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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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Coupled Reactor and Engine Nuclear Thermal Propulsion Modeling Methodology

The design and development process of a Nuclear Thermal Propulsion (NTP) system requires extensive multiphysics modeling to couple the neutron physics and thermal feedback effects to determine the reactor’s power shape. Propulsion system performance codes utilize this power shape to determine NTP key performance parameters. While the power shape is heavily dependent on the temperature profile and geometry of the reactor, many analyses either assume a constant power shape, or use neutronics analysis to determine a power shape for a specific reactor configuration. The development of a coupling interface for a propulsion system performance code and a Monte Carlo neutron transport code (OpenMC) allows for the reactor power shape to be calculated in an iteration loop. The interface utilizes a file share system to transfer geometry dimensions, temperatures, and material identifiers to OpenMC, which is used to perform a neutron transport simulation of a design like the government Testing Reference Design reactor. The interface is then able to post-process the results from OpenMC and use the same file share system to share a power shape and other important neutron transport parameters to the system performance code. Initial results show that neglecting the changes to power shape when comparing reactor configurations can yield inaccurate results. Furthermore, utilizing propellants other than hydrogen gas can cause significant changes to the power shape, and thus, the thermal performance of a specific reactor design. This methodology is being expanded to allow for multiple families of NTP reactors to be analyzed, including block moderator, particle bed, and NERVA-derived reactors.

multiphysics coupling↗
DOE OSTI2017

Surrogate Models for TREAT Transient Calculations

The Transient Reactor Test Facility (TREAT) at Idaho National Laboratory (INL) is currently preparing for resumption of operation after more than 20 years in a long-term standby state. In parallel with preparation for operations and a new transient testing program, the DOENE Advanced Modeling and Simulation program (NEAMS) has been supporting the development of three-dimensional transient multi-physics modeling capabilities within the reactor physics application MAMMOTH. Recently, the MAMMOTH reactor physics team has begun development of uncertainty and sensitivity analysis for the TREAT core. This research will be used to support the analysis of reactor operation and experiment planning. Traditional approaches, i.e., Monte Carlo simulations, for such tasks require a large number of model evaluations under both steady state and transient conditions. However, exhaustive sets of sampling runs are simply not practical for TREAT since evaluations of each model can take a substantial amount of time. A solution to this problem is to build a surrogate model employing a smaller number of model evaluations. The surrogate model is designed to provide an accurate and fast approximation to the detailed TREAT model. In this manner, the surrogate model can be used in place of the TREAT transient model for uncertainty and sensitivity analysis at a fraction of the computational cost. The high dimensional model representation (HDMR) method is employed here for approximating the responses of interest in terms of functions of lower dimensions. This method has been implemented in RAVEN and all TREAT transient calculations are performed using the multiphysics code MAMMOTH. In addition, a code interface has also been developed in order to couple RAVEN with MAMMOTH. The surrogate model is then tested and compared for TREAT startup testing program Transient Test no. 15 core, and its accuracy is measured by its ability to estimate the mean, coefficient of variance, skewness, excess kurtosis and probability density function of the outputs of Transient Test no. 15 model, as well as root mean square error metric.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

A Refined BISON-Griffin Workflow For Designing Targeted TRISO Transient Experiments In The Transient Reactor Test Facility

U.S. industry is expected to deploy tristructural isotropic (TRISO) particle fuel technologies for commercial reactors within the next decade. In our previous work, we defined a preliminary transient design space for TRISO fuels, identified potential gaps in the available data, and began to develop multiphysics modeling tools that could be applied to design targeted Transient Reactor Test Facility (TREAT) experiments to fill these gaps. This work builds on that foundation by (1) updating BISON fuel performance and Griffin reactor physics models to reflect the current TREAT experiment tube and capsule designs,(2) coupling the codes to improve the accuracy and usability of the transient design analyses, and (3) demonstrating their use over an expanded design space that includes fuel burnup. The simulated mechanical responses of the TRISO particles were complex functions of fission product accumulation, fission gas release, and irradiation-induced dimensional change in the pyrolytic carbon layers. Predicted tangential stresses in particle silicon carbide layers were least compressive for preheated tests involving fresh fuels but remained compressive throughout the ranges of temperature, heat rate, and burnup considered in this work. Finally, comparisons between the potential TREAT transients and historical test reactor irradiations showed that the TREAT tests would produce significantly lower average energy deposition rates, yielding less severe transients with greater relevance to near-term commercial applications. Use of these predictive capabilities has the potential to increase the value of each test, improving the overall efficiency and cost effectiveness of transient testing for TRISO and other advanced fuels.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Building a new multiphysics workflow in MOOSE: application to tritium migration, trapping and advection in TMAP8

Fusion devices are anticipated to produce and consume several kilograms of tritium per year. This rare fuel resource is both highly mobile and radioactive, making tracking inventories a priority for operation and safety. The fusion safety program at the Idaho National Laboratory has been developing the Tritium Migration and Analysis Program (TMAP), of which the latest version is a MOOSE-based application. TMAP8 is verified against its predecessors and possesses additional multi-dimensional tritium migration modeling capabilities. As we extend its capabilities towards both whole device (in multiple dimensions) and whole plant (with multiple components) simulations, the syntax of inputs must become compact, descriptive, compatible with quality assurance processes, and as error-proof as achievable. The new Physics system developed MOOSE can set up equations and instantiating them on plant components. The system permits the automatic definition of complex discretization with a consistency between object parameters achieved programmatically. The Physics system can currently instantiate the equations for heat conduction and Navier Stokes weakly compressible flow. In MOOSE-terms, it automates the definition of kernels, boundary conditions, and several core and helper materials and fields. As part of this effort, Physics classes were developed for tritium migration, trapping and advection within either a multi-dimensional Navier Stokes fluid dynamics simulation, or a 1D thermal hydraulics piping system. In this presentation, we will showcase the new syntax, its application to several verification and validation cases which were already studied using the classical TMAP8 syntax, and a demonstration of the new coupling capabilities for the migration of tritium into blanket coolant channels and the subsequent advection into the coolant loop.

70 - PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Refinement and demonstration of a coupled BISON-Griffin workflow for designing targeted TRISO transient experiments in TREAT

The U.S. nuclear industry is expected to deploy tristructural isotropic (TRISO) particle fuel technologies for commercial reactors within the next decade. In previous work, we defined a preliminary transient design space for TRISO fuels, identified potential gaps in the available data, and began to develop multiphysics modeling tools that could be applied to design targeted Transient Reactor Test Facility (TREAT) experiments to fill these gaps. Here, this work builds on that foundation by (1) updating BISON fuel performance and Griffin reactor physics models to reflect the current TREAT experiment tube and capsule designs, (2) coupling the codes to improve the accuracy and usability of the transient design analyses, and (3) demonstrating their use over an expanded design space that includes fuel burnup. The simulated mechanical responses of the TRISO particles were complex functions of fission product accumulation, fission gas release, and irradiation-induced dimensional change in the pyrolytic carbon layers. The predicted tangential stresses in the particles' silicon carbide layers were least compressive for preheated tests involving fresh fuels but remained compressive throughout the ranges of temperature, heat rate, and burnup considered in this work. Finally, comparisons between the potential TREAT transients and historical test reactor irradiations showed that the TREAT tests would produce significantly lower average energy deposition rates, yielding less severe transients with greater relevance to near-term commercial applications. The use of these predictive capabilities has the potential to increase the value of each test, improving the overall efficiency and cost-effectiveness of transient testing for TRISO and other advanced fuels.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

Automated Design-for-Reliability of a Power Electronics Module

The design of a power electronics module is a multiphysics problem and involves electrical, thermal, and reliability targets and constraints. Although the electrical and thermal design consider multiple aspects such as materials, geometry, and energy losses, reliability design is often limited to the selection of the attachment materials and electrical interconnect types. In this paper, we incorporate reliability metrics in the design phase by investigating the impact of package geometry on the thermomechanical behavior of the die-attachment material. To this end, we conducted thermal and power cycling simulations of a commercial six-pack power module with silicon carbide devices to compute junction temperature and strain energy density per cycle, respectively. We performed multiple simulations with different geometric dimensions and established a correlation between input features and output variables using subspace-based dimension reduction. The machine learning-based dimension reduction method serves as a surrogate model, which can be employed to identify the optimal module design from a thermal and reliability standpoint.

design-for-reliability↗
DOE OSTI2024

Adaptively remeshed multiphysical modeling of resistance forge welding with experimental validation of residual stress fields and measurement processes

Welding processes used in the production of pressure vessels impart residual stresses in the manufactured component. Computational modeling is critical to predicting these residual stress fields and understanding how they interact with notches and flaws to impact pressure vessel durability. Here, in this work, we present a finite element model for a resistance forge weld and validate it using laboratory measurements. Extensive microstructural changes, near-melt temperatures, and large localized deformations along the weld interface pose significant challenges to Lagrangian finite element modeling. The proposed modeling approach overcomes these roadblocks in order to provide a high-fidelity simulation that can predict the residual stress state in the manufactured pressure vessel; a rich microstructural constitutive model accounts for material recrystallization dynamics, a frictional-to-tied contact model is coordinated with the constitutive model to represent interfacial bonding, and adaptive remeshing is employed to alleviate severe mesh distortion. An interrupted-weld approach is applied to the simulation to facilitate comparison to displacement measures. Several techniques are employed for residual stress measurement in order to validate the finite element model: neutron diffraction, the contour method, and the slitting method. Model-measurement comparisons are supplemented with detailed simulations that reflect the configurations of the residual-stress measurement processes themselves. The model results show general agreement with experimental measurements, and we observe some similarities in the features around the weld region. Factors that contribute to model-measurement differences are identified. Finally, we conclude with some discussion of the model development and residual stress measurement strategies, including how to best leverage the efforts put forth here for other weld problems.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Review of Tools for Modeling Core Radial Expansion in Liquid Metal-Cooled Fast Reactors

Core radial expansion in liquid-metal cooled fast reactor systems is a well-known phenomenon that produces strong reactivity feedback effects. It is crucial from a safety standpoint to design a reactor with the proper core restraint system to guide expansion of the fuel assemblies into a formation that produces negative reactivity feedback in accident conditions. However, the modeling of core radial expansion and its associated reactivity feedback is extremely challenging. Liquid metal-cooled fast reactor designers (both industry and commercial) have pointed to improved modeling of core radial expansion as a key modeling challenge for these types of reactors. The Department of Energy Nuclear Energy Advanced Modeling and Simulation (DOE-NEAMS) program has an important role to play in helping to develop a robust, predictive tool for this phenomenon. A literature review has been performed to identify current simulation capabilities applicable to the prediction of core radial expansion in liquid metal-cooled fast reactors and the resultant reactivity feedback effects. An overview as well as a detailed description of the multi-physics phenomena underlying core radial expansion is given in the first two chapters. The objective of this report is to identify existing software that has been or could be applied to the core radial expansion problem, and then to identify possible paths to develop a robust, coupled Multiphysics tool for advanced analysis, in which all three physics (radiation transport, structural mechanics, thermal fluids) are taken into account considering feedback effects from each physics to the other. Several computer codes and workflows have been developed in the United States and abroad to perform individual aspects of radial expansion calculations or to perform loosely coupled analysis. No code system currently exists which tightly and robustly couples the neutronics, thermal hydraulics, and thermal mechanical physics with enough detail to fully resolve the complex core radial expansion reactivity feedback effects. The future availability of such a code system is of vital importance to fully understanding the reactivity feedback effects that occur due to radial expansion, and consequently to optimizing the design of the core restraint system. A potential code development path forward using MOOSE-based tools is suggested in order to leverage the natural tight coupling and robustness of MOOSE-based applications. Additionally, potential gaps for modeling and common assumptions are listed which require further investigation to ensure accuracy for prediction of deformations.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

Coupled Monte Carlo and thermal-hydraulics modeling of a prismatic gas reactor fuel assembly using Cardinal

Cardinal is a MOOSE application that couples OpenMC Monte Carlo transport and NekRS computational fluid dynamics to the MOOSE framework, closing the neutronics and thermal-fluid gaps in conducting tightly-coupled, high-resolution multiscale and multiphysics analyses. By leveraging MOOSE's interfaces for wrapping external codes, Cardinal overcomes many challenges encountered in earlier multiphysics coupling works, such as file-based I/O or overly-restrictive geometry mapping requirements. In this work, we leverage a subset of the multiphysics interfaces in Cardinal to perform coupling of OpenMC neutron transport, MOOSE heat conduction, and THM thermal-fluids for steady-state modeling of a prismatic gas reactor fuel assembly.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
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 OSTI2023

Multiphysics analysis of fuel fragmentation, relocation, and dispersal susceptibility–Part 3: Thermal hydraulic evaluation of large break LOCA under high-burnup conditions

Increasing the peak rod average burnup of pressurized water reactor (PWR) fuel beyond 62 GWd/tU may increase fuel fragmentation, relocation, and dispersal (FFRD) susceptibility during a large break loss of coolant accident (LBLOCA). TRACE thermal hydraulic (TH) LBLOCA analyses were performed for a realistic 24-month high-burnup PWR equilibrium cycle, to inform subsequent transient BISON high-burnup FFRD susceptibility evaluations. Realistic LBLOCA systems behavior was first established by configuring to and comparing with the BEMUSE OECD LBLOCA benchmark. Fuel and operating conditions were then applied from high-burnup VERA depletion calculations. LBLOCA simulations were performed for 281 selected high-burnup rods, for which transient TH boundary conditions were collected for later use in BISON. The TRACE results indicated that rod linear heat rate (rather than burnup) is the main predictor of peak cladding temperature (PCT) during the event. PCT typically occurred at a local burnup lower than the rod-average burnup, especially for twice-burned fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

On a fully-implicit VMS-stabilized FE formulation for low Mach number compressible resistive MHD with application to MCF

This study presents the development and evaluation of a fully-implicit variational multiscale (VMS) stabilized unstructured finite element (FE) formulation for compressible magnetohydrodynamics (MHD) model, at low Mach number regime. The model describes the dynamics of a compressible conducting fluid in the low Mach number limit in the presence of electromagnetic fields and can be used to study aspects of astrophysical phenomena, important science and technology applications, and basic plasma physics phenomena. The specific applications that motivate this study are macroscopic simulations of the longer time-scale stability and disruptions of magnetic confinement fusion (MCF) devices, specifically the ITER tokamak. The discussion considers the development of the VMS FE representation, the structure of the stabilizing terms that deal with significant convective flows, the stabilization of the nearly incompressible response of the fluid flow, and the stabilization of the constraint that enforces the solenoidal involution on the magnetic field. The nonlinear discretized system is solved with scalable preconditioned Newton–Krylov iterative methods, which employs a multiphysics block preconditioning method based on approximate block factorizations and Schur complements. The study presents an evaluation of the VMS method on a 2D cartesian tearing mode instability, and illustrates the scalability of the solvers on MCF relevant problems. A set of results are also presented for longer time-scale stability and disruptions for the ITER tokamak. These include a vertical displacement event (VDE), and a (1,1) internal kink mode. Here, the formulation is demonstrated to be scalable and also reasonably robust with respect to the Lundquist number scaling.

42 ENGINEERING↗
DOE OSTI2024

Scalable Multiphysics Block Preconditioning for Low Mach Number Compressible Resistive MHD with Application to Magnetic Confinement Fusion

This study investigates multiphysics block preconditioners that are critical in devising scalable Newton–Krylov iterative solvers for longer time-scale fully implicit fluid plasma models. The specific model of interest is the visco-resistive, low Mach number, compressible magnetohydrodynamics (MHD) model. This model describes the dynamics of conducting fluids in the presence of electromagnetic fields and can be used to study aspects of astrophysical phenomena, important science and technology applications, and basic plasma physics. The specific application of interest that motivates this study is the macroscopic simulation of longer time-scale stability and disruptions of magnetic confinement fusion devices, specifically the ITER Tokamak. The computational solution of the governing balance equations for mass, momentum, heat transfer, and magnetic induction for resistive MHD systems can be extremely challenging. These difficulties arise from both the strong nonlinear, nonsymmetric coupling of fluid and electromagnetic phenomena as well as the significant range of time and length scales that the interactions of these physical mechanisms produce. To handle the range of time and spatial scales of interest, a fully implicit unstructured variational multiscale finite element formulation is employed. For the scalable solution of the Newton linearized systems, fully coupled block preconditioners are designed to leverage algebraic multigrid subsolves. In conclusion, results are presented for the strong and weak scaling of the method as well as the robustness of these techniques for a large range of Lundquist numbers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Q1 Report for FY25 Theory and Simulation Performance Target: Development of an integrated modeling framework for fusion reactor design and assessment

This report describes the work and activities carried out towards the completion of each of the following milestones in FY25 Q1: 1. Demonstrate workflow for generating self-consistent CESOL plasma profiles + first wall and divertor loading prediction and generate the CAT plasma and neutron loading needed for further engineering analysis: $/circ$ Initially run CESOL with SOLPS and map heat flux using simple HEAT method: ▪ Generate SOLPS grid for CAT reference case, ▪ Implement and apply ‘lower’ fidelity method of using HEAT-like analytic method to map SOLPS heat flux from charged particles to first wall, and ▪ Provide initial heat flux + neutron loading for further engineering analysis. 2. Demonstrate multiphysics magnet analysis: $/circ$ Demonstrate validation of the Elmer workflow by comparing induced stresses due to EM forces generated by TF coils using multiple codes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Modeling and Design Parameter Optimization to Improve the Sensitivity of a Bimorph Polysilicon-Based MEMS Sensor for Helium Detection

Helium is integral in several industries, including nuclear waste management and semiconductors. Thus, developing a sensing method for detecting helium is essential to ensure the proper operation of such facilities. Several approaches can be used for helium detection, including based on the high thermal conductivity of helium, which is several times higher than air. This work utilizes the high thermal conductivity of helium to design and analyze a bimorph MEMS sensor for helium sensing applications. COMSOL Multiphysics software (version 6.2) is used to carry out this investigation. The sensor is constructed from poly-silicon and SiO 2 materials with a trenched cantilever beam configuration. The sensor is electrically heated, and its morphed displacement depends on the surrounding gas’s composition, which decreases in the presence of helium. Several factors were investigated to probe their effect on the sensor’s sensitivity to helium, including the thickness of the poly-silicon layer, the configuration of the trench, and the thickness and location of SiO 2 layer. The simulations showed that the best performance, up to 2 ppm helium detection level, can be achieved with thinner beams and medium trench lengths.

47 OTHER INSTRUMENTATION↗
DOE OSTI2024

Toward digital design at the exascale: An overview of project ICECap

High performance computing has entered the Exascale Age. Capable of performing over 1018 floating point operations per second, exascale computers, such as El Capitan, the National Nuclear Security Administration's first, have the potential to revolutionize the detailed in-depth study of highly complex science and engineering systems. However, in addition to these kind of whole machine “hero” simulations, exascale systems could also enable new paradigms in digital design by making petascale hero runs routine. Currently, untenable problems in complex system design, optimization, model exploration, and scientific discovery could all become possible. Motivated by the challenge of uncovering the next generation of robust high-yield inertial confinement fusion (ICF) designs, project ICECap (Inertial Confinement on El Capitan) attempts to integrate multiple advances in machine learning (ML), scientific workflows, high performance computing, GPU-acceleration, and numerical optimization to prototype such a future. Built on a general framework, ICECap is exploring how these technologies could broadly accelerate scientific discovery on El Capitan. In addition to our requirements, system-level design, and challenges, we describe some of the key technologies in ICECap, including ML replacements for multiphysics packages, tools for human-machine teaming, and algorithms for multifidelity design optimization under uncertainty. As a test of our prototype pre-El Capitan system, we advance the state-of-the art for ICF hohlraum design by demonstrating the optimization of a 17-parameter National Ignition Facility experiment and show that our ML-assisted workflow makes design choices that are consistent with physics intuition, but in an automated, efficient, and mathematically rigorous fashion.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Optical neural engine for solving scientific partial differential equations

Abstract Solving partial differential equations (PDEs) is the cornerstone of scientific research and development. Data-driven machine learning (ML) approaches are emerging to accelerate time-consuming and computation-intensive numerical simulations of PDEs. Although optical systems offer high-throughput and energy-efficient ML hardware, their demonstration for solving PDEs is limited. Here, we present an optical neural engine (ONE) architecture combining diffractive optical neural networks for Fourier space processing and optical crossbar structures for real space processing to solve time-dependent and time-independent PDEs in diverse disciplines, including Darcy flow equation, the magnetostatic Poisson’s equation in demagnetization, the Navier-Stokes equation in incompressible fluid, Maxwell’s equations in nanophotonic metasurfaces, and coupled PDEs in a multiphysics system. We numerically and experimentally demonstrate the capability of the ONE architecture, which not only leverages the advantages of high-performance dual-space processing for outperforming traditional PDE solvers and being comparable with state-of-the-art ML models but also can be implemented using optical computing hardware with unique features of low-energy and highly parallel constant-time processing irrespective of model scales and real-time reconfigurability for tackling multiple tasks with the same architecture. The demonstrated architecture offers a versatile and powerful platform for large-scale scientific and engineering computations.

Tang, Yingheng (ORCID:0009000153622546)↗
DOE OSTI2017

Developing strong concurrent multiphysics multiscale coupling to understand the impact of microstructural mechanisms on the structural scale

The heterogeneity in mechanical fields introduced by microstructure plays a critical role in the localization of deformation. To resolve this incipient stage of failure, it is therefore necessary to incorporate microstructure with sufficient resolution. On the other hand, computational limitations make it infeasible to represent the microstructure in the entire domain at the component scale. In this study, the authors demonstrate the use of concurrent multi- scale modeling to incorporate explicit, finely resolved microstructure in a critical region while resolving the smoother mechanical fields outside this region with a coarser discretization to limit computational cost. The microstructural physics is modeled with a high-fidelity model that incorporates anisotropic crystal elasticity and rate-dependent crystal plasticity to simulate the behavior of a stainless steel alloy. The component-scale material behavior is treated with a lower fidelity model incorporating isotropic linear elasticity and rate-independent J 2 plas- ticity. The microstructural and component scale subdomains are modeled concurrently, with coupling via the Schwarz alternating method, which solves boundary-value problems in each subdomain separately and transfers solution information between subdomains via Dirichlet boundary conditions. Beyond cases studies in concurrent multiscale, we explore progress in crystal plastic- ity through modular designs, solution methodologies, model verification, and extensions to Sierra/SM and manycore applications. Advances in conformal microstructures having both hexahedral and tetrahedral workflows in Sculpt and Cubit are highlighted. A structure-property case study in two-phase metallic composites applies the Materials Knowledge System to local metrics for void evolution. Discussion includes lessons learned, future work, and a summary of funded efforts and proposed work. Finally, an appendix illustrates the need for two-way coupling through a single degree of freedom.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗