News & Views, Volume 53 | PEGASUSTM Nuclear Fuel Code


By:  Bill Lyon

The PEGASUS nuclear fuel behavior code features a robust 3D, finite element modeling (FEM) computational foundation capable of performing both thermo-mechanical and structural non-linear analyses within a highly versatile and customizable computational platform. The first applications of PEGASUS were for light water reactor (LWR) fuels and materials. Development work on PEGASUS has been extended to advanced fuel designs such as those proposed for Advanced Technology Fuel (ATF) LWR applications and Gen IV reactor designs, including gas and liquid metal-cooled reactors (GCRs and LMRs). 

The versatility and adaptability of PEGASUS is key in enabling extensions to non-conventional operating environments, materials, fuel forms, and geometries.

SiC Cladding

Figure 1. SiGA cladding is a multi-layered composite design composed of SiC fiber in a SiC matrix.

A project is underway to further the development and irradiation testing of a composite silicon carbide matrix as an ATF cladding material. This research is supported through a DOE Funding Opportunity award (DE-FOA-0002308) for the irradiation of a composite silicon-carbide (SiC) ceramic matrix material in an existing U.S. commercial LWR. This work is led by General Atomics – Electromagnetic Systems (GA-EMS) with Structural Integrity Associates (SIA) as a primary subcontractor. For this work, PEGASUS is being adapted to model monolithic and composite SiC manufactured by GA-EMS, SiGA [1], through the incorporation of proprietary material constitutive models. PEGASUS will then be used to provide independent test performance analyses aiding in the design of the irradiation vehicle and predicted material performance. The goal of the testing is to gather irradiation data under prototypic LWR operating conditions and to inform and confirm material performance models for the SiGA-based cladding. A follow-on activity is planned to evaluate the predicted performance compared to data gathered during the post-irradiation examination phase of the project.

Figure 2. Lightbridge Fuel Design PEGASUS Models

Cruciform Metallic Fuel
An additional fuel concept that has been explored using PEGASUS is a cruciform, extruded metallic fuel design proposed by Lightbridge Corporation [2]. This fuel is characterized by a unique multi-lobed fuel cross-section and features a U-50Zr fuel composition. Recent work has been published on fabrication testing of this proposed fuel design by Pacific Northwest National Laboratory (PNNL) [3]. PEGASUS has been used previously to prototype 2D and 3D geometric models and meshes of Lightbridge fuel and to perform fundamental temperature and stress distributions for this fuel under prototypic LWR conditions. PEGASUS has specific modeling tools designed to facilitate “extruded” 3D fuel designs that automate the meshing of these geometries. More work in this area is planned as a proposal has recently been awarded under the DOE NEUP program (DE-FOA-0002732) funding a collaborative project led by Texas A&M University along with Lightbridge, NuScale, and Structural Integrity Associates, Inc. (SI) for modeling this type of fuel for application in a LWR SMR.


The initial implementation of metallic alloy fuel and stainless-steel cladding material constitutive models for prototypic fast reactor fuel designs in PEGASUS has been completed. Material properties and behavioral models for U-Pu-Zr fuel and HT-9 (high Chromium, martensitic stainless steel) cladding have been added. Ongoing work includes the implementation of a gaseous swelling and fission gas release behavior model for U-Pu-Zr fuel, a Zr-redistribution model, and a fuel-cladding chemical interaction (FCCI) model that includes the effect on cladding wall thinning.

To test the implementation of these models, benchmark tests were prepared that provided comparative data for assessment of the models’ performance. Test cases were chosen from two experimental series irradiated in EBR-II: X430, a 37-pin hexagonal sub-assembly, and X441, a 61-pin bundle. These experiments were designed to test numerous fuel rod design variables and fuel response as a function of fuel alloy composition, smear density, plenum-to-fuel volume ratio, power, and coolant conditions [4]. The general experimental fuel rod design corresponds to the typical driver fuel configuration shown in Figure 3.

Figure 3. Typical EBR-II Mark-III or Mark-IIIA Fuel Element [5]

Figure 4. Left: 2D Computational Model of Rod DP2, Right: Temperature Contour Plot of the Fuel Stack Region for Rod DP21 at Peak Power (plenum region removed for detail)

An illustration of the model and selected results from the initial analysis of rod DP21, assembly X441 are shown in the figures above. Figure 4 provides a diagram of the computational model showing the primary components of the model and a plot of the temperature distribution throughout the fueled region of the rod at peak power. Figure 5 provides the radial temperature profile across the fuel rod from the center to the cladding outer surface at peak power near the end of the irradiation period. Temperatures vary from just ~900 K at the pellet center to ~650 K at the cladding surface. The temperature differential is fairly low at ~250 K, as would be expected from a high-conductivity metal fuel rod with a Na-bonded fuel cladding gap. These results are consistent with published experimental observations.

Several advanced fuel material models have been implemented specifically for TRISO fuel in PEGASUS, including thermal and mechanical models for UCO or UO2 kernels, PyC, SiC materials, and a fission gas release model for computing the release of gaseous fission products such as Xe and Kr. In addition to the standard 3D and 2D axisymmetric modeling FEM capabilities in the code, PEGASUS contains several unique tools designed specifically to support TRISO fuel modeling and analysis. These include a “spherical mesh object” tool that can automate the process of generating 2D/3D TRISO spheres, meshing them, and embedding them into a fuel matrix to allow modeling of individual TRISO kernels or fully encapsulated TRISO fuel forms. An example of models generated using the spherical mesh object tool is shown in Figure 6. The spherical mesh object capability is, to our knowledge, unique to PEGASUS and not found in any other fuel performance or general-purpose FEM code. PEGASUS also has a “reshape” function that can automate the process of meshing and modeling deformed TRISO particles to increase user efficiency. Figure 7 illustrates particle meshes that were created using the reshape meshing tool.

These modeling capabilities allow PEGASUS to be used to investigate very detailed mechanical and structural effects in TRISO fuel forms. For example, enabling the detailed analysis of the mechanical interaction between TRISO fuel layers explicitly examining the effects of cracking, debonding, and asphericity within whole or damaged particles.

Figure 5. Radial Temperature Distribution Across the Fuel Rod Model at ~ 486 Days of Irradiation

Planned future development work includes the integration of damage-mechanics modeling and fission product diffusion in the TRISO particle, fuel compact, ad matrix. One failure mode of particular interest that has been identified is cracking of the IPyC layer which propagates through the SiC outer layer. This can create a pathway for enhanced fission product release from the TRISO particle to the surrounding fuel matrix. This failure mechansim appears to occur when the buffer layer remains bonded to the IPyC layer providing the conditions for a synergistic mechanical and chemical failure mechanism that combines cracking, stress concentration, and chemical corrosion (localized Pd-induced corrosion in the SiC [6]. This failure mode is of interest because it can have a strong impact on fuel source term determination for operational TRISO fuel.

Figure 6. Temperature distribution in a cross-section of a 3D slab of a TRISO compact matrix model with a “sparse”, random kernel distribution under prototypic gas-cooled reactor conditions. (Generated using the “spherical mesh object” tool.)

PEGASUS is an advanced analysis tool developed for industry applications that can provide a complimentary and independent capability for nuclear fuel performance. Recent development work on PEGASUS has focused on expanding the applicability of the code to the advanced fuel (ATF) and advanced reactor arena. Future development is planned for PEGASUS that will continue along multiple avenues with an emphasis on advanced fuels and specific thermo-mechanical issues within the industry, such as deterministic failure model development. One example of this is the aforementioned Pd-induced failure mechanism identified for TRISO fuel. SI is actively seeking partners within the advanced fuel community to collaborate with on this work and would welcome inquiries and proposals for expanded application of PEGASUS.


Figure 7. Deformed 3D TRISO particle meshes generated using the “reshape” function tool in PEGASUS.


  1.   C. P. Deck et al., Overview of General Atomics SiGA™ SiC-SiC Composite Development for Accident Tolerant Fuel, Transactions of the American Nuclear Society, Vol. 120, Minneapolis, Minnesota, June 9–13, 2019.
  2.   J. Malone, A. Totemeier, N. Shapiro, and S.  Vaidyanathan, Lightbridge Corporation’s Advanced Metallic Fuel, Nuclear Technology, Vol 180, Dec. 2012.
  3.  Z. Huber and E. Conte, Casting and Characterization of U-50Zr, PNNL-33873, Pacific Northwest National Laboratory, Richland, Washington 99354, Jan. 2023.
  4.  C. E. Lahm, J. F. Koenig, R. G. Pahl, D. L. Porter, and D. C. Crawford, “Experience with Advanced Driver Fuels in EBR-II,” J. Nucl. Mat. 204 (1993) 119-123.
  5. G. L. Hofman, M. C. Billone, J. F. Koenig, J. M. Kramer, J. D. B. Lambert, L. Leibowitz, Y. Orechwa, D. R. Pedersen, D. L. Porter, H. Tsai, and A. E. Wright. Metallic fuels handbook, Technical Report ANL-NSE-3, Argonne National Laboratory, 2019.
  6. J.D Hunn, C.A. Baldwin, T.J. Gerzak, F.C. Montgomery, R.N. Morris, C.M. Silva, P.A Demkowicz, J.M. Harp, and S.A. Ploger, Detection and Analysis of Particles with Failed SiC in AGR-1 Fuel Compacts, Nuclear Engineering and Design, April 2016.

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News & Views, Volume 52 | PEGASUS: Development for TRISO Fuel and Advanced Reactor Applications


By:  Bill Lyon

The Pegasus code allows the user to develop more realistic models of fuel behavior by utilizing an innovative 3D framework that delivers a more detailed and rigorous solution. This solution allows the user to remove conservative assumptions, simplifications, and uncertainties resulting from 2D or 1D simplified/empirical solutions. 

Figure 1. A PEGASUS TRISO fuel particle model and mesh showing geometry and composition

Remove the conservativism and start using the calculated operational margins to increase efficiencies and reduce the capital outlay for refueling.


  • Independently developed 3D FEM code; fuel vendor independent code provides best-estimate performance modeling
  • Focused on fuel structure
  • Provides high-fidelity results
  • Addresses existing fuel performance
  • Aids in the development of advanced fuel designs
  • Ready for Gen IV Reactors and TRISO Fuels


  • Reduced conservatism
  • Increased efficiencies
  • Potential for significant fuel cost savings

The PEGASUS nuclear fuel behavior code is a robust 3D, finite element modeling (FEM) computational software platform capable of thermo-mechanical and structural non-linear analyses of nuclear fuel and reactor components. Focused initially on light water reactor (LWR) fuels and materials, PEGASUS is being adapted and applied to a broader range of emerging industry priorities for proposed Gen IV (Generation IV) advanced reactor designs such as high-temperature gas (HTGRs) and molten salt-cooled reactors (MSRs). These applications require modeling various fuel forms, geometries, and materials such as high assay, low enrichment uranium (HALEU), advanced cladding alloys, and other fuels with integrated containment such as tri-structural isotropic (TRISO) fuel particles and encapsulated particle fuel types. PEGASUS is perfectly positioned to evaluate these challenging structures with realistic modeling and simulation results.

One of the significant efforts underway in the continued development of PEGASUS is the introduction of material constitutive and behavioral models for TRISO fuel and the materials that comprise this fuel form. The initial research on the needed material property and behavior model data comes from a variety of sources, including the Department of Energy’s (DOE’s) Advanced Gas Reactor (AGR) fuel development and qualification experimental program [1] and numerous DOE-supported modeling efforts such as those from Hales et al. [2,3]. In parallel to those efforts, geometric modeling and meshing techniques specifically designed to address the complex TRISO fuel geometric configurations are being explored and developed. These exploit the CAD-like modeling environment and the already available automated meshing tools and capabilities in PEGASUS.

TRISO fuel forms are comprised of multi-layered particles embedded into fuel compacts of various compositions and shapes. The TRISO particle layers are designed to encapsulate and contain the nuclear fuel and the fission products produced during operation. It is this characteristic that creates the robust nature of TRISO-based fuels. The fuel particles are typically composed of a fuel kernel, such as uranium oxycarbide (UCO), surrounded by layers of 1) a porous carbon buffer, 2) an inner pyrolytic carbon (PyC) shell, 3) a silicon carbide (SiC) layer, and 4) an outer PyC shell. The orientation and relative thicknesses of these layers are shown in Figure 1, which depicts a basic PEGASUS TRISO particle model.

Material constitutive models have been developed for UCO fuel, porous and pyrolytic carbon, and SiC and are currently being tested for application in PEGASUS.

In addition to conventional FEM-based modeling and meshing capabilities, PEGASUS also contains several tools explicitly designed to facilitate advanced reactor and fuel analysis. These include: 1) a 3D and hybrid 2D/3D meshing capability to optimize computational efficiency (currently under development), 2) a “spherical mesh object” tool to generate 3D/2D spheres and embedded spheres for modeling TRISO and fully encapsulated TRISO fuel forms, and 3) a “spiral extrusion” tool which can generate complex, spiral 3D fuel geometries and meshes such as those required for helical multi-lobed advanced fuel designs.

The spherical mesh object and spiral extrusion tools are unique to PEGASUS and, to our knowledge, not found in any other fuel performance or general-purpose FEM code. 

Figure 2. Example TRISO particle distribution: (a) micrograph of a TRISO fuel compact (adapted from Nelson [5]), (b) random particle distribution pattern algorithm output.

Figure 3. Cross-sectional view of embedded TRISO particles in a 3D fuel compact matrix.

These modeling capabilities allow PEGASUS to be used to investigate very detailed mechanical and structural effects in highly complex fuel forms. For example, the mechanical interaction between TRISO fuel layers, including the effects of cracking, debonding, and asphericity, can be modeled explicitly. Future work is planned to integrate damage-mechanics modeling capability into PEGASUS that is specifically applicable to TRISO-based fuels.

Given the complexity of typical TRISO fuel forms, another critical aspect for analysis is the development of a consistent methodology for generating configurations that mimic the distribution of TRISO particles in a fuel matrix. A technique has been developed based on a “passive randomization method” originated by Sukharev [4] that yields distribution patterns approximating those of TRISO fuels observed during fuel examinations. An example of an early application of this technique is shown in Figure 2, which compares a fuel micrograph to a generated TRISO particle configuration pattern.

For application in PEGASUS, geometric configurations such as shown in Figure 2b are converted into 2D and 3D FEM meshes with TRISO kernels embedded in meshed substrates using automated tools. Models such as these can provide the bases for computational studies of TRISO fuel performance, from detailed kernel multilayer response to interactions between multiple kernels and their surrounding matrix. Several examples of TRISO meshes generated with PEGASUS are shown in Figures 3, 4, and 5. Figure 3 illustrates the cross-section of a 3D TRISO fuel compact with embedded TRISO particles. The appearance of multiple particle sizes is an indication of varying particle depths within the matrix. This figure was generated using the spherical object meshing tool in PEGASUS.

Figure 4. Cross section of an array of discrete 3D TRISO particles embedded into a graphite compact pellet.

A more complex 3D model of encapsulated TRISO particles is shown in Figure 4.  This model features a sparse particle distribution generated using the randomization technique applied in Figure 2b coupled with 3D automated meshing capabilities. This model was meshed in PEGASUS using an automated scripting tool and tested early in the development project using simplified approximations of thermal and mechanical properties of the kernel and matrix materials. Boundary conditions simulating prototypic gas reactor conditions were used in the simulation. Figure 5 shows the plotted temperature distribution from a portion of the model in figure 4.

Figure 5. Temperature distribution in a cross-section of a 3D slab of a TRISO compact matrix model under prototypic gas-cooled reactor conditions.

Further development of the TRISO fuel modeling capabilities in PEGASUS is ongoing. Detailed 3D modeling of TRISO kernels with irregular geometries such as non-uniform thicknesses and shapes in the pyrolytic carbon and SiC layers has been identified as a high priority as we advance. Additional priorities for future development include 1) implementation of mechanistically based, deterministic TRISO kernel and fuel compact failure models integrated into the material constitutive relations and 2) the calculation and tracking of fission product species diffusion and concentrations which incorporate the effects of chemical interactions, kernel layer, and substrate cracking.

The PEGASUS nuclear fuel behavior code is an advanced, independently developed 3D FEM computational software program capable of conducting complex, coupled thermo-mechanical and structural non-linear analyses. The role of PEGASUS is envisioned as complementary to existing regulatory-based assessment and licensing tools, where there is a need to address conservatism, perform an independent assessment, or provide additional fidelity to laboratory-sponsored research where wider materials, phenomena, or fidelity is needed. Current development activity is focused on application to proposed GEN IV advanced reactor designs featuring unique fuel materials and design configurations such as TRISO-based ceramic fuels to be deployed in HTRGs and MSRs. Future development work on PEGASUS will continue along multiple avenues, emphasizing TRISO constitutive and deterministic failure model development, implementation, and modeling. In summary, PEGASUS provides high fidelity and independent advanced analysis capability that can be used to address existing fuel performance. It allows for less conservatism and accelerates the development, design, and regulatory processes for new fuel concepts and advanced fuel designs such as those employing TRISO-based fuels.


  1. D. A. PETTI, G. BELL, and the AGR Team, “The DOE Advanced Gas Reactor (AGR) Fuel Development and Qualification Program,” INEEL/CON-04-02416, 2005 International Congress on Advances in Nuclear Power Plants, May 15-19, 2005.
  2. J. D. HALES et al., “Multidimensional Multiphysics simulation of TRISO particle fuel,” J. Nucl. Mat. 443 (2013) 531-543.
  3.  J. D. HALES et al. “BISON TRISO Modeling Advancements and Validation to AGR-21 Data,” INL/EXT-20-59368, September 2020.
  4.  A. G. SUKHAREV, Optimal strategies of the search for an extremum, U.S.S.R. Computational Mathematics and Mathematical Physics, 11(4), 1971.
  5. A. T. NELSON, Features that Further Performance Limits of Nuclear Fuel Fabrication: Opportunities for Additive Manufacturing of Nuclear Fuels, ORNL/SPR-2019/1183, May 2019.

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News & Views, Volume 49 - PEGASUS- Advanced Tool for Assessing Pellet-Cladding Interaction

News & Views, Volume 49 | PEGASUS: Advanced Tool for Assessing Pellet-Cladding Interaction

By:  Bill Lyon, PE and Michael Kennard

News & Views, Volume 49 - PEGASUS- Advanced Tool for Assessing Pellet-Cladding Interaction

PEGASUS provides a fully capable computational environment to solve the unique, detailed 3D analyses required for the evaluation of PCI.

In the current economic environment in which nuclear units compete with less costly energy sources, a quicker return to full power correlates to more power generated and increased operating efficiency.  This may be achieved with shorter startup post-refueling or a quicker return-to-power following any number of plant evolutions including load follow, control blade repositioning, equipment outage or maintenance, testing, extended low power operation, scram, etc.  Such strategies to increase operating efficiency may enhance the risk of pellet-cladding interaction (PCI), a failure mechanism that occurs under conditions of high local cladding stress in conjunction with the presence of aggressive chemical fission product species present at the cladding inner surface.  These conditions can occur during rapid and extensive local power changes and can be further enhanced by the presence of fuel pellet defects (e.g., missing pellet surface, MPS).  Several commercial reactor fuel failure events in the last eight years, as recently as early 2019, suggest a PCI-type failure cause.  To safely manage changes in core operation, the margin to conditions leading to PCI-type failures must be determined prior to implementation of such operating changes.


News & View, Volume 47 | PEGASUS State-of-the-Art Nuclear Fuel Behavior

News & Views, Volume 47 | Introducing Pegasus: Optimize Fuel Performance

By:  Vick Nazareth and Bill LyonNews & View, Volume 47 | PEGASUS State-of-the-Art Nuclear Fuel Behavior

The Pegasus code is a culmination of nuclear fuel behavior knowledge and experience that spans a period of over five decades. It is a total fuel-cycle simulation of fuel response from initial insertion in reactor to deposition in permanent storage. The goal of Pegasus is to treat, with equal fidelity, the modeling of fuel behavior during the active fuel cycle and the back-end cycle of spent-fuel storage and transportation in a single, self-consistent, and highly cost-effective analysis approach. In the active part of the fuel cycle, Pegasus’s superior three-dimensional thermo-mechanics, coupled with validated nuclear and material behavior models, and robust fuel-cladding interface treatment make it a high-fidelity predictor of fuel-rod response during flexible power operations and operational transients.


News & View, Volume 46 | Evaluation of Reconfiguration and Damage of BWR Spent Fuel During Storage and Transportation Accidents

News & Views, Volume 46 | Evaluation of Reconfiguration and Damage of BWR Spent Fuel During Storage and Transportation Accidents

By:  Bill Lyon

News & View, Volume 46 | Evaluation of Reconfiguration and Damage of BWR Spent Fuel During Storage and Transportation AccidentsStructural Integrity Associates is participating in a Department of Energy (DOE) Integrated Research Projects (IRP) program focused on storage and transportation of used nuclear fuel (UNF). The project, entitled Cask Mis-Loads Evaluation Techniques, was awarded to a university-based research team in 2016 under the DOE Nuclear Fuels Storage and Transportation (NFST) project. The team is led by the University of Houston (U of H) and includes representatives from the University  of Illinois at Urbana-Champaign, the University of Southern California, the University of Minnesota, Pacific Northwest National Laboratory, and staff members from the Nuclear Fuel Technology and Critical Structures and Facilities divisions of SI. The primary objectives of NFST are to 1) implement interim storage, 2) improve integration of storage into an overall waste management system, and 3) prepare for large-scale transportation of UNF and high-level waste.  The goal of the cask mis-load project is to develop a probabilistically informed methodology, utilizing innovative non-destructive evaluation (NDE) techniques, determining the extent of potential damage or degradation of internal components of UNF canisters/casks during normal conditions of transport (NCT) and hypothetical accident conditions (HAC).