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DOE OSTI2020

Three-dimensional modeling and simulations of single-crystal and bi-crystal titanium for high-strain-rate loading conditions

High purity single crystal titanium (Ti) under shock wave loading is modeled under both one-dimensional and three-dimensional cylindrical conditions. Cylinder sizes of 10 μm and 20 μm radius are both considered in order to assess influence of boundary conditions. A thermodynamically consistent single crystal model for application to shock conditions is presented. The model accounts for the coupled non-linear elastic, dislocation slip, deformation twinning, and structural phase transformation response of the titanium material. Plate impact experiment results using a copper flyer are used to compare against the simulations for crystals oriented in [0001] and [10$\overline1$1] crystallographic directions. The one-dimensional and threedimensional simulations of the two differently oriented single crystals indicate differences between the one-dimensional and three-dimensional representation, especially for the [10$\overline1$1] oriented single crystal. This orientation breaks the relative orientation symmetry between the crystal and cylinder which otherwise exists for the [0001] oriented single crystal. A significant amount of heterogeneity in the field response of the[10$\overline1$1] oriented simulation was demonstrated due to the highly coupled nature of the deformation. A bi-crystal model composed of both the [0001] and [10$\overline1$1] orientations with the boundary between the two along the axis of the cylinder is also considered for a cylinder model size of 10 μm. The results indicate a strong interaction between the two grains that affects the ω phase volume fraction achieved relative to the single crystal calculations.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Enhanced multiscale restriction-smoothed basis (MsRSB) preconditioning with applications to porous media flow and geomechanics

A novel method to enable application of the Multiscale Restricted Smoothed Basis (MsRSB) method to non M-matrices is presented. The original MsRSB method is enhanced with a filtering strategy enforcing M-matrix properties to enable the robust application of MsRSB as a preconditioner. Through applications to porous media flow and linear elastic geomechanics, the method is proven to be effective for scalar and vector problems with multipoint finite volume (FV) and finite element (FE) discretization schemes, respectively. Realistic complex (un)structured two- and three-dimensional test cases are considered to illustrate the method's performance.

58 GEOSCIENCES↗

DOE OSTI2026

Hourglass control in staggered-grid hydrodynamics using virtual element stabilization techniques

Numerical simulations using the staggered-grid hydrodynamics (SGH) discretization suffer from hourglass instabilities. In this work, we develop a stabilization method to suppress the hourglass instabilities using techniques from the virtual element method (VEM). The stiffness matrix of the VEM consists of two terms: the consistency matrix which is rank deficient and the stability matrix. Here, we first show that in two dimensions and on general polygons, the stiffness matrix of the SGH is identical to the consistency matrix of the linear VEM for both the diffusion equation and the linear elasticity equation. These analyses explain the origin of the hourglass instabilities of the SGH discretization method, and establish a theoretical foundation for our proposed stabilization method by augmenting the stiffness matrix of the SGH discretization using the VEM stability matrix. Then, we present numerical examples using Lagrangian SGH simulations. The numerical experiments demonstrate that the proposed VEM stabilization method is effective at eliminating hourglass modes in the SGH discretization.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

A general solution for accelerating screw dislocations in arbitrary slip systems with reflection symmetry

Solutions to the differential equations of linear elasticity in the continuum limit in arbitrary crystal symmetry are known only for steady-state dislocations of arbitrary character, i.e. line defects moving at constant velocity. Troubled by singularities at certain ‘critical’ velocities (typically close to certain sound speeds), these dislocation fields are thought to be too idealized, and divergences are usually attributed to neglecting the finite size of the core and to the restriction to constant velocity. In the isotropic limit, accelerating pure screw and edge dislocations were studied some time ago. A generalization to anisotropic crystals has been attempted for pure screw and edge dislocations only for some special cases. This work aims to fill the gap of deriving a general anisotropic solution for pure screw dislocations applicable to slip systems featuring a reflection symmetry, a prerequisite to studying pure screw dislocations without mixing with edge dislocations. Finally, further generalizations to arbitrary mixed dislocations as well as regularizations of the dislocation core are beyond the scope of this paper and are left for future work.

42 ENGINEERING↗

DOE OSTI2022

The role of surface forces in environment-enhanced cracking of brittle solids

Fracture initiation and propagation in brittle materials is promoted in surface-reactive (sorptive) environments, a phenomenon known as subcritical crack growth (SCG). Laboratory measured crack-propagation velocity vs. stress intensity factor relationships typically exhibit highly nonlinear, multi-stage characteristics that are sensitive to environmental factors such as adsorbate concentration and temperature. For practical purposes, empirical relationships (e.g., a power law) have been used to describe this complex phenomenon. However, how the overall SCG behavior emerges from the underlying fundamental processes near the crack tip, such as the interaction of the crack surfaces separated by only a few nanometers and mass transport within the nano-confined space, is still not well understood. This paper develops a mechanistic, surface-force-based fracture theory (SFFT) which integrates surface force models, fluid transport models, and linear elastic fracture mechanics to quantitatively explain the multi-stage characteristics of SCG in brittle solids. A numerical model is developed based on SFFT and solved through an implicit partitioned scheme for efficiency and modularity. The results are validated by Wiederhorn's data on crack propagation in soda-lime glasses at a wide range of relative humidity levels. We show that, for the first time, the entire range of an SCG curve can be captured by a single physics-based model. The predicted SCG curves reveal that the development of repulsive disjoining pressure behind the crack tip can be responsible for the reduced apparent fracture toughness in a sorptive environment. In conclusion, the shape of the SCG curve, and its changes with respect to the environment, is found to critically depend on the assumed transport models.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Dynamic crushing of metal lattice metamaterials: Shock mode diagrams and transition to topology-independent compaction regime

Additively manufactured lattice metamaterials offer design versatility in strength and energy absorption and provide an additional degree of freedom through the selection of the lattice topology. Under quasistatic loading, the unit cell structure can strongly affect the stiffness, yield, and post-yield behavior, but whether and to what degree the effect of lattice topology persists into dynamic loading scenarios, up to the compaction shock regime, has not been established. LLNL’ s ALE3D hydrocode was used to perform a computational investigation of dynamic loading in multiple lattice types, including the gyroid, octet, Schwarz D, and rhombic dodecahedron, under impact velocities from 0.25 to 2.25 km/s. Shock Hugoniots for each lattice topology are generated and compared, suggesting that above a critical velocity, distinctions between architectures may not persevere and compacted lattices behave similarly. Here, to investigate the transition between topology-dependent quasistatic compression and the topology-independent regime above the critical velocity, a one-dimensional elastic-linear hardening plasticity-densified solid (E-LHP-DS) shock model for lattice materials was developed that relies upon confined compression to link the quasistatic and shock mechanics. Unlike similar works, the model does not assume rigid behavior prior to yield or locking behavior at densification, allowing a richer exploration of lattice mechanics. With only six parameters, the analytical model simultaneously fit quasistatic confined compression simulations for relative densities 0.1 $≤ \bar{ρ} ≤$ 0.9 and predicted dynamic compaction behavior to traverse several distinct shock modes, each defined by a critical impact speed (equivalently, critical stresses). Comparing the numerical results to the one-dimensional E-LHP-DS shock model predictions suggests that the topology-independence under strong shocks is linked to the onset of densification, which can be predicted based on quasistatic confined compression results.

Cellular material↗

DOE OSTI2020

Assessing mechanical response of CO 2 storage into a depleted carbonate reef using a site-scale geomechanical model calibrated with field tests and InSAR monitoring data

Geomechanical risks of injection have raised concerns regarding secure CO 2 storage. In this work, a combined monitoring and modeling approach is used to assess the stress changes and surface uplift associated with CO 2 injection into a depleted carbonate reef of the Michigan basin. A site-scale geomechanical model is built by assigning mechanical properties of formations using well-log and experimental data. Gravity load is applied to the model to estimate the vertical component of stress as well as different lateral boundary displacement scenarios to estimate horizontal stresses. We used a poroelastic pressure-dependent model (instead of a linear elastic mechanical earth model) to calibrate initial stresses using hydraulic fracture test data measured at depleted reservoir status. Multi-phase fluid flow-geomechanical simulations are performed to estimate the poroelastic response during (1) primary depletion (2) field-scale CO 2 injection phase (3) a hypothetical forecast scenario in which well bottom hole pressure (BHP) reach 45000 KPa. The predicted surface uplift is less than 1 mm at the end of the field-scale CO 2 injection phase which is in good agreement with Interferometric Synthetic Aperture Radar (InSAR) uplift measurement. Although the InSAR data shows an insignificant uplift, hydromechanical modeling of injection shows that CO 2 injection still causes reservoir deformation emphasizing the role of carbonate overburden and reservoir formation mechanical properties and limited size of reef on diminishing the surface deformation. Modeling indicates poroelastic response of caprock matters to estimate uplift. The lower permeability of the top two layers provides additional barrier to large uplift. Also, history of subsidence due to production should be accounted to predict uplift due to a follow up injection correctly. This report shows the significance of combining a calibrated geomechanical model with field measured stresses and monitoring data to be used as a tool to ensure the safety of CO 2 storage.

42 ENGINEERING↗

DOE OSTI2024

Post-irradiation examination of UN-Mo-W fuels for space nuclear propulsion

The National Aeronautics and Space Administration's return to space nuclear propulsion stems from the need for a more efficient method of space travel. Nuclear thermal propulsion systems have been shown to be two times more efficient than chemical propulsion. NASA's Sirius program was created to fabricate and test fuels for space nuclear propulsion, specifically to determine their performance under prototypical startup conditions. The Sirius project featured 4 test capsules, Sirius-1 featured uranium nitride fuel dispersed in a matrix of tungsten and rhenium, while Sirius-2A, -2B, and -3 featured uranium nitride-molybdenum-tungsten fuel (UN-Mo-W). This study discusses the Sirius-2A and -2B irradiation experiments at the Idaho National Laboratory, specifically their performance under irradiation at the Transient Reactor Test Facility. It was found that the fuel samples overall did not exhibit significant cracking, though the Sirius-2A fuel did have one large crack on the surface of the fuel. There was minimal hydrogen absorption in the samples, though it is unknown if the absorption occurred during irradiation or during fabrication. Mechanical testing indicated that the UN fuel demonstrated ceramic behavior as expected, and the Mo/W matrix demonstrated linear elastic behavior to failure.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2021

Mechanical characterization of 304L-VAR stainless steel in tension with a full coverage of low, intermediate, and high strain rates

A 304L-VAR stainless steel is mechanically characterized in tension over a full range of strain rates from low, intermediate, to high using a variety of apparatuses. While low- and high-strain-rate tests are conducted with a conventional Instron and a Kolsky tension bar, the tensile tests at intermediate strain rates are conducted with a fast MTS and a Drop-Hopkinson bar. The fast MTS used in this study is able to obtain reliable tensile response at the strain rates up to 150 s -1 , whereas the lower limit for the Drop-Hopkinson bar is 100 s -1 . Combining the fast MTS and the Drop-Hopkinson bar closes the gap within the intermediate strain rate regime. Using these four apparatuses, the tensile stress-strain curves of the 304L-VAR stainless steel are obtained at strain rates on each order of magnitude ranging from 0.0001 to 2580 s -1 . All tensile stress-strain curves exhibit linear elasticity followed by significant work hardening prior to necking. After necking occurrs, the specimen load decreases, and the deformation becomes highly localized until fracture. The tensile stress-strain response of the 304L-VAR stainless steel exhibits strain rate dependence. The flow stress increases with increasing strain rate and is described with a power law. The strain-rate sensitivity is also strain-dependent, possibly due to thermosoftening caused by adiabatic heating at high strain rates. The 304L-VAR stainless steel shows significant ductility. The true strains at the onset of necking and at failure are determined. The results show that the true strains at both onset of necking and failure decrease with increasing strain rate. The true failure strains are approximately 200% at low strain rates but are significantly lower (~100%) at high strain rates. The transition of true failure strain occurs within the intermediate strain rate range between 10 -2 and 10 2 s -1 . A Boltzmann description is used to present the effect of nominal strain rate on true failure strain.

304L-VAR stainless Steel↗

DOE OSTI2025

Effect of alloying on intrinsic ductility in WTaCrV high entropy alloys

Tungsten (W) exhibits desirable properties for extreme applications, such as the divertor in magnetic fusion reactors, but its practicality remains limited due to poor formability and insufficient irradiation resistance. In this work, we study the intrinsic ductility of body-centered cubic WTaCrV based high entropy alloys (HEAs), which are known to exhibit excellent irradiation resistance. The ductility evaluations are carried out using a criterion based on the competition between the critical stress intensity factors for emission (K Ie ) and cleavage (K Ic ) in the {110} slip planes and {110} crack planes, which are evaluated within the linear elastic fracture mechanics framework and computed using density functional theory. The results suggest that increasing the alloying concentrations of V and reducing the concentrations of W can significantly improve the ductility in these HEAs. The elastic anisotropy for these HEAs is analyzed using the Zener anisotropy ratio and its correlation with the concentration of W in the alloys is studied. Results indicate that these alloys tend to be fairly isotropic independently from the concentration of W in them. The computed data for the elastic constants of these HEAs is also compared against available experimental data. The results are in good agreement, validating the robustness and accuracy of the computational methods. Multiple phenomenological ductility metrics were also computed and analyzed against the analytical model. Some metrics, mainly the surrogate D parameter, show a good correlation with the Rice model. The potential of these empirical metrics to serve as surrogate screening models for optimizing the compositional space is also discussed.

Anisotropy↗

DOE OSTI2021

A process to verify numerical models for seismic fluid-structure interaction in advanced reactor vessels

Seismic design and qualification of a liquid-filled advanced nuclear reactor will have to account for fluid-structure interaction (FSI). Interaction between the tank, internal components, and contained liquid will rely on analysis of numerical models that must be verified and validated. Here this study demonstrates a verification process for models of a base-supported cylindrical tank by comparing numerical predictions and analytical solutions. The numerical models are consistent with the assumptions made to derive analytical solutions, namely, either a rigid or a linear elastic tank, ideal fluid, and small-amplitude, unidirectional, horizontal inputs. One software platform is used to illustrate the process. Seismic FSI analysis is performed using the Arbitrary Lagrangian-Eulerian (ALE) and Incompressible Computational Fluid Dynamics (ICFD) solvers in LS-DYNA. Reported responses are those used for design, including hydrodynamic pressures on the tank wall, shear forces and moments at the tank base, and wave heights of the contained liquid. The accuracy of the numerical results is discussed. The numerical models are verified for calculating the pressures on the tank wall and reactions at its base. Accurate simulation of wave action is challenging for both solvers. Recommendations for modeling, code development, and steps for verification are provided. Although focused on reactor vessels and one software platform, the verification process described herein is broadly applicable to liquid-filled vessels and other finite element codes.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Characterizing and modeling the mechanical behavior of an anion exchange membrane for carbon capture applications

A new direct air capture (DAC) technology uses a moisture swing (MS) process with anion exchange membranes, potentially offering a more energy-efficient way to remove CO₂ from the air. In this MS process, the membrane absorbs CO₂ as it dries and releases it when water is added. Understanding the mechanical behavior of these membranes is essential for improving the design and efficiency of DAC systems and prolonging sorbent lifetime. This study tested one anion exchange membrane, Fumasep’s FAA-3, under mechanical loading and various temperature and humidity conditions to measure its swelling, stiffness, strength, plastic deformation, and stress relaxation. Experimental results were used to identify a mechanical model for FAA-3 that can be used to predict the material’s nonlinear viscous behavior under various loads and environments. Unlike prior studies that assumed linear elastic behavior, this work incorporates humidity-dependent swelling, thermal expansion, and nonlinear viscoelasticity of FAA-3 in both the experiments and the model.

Direct air capture↗

DOE OSTI2022

A phase-field model of quasi-brittle fracture for pressurized cracks: Application to UO 2 high-burnup microstructure fragmentation

Here, in this paper, we present a phase-field model of quasi-brittle fracture with pressurized cracks, with dedicated applications for polycrystalline materials. The model is formulated as a minimization problem within the variational framework. The external work done by pressure on the crack surfaces is included in the objective function. Several careful modeling choices lead to a regularization-length-independent critical strength. The model is constructed to give a softening response with an underlying linear traction-separation law. The pressure-dependent softening response and the regularization of the prescribed pressure are demonstrated with a (quasi) one-dimensional numerical analysis. In a two-dimensional numerical analysis under plane strain assumptions, the critical stress corresponding to crack propagation (as predicted by our quasi-brittle fracture model) is compared with linear elastic fracture mechanics (LEFM) analytical solutions. Our model is further utilized to simulate fission-gas-induced fragmentation of the UO 2 high-burnup structure (HBS). Simulation results show that pressurized bubbles can cause crack nucleation and propagation, and that the bubble size and the surrounding external pressure affect the critical pressure corresponding to crack nucleation. Simulations of a partial HBS at different recrystallization stages show that different grain structures (due to recrystallization) also influence crack paths and fragmentation morphology.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Spatio-Temporal Clustering of Seismicity Enabled by Off-Fault Plasticity

While significant progress has been made in understanding earthquake source processes in linear elastic domains, the effect of more realistic rheologies including plasticity is poorly understood. Here, in this work, we simulate the sequence of earthquake and aseismic slip of a 2D antiplane rate-and-state fault embedded in a full-space elastic-plastic bulk. We show that off-fault plasticity may lead to partial ruptures as well as temporal clustering of seismic events. Furthermore, the interaction of fault slip and off-fault plasticity results in pockets of slip deficit. While the energy dissipated through plastic deformation remains a small fraction of the total energy budget, its impact on the source characteristics is disproportionally large through the redistribution of stresses and viscous relaxation. Our results suggest a new mechanism of dynamic heterogeneity in earthquake physics that may have important implications on earthquake size distribution and energy budget.

58 GEOSCIENCES↗

DOE OSTI2023

Deep material network via a quilting strategy: visualization for explainability and recursive training for improved accuracy

Recent developments integrating micromechanics and neural networks offer promising paths for rapid predictions of the response of heterogeneous materials with similar accuracy as direct numerical simulations. The deep material network is one such approaches, featuring a multi-layer network and micromechanics building blocks trained on anisotropic linear elastic properties. Once trained, the network acts as a reduced-order model, which can extrapolate the material’s behavior to more general constitutive laws, including nonlinear behaviors, without the need to be retrained. However, current training methods initialize network parameters randomly, incurring inevitable training and calibration errors. Here, we introduce a way to visualize the network parameters as an analogous unit cell and use this visualization to “quilt” patches of shallower networks to initialize deeper networks for a recursive training strategy. The result is an improvement in the accuracy and calibration performance of the network and an intuitive visual representation of the network for better explainability.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Solving sparse finite element problems on neuromorphic hardware

The finite element method (FEM) is one of the most important and ubiquitous numerical methods for solving partial differential equations (PDEs) on computers for scientific and engineering discovery. Applying the FEM to larger and more detailed scientific models has driven advances in high-performance computing for decades. Here we demonstrate that scalable spiking neuromorphic hardware can directly implement the FEM by constructing a spiking neural network that solves the large, sparse, linear systems of equations at the core of the FEM. We show that for the Poisson equation, a fundamental PDE in science and engineering, our neural circuit achieves meaningful levels of numerical accuracy and close to ideal scaling on modern, inherently parallel and energy-efficient neuromorphic hardware, specifically Intel’s Loihi 2 neuromorphic platform. We illustrate extensions to irregular mesh geometries in both two and three dimensions as well as other PDEs such as linear elasticity. Our spiking neural network is constructed from a recurrent network model of the brain’s motor cortex and, in contrast to black-box deep artificial neural network-based methods for PDEs, directly translates the well-understood and trusted mathematics of the FEM to a natively spiking neuromorphic algorithm.

Applied mathematics↗

DOE OSTI2024

A soft departure from jamming: the compaction of deformable granular matter under high pressures

Here, the high-pressure compaction of three-dimensional granular packings is simulated using a bonded particle model (BPM) to capture linear elastic deformation. In the model, grains are represented by a collection of point particles connected by bonds. A simple multibody interaction is introduced to control Poisson's ratio and the arrangement of particles on the surface of a grain is varied to model both high- and low-frictional grains. At low pressures, the growth in packing fraction and coordination number follows the expected behavior near jamming and exhibit friction dependence. As the pressure increases, deviations from the low-pressure power-law scaling emerge after the packing fraction grows by approximately 0.1 and results from simulations with different friction coefficients converge. These results are compared to predictions from traditional discrete element method simulations which, depending on the definition of packing fraction and coordination number, may only differ by a factor of two. As grains deform under compaction, the average volumetric strain and asphericity, a measure of the change in the shape of grains, are found to grow as power laws and depend heavily on the Poisson's ratio of the constituent solid. Larger Poisson's ratios are associated with less volumetric strain and more asphericity and the apparent power-law exponent of the asphericity may vary. The elastic properties of the packed grains are also calculated as a function of packing fraction. In particular, we find the Poisson's ratio near jamming is 1/2 but decreases to around 1/4 before rising again as systems densify.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Modeling the contributions to acoustic nonlinearity from complex dislocation networks using 3D dislocation dynamics

Nonlinear ultrasonic parameters are highly sensitive to microstructural features that affect macroscale material behavior, providing a nondestructive means to characterize their evolution. Although dislocations are known to be a strong source of acoustic nonlinearity, establishing quantitative links between the acoustic nonlinearity parameter (β), measured via Second Harmonic Generation, and dislocation morphology—such as dislocation length and density—remains an open challenge. This work advances the numerical modeling of dislocation–β relationships using 3D dislocation dynamics (DD) simulations in two approaches: a “static” method computing strain and stress fields from dislocation configurations in the absence of external loading, and a “quasi-static” method to estimate β from the curvature of dislocation lines under applied load. First, the static method is combined with finite element analysis to investigate a recent assertion that heterogeneous initial strain fields can induce higher harmonic generation in a linear elastic medium; the present results do not corroborate this outcome. Then, the quasi-static method is applied to multiple-dislocation scenarios through parametric studies, revealing behaviors not predicted by analytical models, such as the competing interactions of edge and screw dislocations and the significant influence of applied stress on β. Finally, the simulations are used to model SHG experimental results and validate the hypothesis that β can decrease during plastic deformation, despite increasing dislocation density. As the DD code used here is open-source, it provides a practical platform for future investigation into microstructure–β relationships important to the interpretation of SHG results.

Materials science↗