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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Finite Element Analysis (FEA) for Water-Foam Fracturing of Granite Rock

In addition to the foam data that were obtained from literature and that were collected from the current study, simulation data was also generated from finite element analysis (FEA) conducted in this study using COMSOL Multiphysics software. The FEA models were built to simulate the experiments conducted at Oak Ridge National Laboratory (ORNL) on cement and granite samples. In these FEA models, temperature was kept at ambient while the pressure profile resembled the loading conditions during the ORNL experiments, where pressure was either monotonically increased or applied cyclically. The cement material was used as a model material and was used to study Von Mises stress and tensile stress distribution for different bore hole length geometry using a parametric sweep with water as fracturing fluid using solid-fluid interaction module. For the granite material, FEA models were developed for stress analysis of cylindrical samples with water or foam fluids. The solid mechanics module in COMSOL was implemented to solve for Von Mises stress and tensile stress. The fluid-structure interaction module was implemented to solve for water-foam interaction on granite cylinder with addition of fluid-loading on structure, i.e., large deformation in solid mechanics with no impact on fluid deformation. Foam was considered as a pseudo single-phase compressible fluid for which material properties were calculated from water and gas (nitrogen) phases. The density of foam is calculated as a function of the densities of water and nitrogen, while viscosity is a function of temperature. Four types of FEA analyses were modelled: 1. Monotonic injection with water 2. Monotonic injection with foam 3. Cyclic injection with water 4. Cyclic injection with foam All the COMSOL files are converted to a zip file which is save in .mph.

15 GEOTHERMAL ENERGY↗
DOE OSTI2021

Development of Digital Twin Predictive Model for PWR Components: Updates on Multi Times Series Temperature Prediction Using Recurrent Neural Network, DMW Fatigue Tests, System Level Thermal-Mechanical-Stress Analysis

The long-term operation (LTO) of nuclear power plant (NPP) beyond their original design life of 40 years, can lead to more material damage associated with cyclic fatigue under thermal-mechanical loading cycles and associated long-term exposure of reactor material to the deleterious reactor-coolant environments. However, under this LTO condition the reactor components can still safely operate but may require more frequent Nondestructive Evaluation (NDE) of reactor components. Frequent NDE requirement may lead to frequent shutdown of the NPP. This in turn can lead to power outage and additional NDE-inspection-cost related economic loss. The economic loss can be minimized by reducing uncertainty in life estimation of safety-critical pressure boundary components and by implementing more digital approach such as by using upcoming digital-twin (DT) technology for predicting the structural states (e.g., time and location dependent inside/outside thickness temperature, stress, strain, plastic deformation, etc.) and associated fatigue life of a component in real time. Towards this goal Argonne National Laboratory (ANL) with the sponsorship of DOE Light Water Reactor Sustainability (LWRS) program is working on the development of a DT framework that can be used for real time environmental fatigue prediction of reactor components. The DT framework is based on limited experiment-data, Artificial-intelligence (AI) – Machine-Learning (ML) - Deep-Learning (DL) based techniques and Multiphysics-computational-mechanics such as finite element (FE) based modeling tools. Towards this overall goal, following are some of the major contributions made during the FY21: 1) Multiple 82/182 dissimilar metal weld (DMW) specimens (both solid-weld and joint-weld representing the actual reactor multi-metal nozzles) were fatigue tested. The resulting fatigue lives were compared to the NUREG-6909 based best-fit and design fatigue curves. Additionally, the results of 52/152 DMW fatigue specimens (which were recently tested at Republic of Korea under the sponsorship of International Nuclear Energy Research Initiative - INERI program) were compared to the NUREG-6909 based best-fit and design fatigue curves. From the comparison of 82/182 and 52/152 DMW test data with NUREG-6909 best-fit curve, most of the reported test data fall way away from the NUREG-6909 suggested best-fit or mean curve. The NUREG-6909 suggested best-fit curve is the best-fit curve of austenitic stainless steel and due to lack of enough data on Nickel-based welds, this is currently being used for predicting the life of Nickel-alloy-based welded components. However, the above observation may require higher scaling factor (e.g., ASME suggested factor of 20 on cycles rather than the current NUREG-6909 suggested factor of 12 on cycles) for scaling the austenitic-stainless-steel best-fit-curve for estimating the design or safe-life of a welded component. Accordingly, for example, if a DMW component experience a strain amplitude of 0.6% the PWR-water life of the component would be 52 cycles instead of 85 cycles. However, more DMW tests are required to further ascertain the above-mentioned observations. 2) A system level CAD and finite element model were developed which consists of reactor pressure vessel (RPV), part of steam generator (SG), part of pressurizer (PRZ), hot leg (HL), and surge line (SL). This is with detailed nozzle geometry and thermal-mechanical material properties of different metals to simulate realistic thermal-mechanical stress under connected system global thermal-mechanical boundary conditions. 3) Different system level heat transfer analyses were performed with estimation of relevant heat transfer coefficients. The resulting data were used in subsequent system level thermal-mechanical stress analysis and for generating spatial-temporal training and validation data for a system level digital-twin based temperature predictor. Transient heat transfer analyses were performed considering thermal boundary condition under design-basis (DB) loading and EDF (Électricité de France) data-based grid-load-following (EDF-GLF) loading cycles. 4) System level thermal-mechanical stress analysis was performed for identifying damage-prone hotspots and for future extension of the model for cyclic state prediction. From the system-level model simulation under DB loading cycle it is found that HL and the SL nozzle that connect to the HL can experience significant stress and strain and could be one of the weakest links in the overall reactor coolant system (RCS). 5) An AI/ML based DT model was developed for multi-time-series temperature prediction at any inside/outside thickness locations of PWR pressure boundary components. This is by using Recurrent-neural-network (RNN) and keras machine learning libraries. The RNN model was validated against two laboratory test-based data sets with one obtained through ANL’s in-air fatigue test system and other through PWR-water test loop. The experimentally validated DT model further validated against FE model results to predict thermal scarification related spatialtemporal temperatures at random locations of a component. The well validated DT model was then used for demonstrating spatial-temporal temperature prediction under 100+ years of reactor operation subjected to combined DB, EDF-GLF and randomized grid-load-following (RANDOMGLF) loading Cycles. The expert-elicitation DT model framework was developed assuming field/input/process measurements can be available from a few existing plant sensors and can readily be used by the NPP operators. The above temperature prediction model will feed to the next-step stress analysis model based on which the life of a component can be predicted in realtime, which is one of our future works.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Machine learning-enabled multiscale modeling of mechanical deformation of aluminum and Al-SiC nanocomposites

A machine learning-enabled multiscale framework is developed for modeling the mechanical response of both pure metal and nanoparticle-reinforced metal matrix nanocomposites (MMNCs). Using aluminum–silicon carbide (Al-SiC) as an example MMNC, atomistic simulations reveal three distinct deformation mechanisms (i.e., defect-free, dislocation-based, and interface separation) governed by the interfaces between the Al matrix and SiC nanoparticles. As compared with single crystal Al, the lattice undergoes a more abrupt failure once the dislocation network becomes extensive and void nucleation initiates, whereas in Al-SiC, nanoparticle interfaces enable a more gradual progression of damage. These mechanisms are captured through a combined classification-regression neural network surrogate model that bridges atomic-scale insights with continuum-scale finite element analysis. Machine learning-enabled multiscale modeling of pure Al accurately predicted strain localization and confirmed by in-situ scanning electron microscopic tensile testing on perforated Al specimens. This study underscores the promise of integrating physics-informed machine learning with hierarchical modeling to capture the interface dominated phenomena and guide the design of advanced MMNCs.

Al-SiC↗
DOE OSTI2020

Compensation of heat load deformations using adaptive optics for the ALS upgrade: a wave optics study

In this paper, a realistic wave optics simulation method has been developed to study how wavefront distortions originating from heat load deformations can be corrected using adaptive X-ray optics. Several planned soft X-ray and tender X-ray insertion-device beamlines in the Advanced Light Source upgrade rely on a common design principle. A flat, first mirror intercepts the white beam; vertical focusing is provided by a variable-line-space monochromator; and horizontal focusing comes from a single, pre-figured, adaptive mirror. A variety of scenarios to cope with thermal distortion in the first mirror are studied by finite-element analysis. The degradation of the intensity distribution at the focal plane is analyzed and the adaptive optics that correct it is modeled. The range of correctable wavefront errors across the operating range of the beamlines is reported in terms of mirror curvature and spatial frequencies. The software developed is a one-dimensional wavefront propagation package made available in the OASYS suite, an adaptable, customizable and efficient beamline modeling platform.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Development of grain-scale slip activity and lattice rotation fields in Inconel 718

Using a combination of in-situ high-resolution digital image correlation (HR-DIC), Heaviside-DIC method (H-DIC), and crystal plasticity finite element (CPFE), we investigate the evolution of intragranular lattice rotations and slip activity during monotonic and cyclic loading in a high performance, polycrystalline face centered cubic material. The CPFE employs a quasi-3D model microstructure, which is a highly resolved mirror representation of the experimental in-situ test sample. In agreement, the measurements and calculations reveal that most grains, regardless of their size and lattice orientation, develop intragranular lattice rotation gradients that span the grain. For a small cluster of grains on the deformed material, we perform HR-DIC analysis of slip lines to demonstrate agreement in the active slip systems and changes in this local slip activity across the individual grains. The combined analysis reveals that deforming grains are divided into sub-granular regions of uniform lattice rotation and these regions are most often associated with only one or two active slip systems. The gradient lines that divide them correspond to changes in the predominant slip system. The model is used to examine the evolution of intragranular lattice rotation in a single fully reversed tension-compression cycle. The calculations indicate that intragranular gradients intensify during the reverse loading path as nearest neighboring regions appear to shed lattice rotation, increasing the lattice rotation in some regions, while shutting down rotation in neighboring regions. So these findings provide insight into the irreversible changes that develop within deforming grains at the scale of the grain, particularly the heterogeneous development of intragranular lattice rotation in early stages of deformation, which could serve as precursors to localization.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Twisting the Hubbard model into the momentum-mixing Hatsugai–Kohmoto model

The Hubbard model is a standard theoretical tool for studying materials with strong electron–electron interactions, such as cuprate superconductors. Unfortunately, interaction-driven phenomena, such as a transition into the strongly correlated Mott insulator phase, are difficult to treat with established theoretical techniques. However, the exactly solvable Hatsugai–Kohmoto model displays similar Mott physics. In this work we show how the Hatsugai–Kohmoto model can be deformed continuously into the Hubbard model. The trick is to systematically reintroduce all the momentum mixing that the original Hatsugai–Kohmoto model omits. This can be accomplished by grouping n momenta into a cell and hybridizing them, resulting in the momentum-mixing Hatsugai–Kohmoto model. We recover the Bethe ansatz ground-state energy of the one-dimensional Hubbard model to within 1% from only ten mixed momenta. Overall, the convergence scales as 1/n2 as opposed to the inverse linear behaviour of standard finite-cluster techniques. Our results for a square lattice reproduce all the known features from state-of-the-art simulations also with only a few mixed momenta. Consequently, we believe that the momentum-mixing Hatsugai–Kohmoto model offers an alternative tool for strongly correlated quantum matter.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Isotopic fractionation as in-situ sensor of subsurface reactive flow and precursor for rock failure

Greater utilization of subsurface reservoirs perturbs in-situ chemical-mechanical conditions with wide ranging consequences from decreased performance to project failure. Understanding the chemical precursors to rock deformation is critical to reducing the risks of these activities. To address this need, we investigated the coupled flow-dissolution- precipitation-adsorption reactions involving calcite and environmentally-relevant solid phases. Experimentally, we quantified (1) stable isotope fractionation processes for strontium during calcite nucleation and growth, and during reactive fluid flow; (2) consolidation behavior of calcite assemblages in the common brines. Numerically, we quantified water weakening of calcite using molecular dynamics simulations; and quantified the impact of calcite dissolution rate on macroscopic fracturing using finite element models. With microfluidic experiments and modeling, we show the effect of local flow fields on the dissolution kinetics of calcite. Taken together across a wide range of scales and methods, our studies allow us to separate the effects of reaction, flow, and transport, on calcite fracturing and the evolution of strontium isotopic signatures in the reactive fluids.

42 ENGINEERING↗
DOE OSTI2026

Instabilities and phase transitions in architected metamaterials: a gradient-enhanced continuum approach

Architected metamaterials such as foams and lattices exhibit a wide range of properties governed by microstructural instabilities and emerging phase transitions. Their macroscopic response–including energy dissipation during impact, large recoverable deformations, morphing between configurations, and auxetic behavior–remains difficult to capture with conventional continuum models, which often rely on discrete approaches that limit scalability. In this work, we propose a nonlocal continuum formulation that captures both stable and unstable responses of elastic architected metamaterials. The framework extends anisotropic hyperelasticity by introducing nonlocal variables and internal length scales reflective of microstructural features. Local polyconvex free-energy models are systematically augmented with two families of non-(poly)convex energies, enabling both metastable and bistable responses. Implementation in a finite element framework enables solution using a hybrid monolithic–staggered strategy. Simulations capture densification fronts, forward and reverse transitions, hysteresis loops, imperfection sensitivity, and globally coordinated auxetic modes. Overall, this framework provides a robust foundation for accelerated modeling of instability-driven phenomena in architected metamaterials, while enabling extensions to anisotropic, dissipative, and active systems as well as integration with data-driven and machine learning approaches.

42 ENGINEERING↗
DOE OSTI2021

Crack tip microplasticity mediated by microstructure gradients

Abstract Traditional fracture theories infer damage at cracks (local field) by surveying loading conditions away from cracks (far field). This approach has been successful in predicting ductile fracture, but it normally assumes isotropic and homogeneous materials. However, myriads of manufacturing procedures induce heterogeneous microstructural gradients that can affect the accuracy of traditional fracture models. This work presents a microstructure‐sensitive finite element approach to explore the shielding effects of grain size and crystallographic orientation gradients on crack tip microplasticity and blunting. A dislocation density‐based crystal plasticity model conveys texture evolution, grain size effects, and directional hardening by computing the constraint from dislocation structures. The results demonstrate that the microstructure can act as a buffer between the local and far fields that affects the crack tip microplasticity variability. For nominal opening loading, grain size and texture affect the local ductility and induce a non‐negligible multiaxial plastic deformation. Furthermore, driving forces based on measuring displacements away from the crack tip are less affected by the microstructure, which suggests that traditional experimental methods smear out important crack tip variability.

Castelluccio, Gustavo M.↗
DOE OSTI2020

Arctic Coastal Erosion: Modeling and Experimentation

Increasing Arctic coastal erosion rates have put critical infrastructure and native communities at risk while also mobilizing ancient organic carbon into modern carbon cycles. Although the Arctic comprises one-third of the global coastline and has some of the fastest eroding coasts, current tools for quantifying permafrost erosion are unable to explain the episodic, storm-driven erosion events. Our approach, mechanistically coupling oceanographic predictions with a terrestrial model to capture the thermo-mechanical dynamics of erosion, enables this much needed treatment of transient erosion events. The Arctic Coastal Erosion Model consists of oceanographic and atmospheric boundary conditions that force a coastal terrestrial permafrost environment in Albany (a multi-physics based finite element model). An oceanographic modeling suite (consisting of WAVEWATCH III, Delft3D-FLOW, and Delft3D-WAVE) produced time-dependent surge and run-up boundary conditions for the terrestrial model. In the terrestrial model, a coupling framework unites the mechanical and thermal aspects of erosion. 3D stress/strain fields develop in response to a plasticity model of the permafrost that is controlled by the frozen water content determined by modeling 3D heat conduction and solid-liquid phase change. This modeling approach enables failure from any allowable deformation (block failure, slumping, etc.). Extensive experimental work has underpinned the ACE Model development including field campaigns to measure in situ ocean and erosion processes, strength properties derived from thermally driven geomechanical experiments, as well as extensive physical composition and geochemical analyses. Combined, this work offers the most comprehensive and physically grounded treatment of Arctic coastal erosion available in the literature. The ACE model and experimental results can be used to inform scientific understanding of coastal erosion processes, contribute to estimates of geochemical and sediment land-to-ocean fluxes, and facilitate infrastructure susceptibility assessments.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Effects of Zn and Ca on the deformation texture evolution of Mg–Zn–Ca alloys at elevated temperatures

This work utilized crystal plasticity simulations and experimental thermo-mechanical processing to examine how Zn and Ca content affects texture evolution in Mg–Zn–Ca alloys during simulated hot rolling. Four different compositions were studied: unalloyed Mg and three Mg alloys of ZX0p50 (Mg- 0.5 wt% Zn- 0.1 wt% Ca), ZX30 (Mg-3 wt% Zn- 0.1 wt% Ca), and ZX31 (Mg-3 wt% Zn- 0.3 wt% Ca). Multi-pass Gleeble experiments simulated hot rolling using plane strain conditions. Unalloyed Mg developed a strong basal texture, while the addition of Zn and Ca significantly weakened the texture in ZX30 and ZX31; this reduction was not seen in ZX0p50. Notably, ZX31 exhibited a split basal texture aligned with the rolling direction. Crystal plasticity simulations revealed that the weaker basal texture in ZX30 and ZX31 resulted from reduced activation of basal and twinning modes compared to unalloyed Mg and Zx0p50. Increased Zn and Ca content raised the ratios of basal to pyramidal critical resolved sheer stress (CRSS) and twin to pyramidal CRSS, enhancing pyramidal slip activity and weakening the basal texture. Extension twinning played a critical role in texture development during the first deformation pass. In unalloyed Mg and ZX0p50, twinning led to a strong basal texture, while ZX30 and ZX31 had weak basal textures that increased only slightly with further deformation. The split basal poles simulated in ZX31 were consistent with the experimental findings, highlighting the interplay between alloy composition and texture evolution.

Crystal plasticity finite element↗
DOE OSTI2024

Chiral limit of 2d QCD revisited with lightcone conformal truncation

We study the chiral limit of 2d QCD with a single quark flavor at finite Nc using LCT. By modifying the LCT basis according to the quark mass in a manner motivated by ’t Hooft’s analysis, we are able to restore convergence for quark masses much smaller than the QCD strong coupling scale. For such small quark masses, the IR of the theory is expected to be well described by the Sine-Gordon model. We verify that LCT numerics are able to capture in detail the spectrum and correlation functions of the Sine-Gordon model. This opens up the possibility for studying deformations of various integrable CFTs using LCT by considering the chiral limit of QCD like theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Seismic Visibility of Eclogite in the Earth’s Upper Mantle—Implications From High Pressure‐Temperature Single‐Crystal Elastic Properties of Omphacite

Abstract Identifying and locating the geochemical and geophysical heterogeneities in the Earth’s interior is one of the most important and challenging tasks for the deep Earth scientists. Subducted oceanic crust metamorphizes into the dense eclogite in the upper mantle and is considered as a major cause of geochemical and geophysical heterogeneities in the deep Earth. In order to detect eclogitic materials inside the Earth, precise measurements of the high pressure‐temperature single‐crystal elasticity of major minerals in eclogite are thus exceedingly important. Omphacite, a Na,Al‐bearing clinopyroxene, constitutes up to 75 vol% of eclogite. In the present study, we performed the first high pressure‐temperature single‐crystal elasticity measurements of omphacite using Brillouin spectroscopy. Utilizing the finite‐strain approach, we obtained the following thermoelastic parameters for omphacite: K S0 ’ = 4.5(1), G 0 ’ = 1.53(5), ∂K S0 /∂ T = −0.029(5) GPa/K, ∂G 0 /∂ T = −0.013(5) GPa/K, with K S0 = 123(3) GPa, G 0 = 74(2) GPa, and ρ 0 = 3.34(1) g/cm 3 . We found that the seismic velocities of undeformed eclogite are similar to pyrolite at the depths of 200–300 and 410–500 km, thus eclogite is seismically invisible at these depths. Combined with the lattice‐preferred orientations of the omphacite in naturally deformed eclogites, we also modeled seismic anisotropy of eclogite at various pressure‐temperature conditions. A 10 km thick subducted eclogitic crust can result in ∼0.2 s shear wave splitting in the Earth’s upper mantle.

Hao, Ming↗
DOE OSTI2024

Multidimensional modeling of fuel-cladding friction in an LWR fuel rod

Solving finite element problems with friction often increases the level of difficulty to obtain properly converged solutions. This type of challenge becomes more salient when advanced, possibly multiscale, material models are employed to capture the thermomechanical behavior of fuel and cladding materials. Here the present work details our recent developments in a nuclear fuel performance finite element code for the systematic consideration of friction in nuclear reactor finite element simulations. We show the application of friction and its effects on the mechanics of light-water reactor rods accounting for various fuel constitutive modeling techniques, model dimensionalities, pellet assumed geometries, and power conditions. In particular, we focus on the fuel rod mechanical behavior as it relates to fuel constitutive models, sensitivity to the coefficient of friction, pellet states of stress, and rod elongation. We discuss the trade-offs between the various multidimensional modeling options and highlight the relevance of frictional effects in the prediction of the fuel rod deformation and interfacial stresses. To relate our modeling results with actual reactor operation, simulations including frictional effects are compared with fuel rod elongation experimental data and some challenges for carrying out a full validation of the axial mechanics are discussed.

42 ENGINEERING↗
DOE OSTI2021

An Analytical Solution for the Initiation and Early Progression of Fretting Wear in Spherical Contacts

Abstract This article derives analytical solutions to calculate the wear volume at the initiation of fretting motion and its early progression over the first few oscillation cycles. The Archard-based model considers a deformable hemisphere that is contact with a deformable flat block. The material pairs investigated are special alloys, the Inconel 617/Incoloy 800H, and Inconel 617/Inconel 617. The analytical study begins with a unidirectional frictional sliding contact, where the local interfacial sliding distance and the nominal sliding distance at the initiation of gross slip are derived. The obtained analytical expressions for unidirectional sliding are then used to derive the corresponding wear volume for the initiation and early progression of gross slip and the wear volume for a general fretting cycle under elastic conditions. These analytical derivations are all verified by the finite element analysis (FEA). The FEA method and the analytical solutions render virtually identical results for both similar and dissimilar material pairs. The effects of plasticity on the wear volume under elastic–plastic conditions are also investigated. It is found that the fretting wear volumes obtained from the FEA simulations, which include plasticity, are close to those obtained from the analytical expressions for purely elastic regimes. All the results are presented in normalized forms, which can be easily generalized and applied to three-dimensional fretting wear of other material pairs.

Engineering↗
DOE OSTI2020

Investigating the Interaction Between Circulating Tumor Cells and Local Hydrodynamics via Experiment and Simulations

Introduction: The biological and mechanical properties of circulating tumor cells (CTCs) in combination with the hemodynamics affect the preference of metastatic sites in the vasculature. Despite the extensive literature on the effects of biological properties on cell adhesion, the effects of hydrodynamic forces on primary attachment remains an active area of research. Here, using simulations in conjunction with experimentation, we provide new insight into the interplay of CTCs dynamics and local hydrodynamics. Methods: A flow experiment of CTC attachment was performed within a bioprinted, double branching endothelialized vessel. Simulations of fluid flow and CTC transport in the reconstructed and idealized bifurcated vessel were respectively performed by HARVEY, our in-house massively parallel computational fluid dynamics solver. HARVEY is based on the lattice Boltzmann and finite element methods to model the fluid and cells dynamics. The immersed boundary method is employed for resolving the fluid–structure interaction. Results: CTC attachment was quantified experimentally at all regions of the complex vessel. The results demonstrate a clear preference for CTCs to attach at the branch points. To elucidate the effect of the vessel topology on the location of attachment, a fluid-only simulation was performed assessing the differences in the hydrodynamics along the vessel. CTC transport in idealized bifurcated vessels was subsequently studied to examine the effects of cell deformability on the local hydrodynamics patterns and, thus, the preference of attachment sites. Conclusions: The current work provides evidence on the correlation of the hydrodynamics forces arising from the vessel topology and CTC properties on the attachment regions.

60 APPLIED LIFE SCIENCES↗
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↗
DOE OSTI2021

Comments on the quantum field theory of the Coulomb gas formalism

The holomorphic Coulomb gas formalism, as developed by Feigin-Fuchs, Dotsenko-Fateev and Felder, is a set of rules for computing minimal model observables using free field techniques. We attempt to derive and clarify these rules using standard techniques of quantum field theory. We begin with a careful examination of the timelike linear dilaton. Although the background charge of the model breaks the scalar field’s continuous shift symmetry, the exponential of the action remains invariant under a discrete shift because the background charge is imaginary. Gauging this symmetry makes the dilaton compact and introduces winding modes into the spectrum. One of these winding operators corresponds to the anti-holomorphic completion of the BRST current first introduced by Felder, and the full left/right cohomology of this BRST charge isolates the irreducible representations of the Virasoro algebra within the degenerate Fock space of the linear dilaton. The “supertrace” in the BRST complex reproduces the minimal model partition function and exhibits delicate cancellations between states with both momentum and winding. The model at the radius $R=\sqrt{pp^{\prime }}$ has two marginal operators corresponding to the Dotsenko-Fateev “screening charges”. Deforming by them, we obtain a model that might be called a “BRST quotiented compact timelike Liouville theory”. The Hamiltonian of the zero-mode quantum mechanics of this model is not Hermitian, but it is PT -symmetric and exactly solvable. Its eigenfunctions have support on an infinite number of plane waves, suggesting an infinite reduction in the number of independent states in the full quantum field theory. Applying conformal perturbation theory to the exponential interactions reproduces the Coulomb gas calculations of minimal model correlation functions. In contrast to spacelike Liouville, these “resonance correlators” are finite because the zero mode is compact. We comment on subtleties regarding the reflection operator identification, as well as naive violations of truncation in correlators with multiple reflection operators inserted. This work is part of an attempt to understand the relationship between the JT model of two dimen- sional gravity and the worldsheet description of the (2 , p ) minimal string as suggested by Seiberg and Stanford.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗