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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Inference of phase field fracture models

The phase field approach to modeling fracture uses a diffuse damage field to represent cracks. This representation mollifies singularities that arise in computations with sharp interface models and some of the resultant difficulties in the mathematical and numerical treatment of fracture. Phase field fracture models have proven effective at representing crack propagation, branching, and merging. Specific formulations, beginning with brittle fracture, have also been shown to converge to classical solutions. Extensions to cover the range of material failure, including ductile and cohesive fracture, lead to an array of possible models. There exists a large body of literature focusing on this class of models and on the impact of model form on the predicted crack evolution. However, there have not been systematic studies into how optimal models may be chosen. Here, we take a first step in this direction by developing formal methods for identification of the best parsimonious model of phase field fracture given full-field data on the damage and deformation fields. We consider some of the main models that have been used for the degradation of elastic response due to damage and its propagation. Our approach builds upon Variational System Identification (VSI), a weak form variant of the Sparse Identification of Nonlinear Dynamics (SINDy). Furthermore, in this first communication we focus on synthetically generated data but we also consider central issues associated with the use of experimental full-field data, such as data sparsity and noise.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Impact of position and density of nanoscale voids on fracture initiation in iron from phase field fracture simulation

Understanding the impact of these bubbles on crack propagation, like that of helium bubble-induced cracking in irradiated materials is incredibly complex. A useful first study towards understanding bubble effects on fracture is to examine how voids impact fracture first. In this work, we used phase-field fracture simulations to examine the influence of voids and their distribution on Mode I fracture in Fe. Assuming brittle fracture, two simulation configurations were considered: (1) nanoscale systems with one or two voids, and (2) nanoscale systems with an experimentally relevant distribution of voids, with up to 20% void area. Results from simulations with one and two voids showed that voids within 10 nm of a crack tip reduce the stress required for crack growth, with the magnitude of reduction depending on void-to-crack orientation. Comparisons with linear elastic fracture mechanics and evaluation of one versus two void systems revealed deviations from linear superposition, implying complex interactions between void and crack tip stress fields. In multi-void simulations, as void sizes increase, the nearest void to the crack tip exerts a greater influence on fracture stress than the overall porosity. Furthermore this study provides valuable insights into the relationship between void size and concentration, and the stress necessary for crack growth, marking a step forward towards understanding He bubble-induced fracture in ferrous materials.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A phase-field fracture formulation for generalized standard materials: The interplay between thermomechanics and damage

Accurately modeling fracture of ductile materials poses open challenges in the field of computational mechanics due to the multiphysics nature of their failure processes. Integrating the interplay between thermodynamics and damage into ductile fracture models is vital for predicting critical failure modes. Here, in this paper, we develop a versatile phase-field (PF) framework for modeling ductile fracture, taking into account finite-strain elasto-plasticity. The framework stems from a variational formulation of constitutive relations for generalized standard materials (GSMs), whose response is described by a Helmholtz free energy and a dissipation pseudo-potential. Its variational structure is based on a minimum principle for a functional that expresses the sum of power densities for reversible and irreversible processes. By minimizing this functional with a constraint on a von Mises yield function, we derive the evolution equation for the equivalent plastic strain and an associative flow rule. This constrained optimization problem is analytically solved for a wide class of thermo-viscoplasticity models. The key innovations of the current work include (i) a cubic plastic degradation function that accounts for a non-vanishing damage-dependent yield stress, (ii) closed-form expressions of the Helmholtz free energy and dissipation pseudo-potential for three thermo-viscoplasticity models, (iii) an extended Johnson–Cook plasticity model with a nonlinear hardening law, and (iv) a plastic work heat source that depends on the plastic degradation function and a variable Taylor–Quinney (TQ) coefficient. The capabilities of the proposed framework are tested with the aid of four ductile fracture problems, including the Sandia Fracture Challenge. In each of these problems, we examine the evolution of relevant field variables such as the PF order parameter, the equivalent plastic strain, the temperature, and the internal power dissipation density, in addition to the overall structural response quantified by the force–displacement curve. These numerical studies demonstrate that the proposed framework effectively represents ductile fracture, yielding computational results that exhibit good agreement with experimental data.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Thermo-Mechanical Phase-Field Modeling of Fracture in High-Burnup UO2 Fuels Under Transient Conditions

This study presents a novel multiphysics phase-field fracture model to analyze high-burnup uranium dioxide (UO2) fuel behavior under transient reactor conditions. Fracture is treated as a stochastic phase transition, which inherently accounts for the random microstructural effects that lead to variations in the value of fracture strength. Moreover, the model takes into consideration the effects of temperature and burnup on thermal conductivity. Therefore, the model is able to predict crack initiation, propagation, and complex morphologies in response to thermal gradients and stress distributions. Several simulations were conducted to investigate the effects of operational and transient conditions on fracture behavior and the resulting cracking patterns. High-burnup fuels exhibit reduced thermal conductivity, elevating temperature gradients and resulting in extensive radial and circumferential cracks. Transient heating rates and temperatures significantly affect fracture patterns, with higher heating rates generating steeper gradients and more irregular crack trajectories. This approach provides critical insights into fuel integrity during accident scenarios and supports the safety evaluation of extended burnup limits.

Chemistry↗
DOE OSTI2024

Arbitrary Order Virtual Element Methods for High‐Order Phase‐Field Modeling of Dynamic Fracture

ABSTRACT Accurate modeling of fracture nucleation and propagation in brittle and ductile materials subjected to dynamic loading is important in predicting material damage and failure under extreme conditions. Phase‐field fracture models have garnered a lot of attention in recent years due to their success in representing damage and fracture processes in a wide class of materials and under a variety of loading conditions. Second‐order phase‐field fracture models are by far the most popular among researchers (and increasingly, among practitioners), but fourth‐order models have started to gain broader acceptance since their more recent introduction. The exact solution corresponding to these high‐order phase‐field fracture models has higher regularity. Thus, numerical solutions of the model equations can achieve improved accuracy and higher spatial convergence rates. In this work, we develop a virtual element framework for the high‐order phase‐field model of dynamic fracture. The virtual element method (VEM) can be regarded as a generalization of the classical finite element method. In addition to many other desirable characteristics, the VEM allows computing on polytopal meshes. Here, we use ‐conforming virtual elements and the generalized‐ time integration method for the momentum balance equation, and adopt ‐conforming virtual elements for the high‐order phase‐field equation. We verify our virtual element framework using classical quasi‐static benchmark problems and demonstrate its capabilities with the aid of numerical simulations of dynamic fracture in brittle materials.

42 ENGINEERING↗
DOE OSTI2024

A Thermo‐Flow‐Mechanics‐Fracture Model Coupling a Phase‐Field Interface Approach and Thermo‐Fluid‐Structure Interaction

This work proposes a novel approach for coupling non-isothermal fluid dynamics with fracture mechanics to capture thermal effects within fluid-filled fractures accurately. This method addresses critical aspects of calculating fracture width in enhanced geothermal systems, where the temperature effects of fractures are crucial. The proposed algorithm features an iterative coupling between an interface-capturing phase-field fracture method and interface-tracking thermo-fluid-structure interaction using arbitrary Lagrangian–Eulerian coordinates. We use a phase-field approach to represent fractures and reconstruct the geometry to frame a thermo-fluid-structure interaction problem, resulting in pressure and temperature fields that drive fracture propagation. We developed a novel phase-field interface model accounting for thermal effects, enabling the coupling of quantities specific to the fluid-filled fracture with the phase-field model through the interface between the fracture and the intact solid domain. We provide several numerical examples to demonstrate the capabilities of the proposed algorithm. In particular, we analyze mesh convergence of our phase-field interface model, investigate the effects of temperature on crack width and volume in a static regime, and highlight the method's potential for modeling slowly propagating fractures.

fracture↗
DOE OSTI2025

Calibrating a finite-strain phase-field model of fracture for bonded granular materials with uncertainty quantification

To study the mechanical behavior of mock high explosives, an experimental and simulation program was developed to calibrate, with quantified uncertainty, a material model of the bonded granular material Idoxuridine and nitroplasticized Estane-5703. This paper reports on the efficacy of such a framework as a generalizable methodology for calibrating material models against experimental data with uncertainty quantification. Additionally, this paper studies the effect of two manufacturing temperatures and three initial granular configurations on the unconfined compressive behavior of the resulting bonded granular materials. In each of these cases, the same calibration framework was used; in that, hundreds of high-fidelity direct numerical simulations using a new, graphics processing unit-enabled, high-performance finite element method software, Ratel, were run to calibrate a finite-strain phase-field fracture model against experimental data. It was found that manufacturing temperature influenced the elastic response of the mock high explosives, with higher temperatures yielding a stiffer response. By contrast, it was found that the initial configuration of the grains had a negligible impact on the overall behavior of the mock high explosives though it remains possible that local damage accumulation within the specimens could be altered by the initial configurations. Overall, the calibration framework was successful at creating well-calibrated models, showing its usefulness as an engineering and scientific tool.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Meso-scale modeling of UO2 nuclear fuel to high burnup

To improve the economics of light water reactors for commercial nuclear energy generation, utility operators are seeking to obtain regulatory approval to run UO2 fuel to higher levels of burnup. One potential impediment to obtaining this approval is the phenomenon of fuel fragmentation, relocation, and dispersal (FFRD). FFRD can result when fuel experiences a rapid temperature transient, such as that occurring during a Loss Of Coolant Accident (LOCA). FFRD has historically been most associated with the rim region in UO2 fuel pellets, where the phenomenon of fragmentation is also referred to as pulverization due to the small size of the fragments. More recent evidence suggests that the so-called “dark zone” (due to its appearance in micrographs) that can be observed in the mid-radial regions of high burnup fuel is also susceptible to FFRD. Although empirical fuel performance models have been developed that can adequately predict pulverization in the rim region under typical LWR conditions, a scientific understanding of what underlies fuel restructuring and subsequent FFRD is lacking even in the rim region, and no models are currently available for the behavior the dark zone. To address these challenges, the U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program has employed a multi-scale modeling approach to improve scientific understanding and develop new fuel performance models. In this talk, I will focus on meso-scale efforts, which form a crucial link between atomic-scale and engineering-scale models. Phase-field modeling combined with cluster dynamics is used to predict the restructuring process in the rim region. Phase-field fracture modeling, informed by atomistic simulations, is used to predict the onset of pulverization in the rim region. Combining these techniques together allows the extent of rim pulverization to be predicted. The formation and evolution of the dark zone has also been simulated with the phase-field method, using an improved approach to vacancy source term parameterization. The work shows the important impact of microstructure on fuel performance.

fracture↗
DOE OSTI2024

Crack opening calculation in phase-field modeling of fluid-filled fracture: A robust and efficient strain-based method

The phase-field method has become popular for the numerical modeling of fluid-filled fractures, thanks to its ability to represent complex fracture geometry without algorithms. However, the algorithm-free representation of fracture geometry poses a significant challenge in calculating the crack opening (aperture) of phase-field fracture, which governs the fracture permeability and hence the overall hydromechanical behavior. Although several approaches have been devised to compute the crack opening of phase-field fracture, they require a sophisticated algorithm for post-processing the phase-field values or an additional parameter sensitive to the element size and alignment. Here, we develop a novel method for calculating the crack opening of fluid-filled phase-field fracture, which enables one to obtain the crack opening without additional algorithms or parameters. Here we transform the displacement-jump-based kinematics of a fracture into a continuous strain-based version, insert it into a force balance equation on the fracture, and apply the phase-field approximation. Through this procedure, we obtain a simple equation for the crack opening which can be calculated with quantities at individual material points. We verify the proposed method with analytical and numerical solutions obtained based on discrete representations of fractures, demonstrating its capability to calculate the crack opening regardless of the element size or alignment.

58 GEOSCIENCES↗
DOE OSTI2025

Mesoscale Modeling for Restructuring and Fragmentation in High Burnup UO 2

This report summarizes the mesoscale modeling conducted in fiscal year 2025 under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, focusing on the microstructural evolution and restructuring in high burnup UO 2 nuclear fuel and its impact on fuel fragmentation. We developed a pioneering phase-field model to simulate restructuring behavior across different regions of high burnup fuel, including the dark zone and rim region. A grand-potential-based phase-field model is employed to concurrently evaluate subgrain formation and the growth of fission gas bubbles within the fuel. An energy-based subgrain formation criterion was introduced to simulate the restructuring process. The effects of temperature and burnup rate were studied to capture how each of these parameters influences the characteristics of the restructured fuel. Subgrain formation was observed to initiate around existing fission gas bubbles and proceed toward triple junctions, grain boundaries, and grain interiors. Under a given subgrain formation rate, the rate of restructuring increases with rising fuel temperature. The restructuring occurs faster with higher burnup rate. A restructuring bias was observed within the microstructure, due to the variation in defect accumulation when comparing different grains. Microstructures corresponding to the dark zone and rim region can be obtained by parameterizing the model with the appropriate defect production rate, as determined based on the burnup rate and temperature. The predicted microstructures are consistent with experimental observations of the restructured regions. Based on the mesoscale simulations, a mechanistic model for restructuring and grain size evolution was implemented in BISON. Thus, this work provides a first-of-its-kind restructuring model for different regions of high-burnup fuel to BISON. It was shown that the model predicts appropriate grain size evolution along fuel radius as those observed in experiments. This model enables BISON to predict the effect of restructuring on the fission gas release. Finally, the phase-field fracture simulation with dark zone specific microstructures were presented to provide the fragmentation criteria for the dark zone. This work introduces a first-of-its-kind restructuring model for high burnup fuel, significantly enhancing BISON's predictive capabilities.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

A variational phase-field framework for thermal softening and dynamic ductile fracture

A variational phase field model for dynamic ductile fracture is presented. Here, the model is designed for elasto-viscoplastic materials subjected to rapid deformations in which the effects of heat generation and material softening are dominant. The variational framework allows for the consistent inclusion of plastic dissipation in the heat equation as well as thermal softening. It employs a coalescence function to degrade fracture energy during regimes of high plastic flow. A variationally consistent form of the Johnson–Cook model is developed for use with the framework. Results from various benchmark problems in dynamic ductile fracture are presented to demonstrate capabilities. In particular, the ability of the model to regularize shear band formation and subsequent damage evolution in two- and three-dimensional problems is demonstrated. Importantly, these phenomena are naturally captured through the underlying physics without the need for phenomenological criteria such as stability thresholds for the onset of shear band formation.

42 ENGINEERING↗
DOE OSTI2024

A phase-field diffraction model for thermo-hydro-mechanical propagating fractures

This paper introduces a novel diffraction based thermo-hydraulic–mechanical (THM) model for fracture propagation using a phase-field fracture (PFF) approach. The key innovation of the THM-PFF model lies in its integrated treatment of four solution variables—displacements, phase-field, pressure, and temperature—each governed by a combination of conservation of momentum (mechanics problem), a variational inequality (constrained minimization problem), mass conservation (pressure problem), and energy conservation (temperature problem). This leads to a new formulation of a coupled variational inequality system. A major advancement is the development of an extended fixed-stress algorithm, where displacements, phase-field, pressures, and temperatures are solved in a staggered sequence. An important aspect of this work is the global coupling of pressures and temperatures across the domain using diffraction systems, with diffraction coefficients defined by material parameters weighted by the diffusive phase-field variable. To ensure robust local mass conservation, we employ enriched Galerkin finite elements (EG) for both pressure and temperature diffraction equations. By enriching the continuous Galerkin basis functions with discontinuous piecewise constants, EG accurately represents solution and parameter discontinuities while preserving local mass and energy conservation—crucial aspects for THM problems and realistic behavior. Moreover, the use of a predictor–corrector local mesh adaptivity scheme is employed, allowing the model to handle small phase-field length-scale parameters while maintaining high numerical accuracy and reasonable computational cost. Furthermore, these new model and algorithmic developments represent significant advances in the field and have been substantiated through rigorous numerical tests.

Diffraction systems↗
DOE OSTI2025

Towards robust surrogate models: Benchmarking machine learning approaches to expediting phase field simulations of brittle fracture

Data-driven approaches have the potential to make modeling complex, nonlinear physical phenomena significantly more computationally tractable. For example, computational modeling of fracture is a core challenge where machine learning techniques have the potential to provide a much needed speedup that would enable progress in areas such as multi-scale modeling and uncertainty quantification. Currently, phase field modeling (PFM) of fracture is one such approach that offers a convenient variational formulation to model crack nucleation, branching and propagation. To date, machine learning techniques have shown promise in approximating PFM simulations. While standard fracture benchmarks represent realistic scenarios frequently observed in practice, they typically do not provide sufficiently challenging tests for data-driven methods. Here, to address this gap, we introduce a challenging dataset based on PFM simulations designed to benchmark and advance ML methods for fracture modeling. This dataset includes three energy decomposition methods, two boundary conditions, and 1000 random initial crack configurations for a total of 6000 simulations. Each sample contains 100 time steps capturing the temporal evolution of the crack field. Alongside this dataset, we also implement and evaluate Physics Informed Neural Networks (PINN), Fourier Neural Operators (FNO), and UNet models as baselines, and explore the impact of ensembling strategies on prediction accuracy. With this combination of our dataset and baseline models drawn from the literature we aim to provide a standardized and challenging benchmark for evaluating machine learning approaches to solid mechanics. Our results highlight both the promise and limitations of popular current models, and demonstrate the utility of this dataset as a testbed for advancing machine learning in fracture mechanics research.

Benchmark dataset↗
DOE OSTI2025

Connecting In Situ Stress and Wellbore Deviation to Near-Well Fracture Complexity Using Phase-Field Simulations

The interactions among in situ stress, rock fabric, wellbore geometry, natural fractures, and other natural or man-made defects create highly complex fracture trajectories in the near-wellbore region, far more intricate than those in the far-field. These near-wellbore complexities are critical for the Utah FORGE project and Enhanced Geothermal Systems (EGS) in general. Frictional pressure loss in the near-wellbore region during stimulation can significantly influence the growth of far-field fractures, while pressure losses during circulation serve as a major source of energy dissipation. Near-wellbore fracture complexities are often observable through image logs, offering valuable insights into in situ stress characteristics. However, leveraging this information requires a high-fidelity model capable of capturing the interplay among the diverse factors influencing fracture behavior.

58 GEOSCIENCES↗