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Predictive Modeling of Carbon Ablators Using Micro and Macro-Scale Modeling

Efforts to build a Predictive Material Modeling (PMM) framework from the micro-scale to the macro-scale are presented in this abstract. To reduce the need for extensive testing, accelerate the design cycle process, and reduce uncertainty margins applied to final designs, NASA is developing simulation and modeling tools that enable characterization of material properties and response to high-enthalpy environments. The Porous Microstructure Analysis (PuMA) code has been developed for computing macroscale (volume averaged) properties of porous materials using microscale images from micro-computed tomography (micro-CT). Microscale modeling requires a realistic representation of a material microstructure; these are obtained either synthetically during the design of the material or through X-ray micro-CT. Volume averaged properties are then used to inform macroscale material response models, such as those implemented in the Porous-material Analysis Toolbox based on OpenFOAM (PATO) software, also actively developed by NASA. The computational model in PATO is a generic heat and mass transfer model for porous reactive materials containing several solid phases and a single gas phase. The detailed chemical interactions occurring between the solid phases and the gas phase are modeled at the pore scale assuming local thermal equilibrium. These tools were developed to efficiently interface with other pre-existing codes such as SPARTA (direct simulation Monte Carlo), DPLR (hypersonic CFD), NEQAIR (radiative transport) and DAKOTA (uncertainty quantification and optimization). Detailed flight data (Mars Science Laboratory [MSL] Entry Descent and Landing Instrument [MEDLI]) is critical for validating these computational tools for NASA applications. Examples of modeling ablative material response using these codes will be presented including 3D simulations of the full-scale heatshield of the MSL capsule. The simulations demonstrate the ability of the modern material response code, PATO, to handle the material response of geometrically complex and large domains, through the use of massively parallel computations.

Thermal Protection Systems↗
DOE OSTI2025

A deep learning and finite element approach for exploration of inverse structure–property designs of lightweight hybrid composites

Hybrid composites have important applications, such as high-performance and lightweight materials in aerospace and automotive industries. Hybrid composites utilize the synergy of diverse fillers to achieve desired material properties, but usually have more complicated microstructures. While topology optimization can optimize a particular property, designing hybrid composites for customized mechanical performances, e.g. full-range stress–strain curve, remains challenging. Here, a computational framework that integrated finite element analysis (FEA) and artificial intelligence (AI) methods of Conditional Generative Adversarial Networks (cGAN) deep learning and transfer learning was developed to establish inverse structure–property relationships and design tailor-made hybrid composites. Based on FEA-generated datasets of hybrid fiber-particle–matrix microstructures and their corresponding full-range stress–strain curves, a cGAN architecture was trained to generate tailored microstructures and establish structure–property relationships. Similarity in microstructural features and well-matched stress–strain curves based on the AI-generated composites were achieved. In conclusion, transfer learning was used to expand the pre-trained model for designing different materials systems.

Hybrid composites↗
DOE OSTI2025

A snapshot of high-entropy alloy processing techniques and their effects on resulting mechanical properties

High-entropy alloys (HEAs) exhibit exceptional strength, corrosion resistance, and thermal stability, making them promising candidates for nuclear, aerospace, and other extreme applications. While most prior work has focused on compositional design, manufacturing techniques themselves can alter microstructure and mechanical properties as dramatically as alloy chemistry. This review compiles and compares the effects of processing routes—including arc melting, induction melting, mechanical alloying with spark plasma sintering, and additive manufacturing—on the structure and properties of HEAs. Quantitative comparisons highlight, for example, that SPS-processed alloys can achieve ∼20–45 % higher yield and tensile strength than arc-melted counterparts, while Bridgman solidification produces nearly single-crystal structures with elongation to failure exceeding 80 %. Additive manufacturing routes such as selective laser melting offer fine microstructures but also introduce anisotropy and porosity, leading to yield strengths spanning 100–600 MPa for the same composition. By synthesizing such results, this review provides actionable insight into how processing routes interact with HEA core effects (high entropy, lattice distortion, sluggish diffusion, and cocktail effect) to determine performance, thereby offering a practical guide for optimizing manufacturing strategies.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Design and characterization of hierarchical aluminosilicate composite materials for Cs entrapment: Adsorption efficiency tied to microstructure

The growing quantity of nuclear waste and the serious threats to the environment challenge researchers to innovate and target new waste form technologies. In the past decades, considerable efforts have been devoted to developing highly selective sorbents followed by safe disposal with the assurance of chemical stability and robust retention performance. Zeolite-containing geopolymers are regarded as a possible 2-in-1 material able to both capture and sequester elements such as Cs in bed fixed column application perspective. Here, these composites show promise for combining extraction properties of zeolite powder due to its crystalline structure (high capacity and selective adsorption), with the tunable microstructure and the shaping feasibility of the geopolymer binder. For the development of materials devoted to Cs immobilization, porous zeolite/geopolymer composites were prepared by dispersing NaY zeolite particles in a geopolymer binder. The influence of the structural properties of such composites on their ability to entrap a large amount of Cs by an ionic exchange process was notably studied. Composites' compositions, porosities, morphologies and crystallinity were analyzed by scanning electron microscopy coupled with energy dispersive x-ray spectroscopy (SEM-EDX), x-ray diffraction analysis (XRD) and nitrogen adsorption/desorption studies. Experimental Cs sorption in batch mode was used to follow the ionic exchange phenomenon in these materials. Along with 5 wt% amount of zeolite in geopolymer improves the Cs adsorption performance offering multiple new adsorption sites. Additionally, the geopolymer mesopores are beneficial facilitating the access of Cs and its role as a binder is advantageous to tailor granular hierarchical structure for safer industrial application.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Nanocellulose toward Advanced Energy Storage Devices: Structure and Electrochemistry

We report that cellulose is the most abundant biopolymer on Earth and has long been used as a sustainable building block of conventional paper. Note that nanocellulose accounts for nearly 40% of wood’s weight and can be extracted using well-developed methods. Due to its appealing mechanical and electrochemical properties, including high specific modulus (~100 GPa/(g/cm 3 )), excellent stability in most solvents, and stability over a wide electrochemical window, nanocellulose has been widely used as a separator, electrolyte, binder, and substrate material for energy storage. Additionally, nanocellulose-derived carbon materials have also drawn increasing scientific interest in sustainable energy storage due to their low-cost and raw-material abundance, high conductivity, and rational electrochemical performance. The inexpensive and environmentally friendly nature of nanocellulose and its derivatives as well as simple fabrication techniques make nanocellulose-based energy storage devices promising candidates for the future of “green” and renewable electronics. For nanocellulose-based energy storage, structure engineering and design play a vital role in achieving desired electrochemical properties and performances. Thus, it is important to identify suitable structure and design engineering strategies and to better understand their relationship. In this Account, we review recent developments in nanocellulose-based energy storage. Due to the limited space, we will mainly focus on structure design and engineering strategies in macrofiber, paper, and three-dimensional (3D) structured electrochemical energy storage (EES) devices and highlight progress made in our group. We first present the structure and properties of nanocellulose, with a particular discussion of nanocellulose from wood materials. We then go on to discuss studies on nanocellulose-based macrofiber, paper, and 3D wood- and other aerogel-based EES devices. Within this discussion, we highlight the use of natural nanocellulose as a flexible substrate for a macrofiber supercapacitor and an excellent electrolyte reservoir for a breathable textile lithium–oxygen battery. Paper batteries and supercapacitors using nanocellulose as a green dispersant, nanocellulose-based paper as a flexible substrate, and nanocellulose as separator and electrolyte are also examined. We highlight recent progress on wood-based batteries and supercapacitors, focusing on the advantages of wood materials for energy storage, the structure design and engineering strategies, and their microstructure and electrochemical properties. We discuss the influence of structure (particularly pores) on the electrochemical performance of the energy storage devices. By taking advantage of the straight, nature-made channels in wood materials, ultrathick, highly loaded, and low-tortuosity energy storage devices are demonstrated. Lastly, we offer concluding remarks on the challenges and directions of future research in the field of nanocellulose-based energy storage devices.

25 ENERGY STORAGE↗
DOE OSTI2018

Theoretical prediction and atomic kinetic Monte Carlo simulations of void superlattice self-organization under irradiation

Nano-structured superlattices may have novel physical properties and irradiation is a powerful mean to drive their self-organization. However, the formation mechanism of superlattice under irradiation is still open for debate. Here we use atomic kinetic Monte Carlo simulations in conjunction with a theoretical analysis to understand and predict the self-organization of nano-void superlattices under irradiation, which have been observed in various types of materials for more than 40 years but yet to be well understood. The superlattice is found to be a result of spontaneous precipitation of voids from the matrix, a process similar to phase separation in regular solid solution, with the symmetry dictated by anisotropic materials properties such as one-dimensional interstitial atom diffusion. This discovery challenges the widely accepted empirical rule of the coherency between the superlattice and host matrix crystal lattice. The atomic scale perspective has enabled a new theoretical analysis to successfully predict the superlattice parameters, which are in good agreement with independent experiments. The theory developed in this work can provide guidelines for designing target experiments to tailor desired microstructure under irradiation. Furthermore, it may also be generalized for situations beyond irradiation, such as spontaneous phase separation with reaction.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Bifurcation and Pattern Symmetry Selection in Reaction-Diffusion Systems with Kinetic Anisotropy

Abstract Ordering and self-organization are critical in determining the dynamics of reaction-diffusion systems. Here we show a unique pattern formation mechanism, dictated by the coupling of thermodynamic instability and kinetic anisotropy. Intrinsically different from the physical origin of Turing instability and patterning, the ordered patterns we obtained are caused by the interplay of the instability from uphill diffusion, the symmetry breaking from anisotropic diffusion, and the reactions. To understand the formation of the void/gas bubble superlattices in crystals under irradiation, we establish a general theoretical framework to predict the symmetry selection of superlattice structures associated with anisotropic diffusion. Through analytical study and phase field simulations, we found that the symmetry of a superlattice is determined by the coupling of diffusion anisotropy and the reaction rate, which indicates a new type of bifurcation phenomenon. Our discovery suggests a means for designing target experiments to tailor different microstructural patterns.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Equilibrium and non-equilibrium effects in high pressure phase transformations of carbon

The behavior of carbon in the range 1–100 GPa and 1–10 kK is central to problems in planetary interiors, inertial confinement fusion targets, and high-pressure synthesis of carbon-based materials, but experiments in this regime are difficult and often provide only indirect constraints on phase behavior. As a result, phase boundary loci, structure, and limits of metastability at high pressure remain uncertain. In this work, machine-learning enhanced atomistic simulations are used to address this knowledge gap. We determine the melt line up to 100 GPa, the graphite-diamond phase boundary up to the melt line, and analyze structure of the coexisting phases. We show that the coexisting liquid evolves smoothly with pressure without evidence for a first-order liquid–liquid transition. Orientation-resolved graphite melting simulations indicate that basal-plane interfaces develop a dewetting layer and undergo layer-by-layer melting, producing kinetic hysteresis and an apparent orientation dependence of the melt line. Non-equilibrium quenches from the melt are used to construct a kinetically limiting graphite–diamond phase boundary for rapid quenches from above the melt line, and show that graphite is metastable at pressures of up to ≈ 25 GPa. These results provide bounds on equilibrium and metastable behavior in carbon relevant for interpreting high-pressure experiments and for designing synthesis pathways to specific carbon microstructures.

Lyu, Yanjun [Department of Materials Science and E↗
DOE OSTI2019

Highly crystalline sodium manganese ferrocyanide microcubes for advanced sodium ion battery cathodes

The microstructure and morphology of the crystal play an important role in the physical and electrochemical properties of electrode materials. Here we report a highly crystalline microcube structure of Na-rich Prussian white Na 1.92 Mn[Fe(CN) 6 ] 0.98 for sodium ion battery cathodes. The obtained structure features high crystallinity of the monoclinic structure with an average cubic size of 3–5 μm. Because of the improvement on microstructural and electrical properties, the cathode design enables promising electrochemical performance. The electrode exhibits an outstanding rate performance with reversible capacities of 152.8 mA h g –1 (10 mA g –1 ), 128.1 mA h g –1 (100 mA g –1 ), 118.7 mA h g –1 (500 mA g –1 ) and 110.3 mA h g –1 (1000 mA g –1 ). It also exhibits a good cycling performance with a capacity retention of 82% after 500 cycles at 100 mA g –1 . More importantly, the XRD analysis reveals a highly reversible monoclinic–cubic–monoclinic structural evolution of the cathode upon Na + extraction/insertion. The good rate and cycling performance can be attributed to the robust crystal structure with few defects and fast Na + transfer kinetics. The high purity single crystal morphology can also reduce the side reactions on the electrode/electrolyte interface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

3D mapping of residual stresses in growing grains of partially recrystallized Gum Metal

The crystallographic orientations and residual stresses within recrystallizing grains in partially recrystallized beta titanium-Gum Metal-were examined non-destructively in 3D using synchrotron Differential Aperture X-ray Microscopy. Contrary to common assumptions, significant local stresses and stress variations are observed within the recrystallizing grains. The results reveal that the development of these local residual stresses depends on the plastic deformation mode and material's elastic constants, rather than grain properties such as size and orientation, or even the material's yield stress. This work provides insights valuable for the design of advanced materials with heterogeneous microstructures.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Multilayer Foil Manufacturability Final Report CRADA No. TSV-1246-96

The work performed under this CRADA was based on developments in multilayer technology made at Lawrence Livermore National Laboratory (LLNL) that enable advanced pyrotechnic material fabrication. We applied our understanding of the performance, composition, and microstructure of these materials to engineering design of application specific structures. The purpose of the project was to assess the feasibility of LLNL’s multilayer technology for application to large scale manufacturing of these advanced pyrotechnic materials for the automobile industry; address any manufacturing limitations; and propose approaches to improve manufacturability. Another purpose was to address issues associated with the design of application-specific materials for their subsequent manufacture, including the establishment of general guidelines for such a manufacturability assessment.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
NASA NTRS2009

Micro-Organ Devices

Micro-organ devices (MODs) are being developed to satisfy an emerging need for small, lightweight, reproducible, biological-experimentati on apparatuses that are amenable to automated operation and that imp ose minimal demands for resources (principally, power and fluids). I n simplest terms, a MOD is a microfluidic device containing a variety of microstructures and assemblies of cells, all designed to mimic a complex in vivo microenvironment by replicating one or more in vivo micro-organ structures, the architectures and composition of the extr acellular matrices in the organs of interest, and the in vivo fluid flows. In addition to microscopic flow channels, a MOD contains one or more micro-organ wells containing cells residing in microscopic e xtracellular matrices and/or scaffolds, the shapes and compositions o f which enable replication of the corresponding in vivo cell assembl ies and flows.

Gonda, Steven R.↗
DOE OSTI2018

Formation of superlattice structure in irradiated materials: a phase field study

The formation and self-organization of fission gas bubbles under irradiation is a unique phenomenon, which affects the swelling behavior and mechanical stability of nuclear materials. We develop a phase field model to investigate the formation mechanism of fission gas bubbles, and associated material properties under different irradiation condition. The thermodynamic and kinetic origin of superlattice formation is systematically analyzed. In particular, the symmetry of the superlattice is dictated by the anisotropic diffusion of interstitial atoms, while the lattice parameter is determined by the instability of vacancy and gas concentration waves. The spatial distribution of gas bubbles strongly depends on the nucleation, growth and coarsening process, which leads to the formation of self-organized superlattice. This study provides a new insight into designing target experiments to tailor desired microstructure under irradiation.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Localized High-Concentration Electrolytes Get More Localized

Liquid electrolytes in batteries are typically treated as macroscopically homogeneous ionic transport media, despite having complex chemical composition and atomistic solvation structures, thus leaving a knowledge gap of microstructural characteristics. A promising electrolyte system design has recently been developed with the title of a localized high-concentration electrolyte (LHCE). These electrolytes are a summation of three components – a charge-carrying salt, a solvent that solvates the salt, and a diluent that is sparingly interactive with the salt in terms of ion solvation. This creates the perception of a high-concentration electrolyte (HCE) with high anion-cation interactions that supports a salt-derived, stable solid-electrolyte interphase, while an LHCE improves bulk electrolyte properties, such as ionic conductivity and viscosity, when compared to an HCE. Much trial by error design of this LHCE concept has been supported by simulations to confirm ionic interactions, cycling data to confirm cell stability, and post-mortem analysis to provide evidence of mechanisms. However, a systematic design to extend the capabilities of LHCEs is still to be desired. Here, we analyzed a specific LHCE mixture to dictate the best viable mixture that extends the localization of solvation structures while maintaining viable cell-level capabilities. We seek to observe and understand solvent-to-salt interactions that impact electrolyte performance. These interactions range from single-ion solvation, multidentate interactions (i.e., solvation-driven clustering), to more widespread network-level interactions. With the support of both experimental and computational analysis of different electrolyte features, we have begun a methodology of formulating the most ideal LHCE mixtures for improving the cyclability of high-capacity battery chemistries.

25 ENERGY STORAGE↗
NASA NTRS2012

A Compendium of Brazed Microstructures For Fission Power Systems Applications

NASA has been supporting design studies and technology development for fission-based power systems that could provide power to an outpost on the Moon, Mars, or an asteroid. Technology development efforts have included fabrication and evaluation of components used in a Stirling engine power conversion system. This investigation is part of the development of several braze joints crucial for the heat exchanger transfer path from a hot-side heat exchanger to a Stirling engine heat acceptor. Dissimilar metal joints are required to impart both mechanical strength and thermal path integrity for a heater head of interest. Preliminary design work for the heat exchanger involved joints between low carbon stainless steel to Inconel 718, where the 316L stainless steel would contain flowing liquid metal NaK while Inconel 718, a stronger alloy, would be used as structural reinforcement. This paper addressed the long-term microstructural stability of various braze alloys used to join 316L stainless steel heater head to the high conductivity oxygen-free copper acceptor to ensure the endurance of the critical metallic components of this sophisticated heat exchanger. The bonding of the 316L stainless steel heater head material to a copper heat acceptor is required to increase the heat-transfer surface area in contact with flowing He, which is the Stirling engine working fluid.

Locci, Ivan E.↗
DOE OSTI2018

Quenching and Partitioning Process Development to Replace Hot Stamping of High Strength Automotive Steel

The present project investigated Quenching and Partitioning (Q&P) to process cold rolled steels to develop high strength sheet steels that exhibit superior ductility compared to available grades with the intent to allow forming of high strength parts at room temperature to provide an alternative to hot stamping of parts. Hot stamping of boron alloyed steel is the current technology to manufacture thinner gauge sections in automotive structures to guarantee anti-intrusion during collisions whilst improving fuel efficiency by decreasing vehicle weight. Hot stamping involves reheating steel to 900 °C or higher followed by deformation and quenching in the die to produce ultra-high strength materials. Hot stamping requires significant energy to reheat the steel and is less productive than traditional room temperature stamping operations. Stamping at elevated temperature was developed due to the lack of available steels with strength levels of interest possessing sufficient ductility enabling traditional room temperature forming. This process is seeing growing demand within the automotive industry and, given the reheating step in this operation, increased energy consumption during part manufacturing results. The present research program focused on the development of steel grades via Q&P processing that exhibit high strength and formability enabling room temperature forming to replace hot stamping. The main project objective consisted of developing sheet steels exhibiting minimum ultimate tensile strength levels of 1200 MPa in combination with minimum tensile elongation levels of 15 pct using Q&P processing through judicious alloy design and heat treating parameter definition. In addition, detailed microstructural characterization and study of properties, processing and microstructure interrelationships were pursued to develop strategies to further enhance tensile properties. In order to accomplish these objectives, alloy design was conducted towards achieving the target properties. Twelve alloys were designed and laboratory produced involving melting, alloying, casting, hot rolling, and cold rolling to obtain sheet steels of approximately 1 mm thickness. Q&P processing of the samples was then conducted. Target properties were achieved and substantially exceeded demonstrating success in the developed and employed alloy design approaches. The best combinations of tensile properties were found at approximately 1550 MPa with a total elongation in excess of 20 pct clearly showing the potential for replacement of hot stamping to produce advanced high strength steels.

36 MATERIALS SCIENCE↗
DOE OSTI2014

Monitoring microstructural evolution of alloy 617 with non-linear acoustics for remaining useful life prediction; multiaxial creep-fatigue and creep-ratcheting

The research built upon a prior investigation to develop a unified constitutive model for design-­by-­analysis of the intermediate heat exchanger (IHX) for a very high temperature reactor (VHTR) design of next generation nuclear plants (NGNPs). Model development requires a set of failure data from complex mechanical experiments to characterize the material behavior. Therefore uniaxial and multiaxial creep-­fatigue and creep-­ratcheting tests were conducted on the nickel-­base Alloy 617 at 850 and 950°C. The time dependence of material behavior, and the interaction of time dependent behavior (e.g., creep) with ratcheting, which is an increase in the cyclic mean strain under load-­controlled cycling, are major concerns for NGNP design. This research project aimed at characterizing the microstructure evolution mechanisms activated in Alloy 617 by mechanical loading and dwell times at elevated temperature. The acoustic harmonic generation method was researched for microstructural characterization. It is a nonlinear acoustics method with excellent potential for nondestructive evaluation, and even online continuous monitoring once high temperature sensors become available. It is unique because it has the ability to quantitatively characterize microstructural features well before macroscale defects (e.g., cracks) form. The nonlinear acoustics beta parameter was shown to correlate with microstructural evolution using a systematic approach to handle the complexity of multiaxial creep-­fatigue and creep-­ratcheting deformation. Mechanical testing was conducted to provide a full spectrum of data for: thermal aging, tensile creep, uniaxial fatigue, uniaxial creep-­fatigue, uniaxial creep-ratcheting, multiaxial creep-fatigue, and multiaxial creep-­ratcheting. Transmission Electron Microscopy (TEM), Scanning Electron Microscopy (SEM), and Optical Microscopy were conducted to correlate the beta parameter with individual microstructure mechanisms. We researched application of the harmonic generation method to tubular mechanical test specimens and pipes for nondestructive evaluation. Tubular specimens and pipes act as waveguides, thus we applied the acoustic harmonic generation method to guided waves in both plates and shells. Magnetostrictive transducers were used to generate and receive guided wave modes in the shell sample and the received signals were processed to show the sensitivity of higher harmonic generation to microstructure evolution. Modeling was initiated to correlate higher harmonic generation with the microstructure that will lead to development of a life prediction model that is informed by the nonlinear acoustics measurements.

36 MATERIALS SCIENCE↗
NASA NTRS2000

HOTCFGM-2D: A Coupled Higher-Order Theory for Cylindrical Structural Components with Bi-Directionally Components with Bi-Directionally Graded Microstructures

The objective of this two-year project was to develop and deliver to the NASA-Glenn Research Center a two-dimensional higher-order theory, and related computer codes, for the analysis and design of cylindrical functionally graded materials/structural components for use in advanced aircraft engines (e.g., combustor linings, rotor disks, heat shields, brisk blades). To satisfy this objective, two-dimensional version of the higher-order theory, HOTCFGM-2D, and four computer codes based on this theory, for the analysis and design of structural components functionally graded in the radial and circumferential directions were developed in the cylindrical coordinate system r-Theta-z. This version of the higher-order theory is a significant generalization of the one-dimensional theory, HOTCFGM-1D, developed during the FY97 for the analysis and design of cylindrical structural components with radially graded microstructures. The generalized theory is applicable to thin multi-phased composite shells/cylinders subjected to steady-state thermomechanical, transient thermal and inertial loading applied uniformly along the axial direction such that the overall deformation is characterized by a constant average axial strain. The reinforcement phases are uniformly distributed in the axial direction, and arbitrarily distributed in the radial and circumferential direction, thereby allowing functional grading of the internal reinforcement in the r-Theta plane. The four computer codes fgmc3dq.cylindrical.f, fgmp3dq.cylindrical.f, fgmgvips3dq.cylindrical.f, and fgmc3dq.cylindrical.transient.f are research-oriented codes for investigating the effect of functionally graded architectures, as well as the properties of the multi-phase reinforcement, in thin shells subjected to thermomechanical and inertial loading, on the internal temperature, stress and (inelastic) strain fields. The reinforcement distribution in the radial and circumferential directions is specified by the user. The thermal and inelastic properties of the individual phases can vary with temperature. The inelastic phases are presently modeled by the power-law creep model generalized to multi-directional loading (within fgmc3dq.cylindrical.f and fgmc3dq.cylindrical.transient.f for steady-state and transient thermal loading, respectively), and incremental plasticity and GVIPS unified viscoplasticity theories (within the steady-state loading versions fgmp3dq.cylindrical.f and fgmgvips3dq.cylindrical.f).

Pindera, Marek-Jerzy↗