicted using the model. Remarkably, the model also predicts recrystallization textures from the deformation textures of the two metals after adjusting tradeoffs between transition-bands and grain boundary nucleation mechanisms. Additionally, rolling and recrystallization of an interstitial-free steel, tension and recrystallization of AA5182-O, and recrystallization of an additively manufacturing cobalt-based alloy MarM-509 are simulated to predict texture evolution. Through these case studies involving multiple alloys and thermo-mechanical processes we show that, in addition to being predictive with good accuracy, the key advantage of the model lies in its versatility. The FF-VPSC model, simulation results, and insights from the results are presented and discussed in this paper.more » « less
-
This research paper presents an experimental, theoretical, and numerical study of the thermomechanical behavior of single-crystal and polycrystal copper under uniaxial stress compression loading at varying rates of deformation. The thermomechanical theory is based on a thermodynamically consistent framework for single-crystal face-centered cubic metals, and assumes that all plastic power is partitioned between stored energy due to dislocation structure evolution (configurational) and thermal (kinetic vibrational) energy. An expression for the Taylor–Quinney factor is proposed, which is a simple function of effective temperature and is allowed by second-law restrictions. This single-crystal model is used for the study of single- and polycrystal copper. New polycrystal thermomechanical experimental results are presented at varying strain rates. The temperature evolution on the surface of the polycrystal samples is measured using mounted thermocouples. Thermomechanical numerical single- and polycrystal simulations were performed for all experimental conditions ranging between 10−3 and 5 × 103 s−1. A Taylor homogenization model is used to represent polycrystal behavior. The numerical simulations of all conditions compare reasonable well with experimental results for both stress and temperature evolution. Given our lack of understanding of the mechanisms responsible for the coupling of dislocation glide and atomic vibration, this implies that the proposed theory is a reasonably accurate approximation of the single-crystal thermomechanics.more » « less
-
A physically-informed continuum crystal plasticity model is presented to elucidate deformation mechanisms, dislocation evolution and the non-Schmid effect in body-centered-cubic (bcc) tantalum widely used as a key structural material for mechanical and thermal extremes. We show the unified structural modeling framework informed by mesoscopic dislocation dynamics simulations is capable of capturing salient features of the large inelastic behavior of tantalum at quasi-static (10−3 s−1) to extreme strain rates (5000 s−1) and at low (77 K) to high temperatures (873 K) at both single- and polycrystal levels. We also present predictive capabilities of the model for microstructural evolution in the material. To this end, we investigate the effects of dislocation interactions on slip activities, instability and the non-Schmid behavior at the single crystal level. Furthermore, ex situ measurements on crystallographic texture evolution and dislocation density growth are carried out for polycrystal tantalum specimens at increasing strains. Numerical simulation results also support that the modeling framework is capable of capturing the main features of the polycrystal behavior over a wide range of strains, strain rates and temperatures. The theoretical, experimental and numerical results at both single- and polycrystal levels provide critical insight into the underlying physical pictures for micro- and macroscopic responses and their relations in this important class of refractory bcc materials undergoing large inelastic deformations.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.jmps.2023.105386
