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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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At least 127 records · Page 7

Mars Exploration Rover Heatshield Observation Campaign

For the first time ever, engineers were able to observe a heatshield on the surface of another planet after a successful entry through the atmosphere. A three-week heatshield observation campaign was conducted in December 2004 after the Mars Exploration Rover Opportunity exited "Endurance Crater." By utilizing the rover's scientific instruments, data was collected to make a qualitative assessment of the performance of the heatshield. This data was gathered to gain a better understanding of how the heatshield performed during entry through the Martian atmosphere. In addition, this unprecedented look at the heatshield offered engineers the opportunity to assess if any unexpected anomalies occurred. Once a survey of the heatshield debris was completed, multiple targets of interest were chosen for the collection of imaging data. This data was then used to assess the char depth of the thermal protection material, which compared well with design and post-flight computational predictions. Extensive imaging data was collected and showed the main seal in pristine conditions, and no observable indications of structure overheating. Additionally, unexpected vehicle dynamics during the atmospheric entry were explained by the observation of thermal blanket remnants attached to the heatshield.

Mars Exploration Rovers↗

Computationally Guided Development of Components for High Energy Density Solid-State Lithium-Sulfur Batteries

All electric vertical take-off and landing vehicles (eVTOL) for urban air mobility (UAM) concepts face numerous challenging technical barriers before their introduction into the consumer marketplace. The most challenging of these technical barriers to overcome is developing an energy storage system capable of meeting the rigorous aerospace safety and performance criteria1. The performance metrics for eVTOL craft, such as specific energy, specific power, and safety, exceed those of electric automobiles by a factor of two to four. Current state-of-the-art (SOA) lithium-ion batteries are incapable of meeting the key performance criteria of energy and safety for eVTOL. Therefore, next generation advanced chemistries and designs must be developed to meet required performance metrics for electric aviation2. Beyond lithium-ion chemistries, such as lithium-sulfur, show promise in their high energy, while limitations exist in their power and cyclability due to low electrical conductivity and high intermediate solubility in organic liquid electrolytes. Several strategies to overcome the low electrical conductivity involve the use of selenium as a dopant in the active sulfur material, along with the incorporation of 2-dimensional electron-conducting holey-graphene to improve the composite cathodes electronic conductivity. Furthermore, combining this chemistry with a solid-electrolyte avoids the components’ dissolution issues3. However, the development of composite solid-state cathodes is non-trivial as several components must be intimately mixed so that the active component has sufficient access to both electrons and lithium ions to undergo full electrochemical conversion. Mathematical modeling of battery components can assist experimental design through a robust and rigorous combination of computational modeling techniques covering multiple length scales. The objective is to leverage modern computational materials methods combined with battery multiphysics tools to develop radically advanced compatible cathode and electrolyte materials, build and test solid state lithium-sulfur cells and packs. A NASA-based cross-organizational team of high-powered experts combined integrated computational predictive modeling, fundamental chemistry analysis, advanced material science, and battery cell development to tackle this very challenging, multidisciplinary problem. This presentation will show a multiscale computational modeling approach that has produced a novel particle dynamics method called Solid Electrolyte Sphere Approximation Model (SESAM). SESAM modeling targets the 1-10 µm scale structures and provides electromechanical and grain interactions for predictive design guidelines for the manufacturing of solid-state components. Parameters such as particle size and volume fraction of the constituent materials were modeled and experimentally fabricated to optimize electrochemical performance through improved microstructure design. Experimental feedback was provided through ionic and electronic conductivity assessment and structural analysis of developed materials and cell components.

battery↗

Trends in aerospace structures

Recent developments indicate that there may soon be a revolution in aerospace structures. Increases in allowable operational stress levels, utilization of high-strength, high-toughness materials, and new structural concepts will highlight this advancement. Improved titanium and aluminum alloys and high-modulus, high-strength advanced composites, with higher specific properties than aluminum and high-strength nickel alloys, are expected to be the principal materials. Significant advances in computer technology will cause major changes in the preliminary design cycle and permit solutions of otherwise too-complex interactive structural problems and thus the development of vehicles and components of higher performance. The energy crisis will have an impact on material costs and choices and will spur the development of more weight-efficient structures. There will also be significant spinoffs of aerospace structures technology, particularly in composites and design/analysis software.

Card, M. F.↗

Physics of debris clouds from hypervelocity impacts

The protection scheme developed for long duration space platforms relies primarily upon placing thin metal plates or 'bumpers' around flight critical components. The effectiveness of this system is highly dependent upon its ability to break up and redistribute the momentum of any particle which might otherwise strike the outer surface of the spacecraft. Therefore it is of critical importance to design the bumpers such that maximum dispersion of momentum is achieved. This report is devoted to an in-depth study into the design and development of a laboratory instrument which would permit the in-situ monitoring of the momentum distribution as the impact event occurs. A series of four designs were developed, constructed and tested culminating with the working instrument which is currently in use. Each design was individually tested using the Space Environmental Effects Facility (SEEF) at the Marshall Space Flight Center in Huntsville, Alabama. Along with the development of the device, an experimental procedure was developed to assist in the investigation of various bumper materials and designs at the SEEF. Preliminary results were used to compute data which otherwise were not experimentally obtainable. These results were shown to be in relative agreement with previously obtained values derived through other methods. The results of this investigation indicated that momentum distribution could in fact be measured in-situ as the impact event occurred thus giving a more accurate determination of the effects of experimental parameters on the momentum spread. Data produced by the instrument indicated a Gaussian-type momentum distribution. A second apparatus was developed and it was placed before the shield in the line of travel utilized a plate to collect impact debris scattered backwards. This plate had a passage hole in the center to allow the particle to travel through it and impact the proposed shield material. Applying the law of conservation of angular momentum a backward momentum vector was determined from the angular velocity of the plate. The forward scattered and backward scattered momentum values were then analyzed to judge the distribution of debris. Loss of momentum was attributed to the inaccuracies of the means of measurement. Assumptions of symmetrical debris for the forward and backward scattered directions also contributed to this loss.

Zee, Ralph↗

Computational Nanotechnology at NASA Ames Research Center, 1996

Some forms of nanotechnology appear to have enormous potential to improve aerospace and computer systems; computational nanotechnology, the design and simulation of programmable molecular machines, is crucial to progress. NASA Ames Research Center has begun a computational nanotechnology program including in-house work, external research grants, and grants of supercomputer time. Four goals have been established: (1) Simulate a hypothetical programmable molecular machine replicating itself and building other products. (2) Develop molecular manufacturing CAD (computer aided design) software and use it to design molecular manufacturing systems and products of aerospace interest, including computer components. (3) Characterize nanotechnologically accessible materials of aerospace interest. Such materials may have excellent strength and thermal properties. (4) Collaborate with experimentalists. Current in-house activities include: (1) Development of NanoDesign, software to design and simulate a nanotechnology based on functionalized fullerenes. Early work focuses on gears. (2) A design for high density atomically precise memory. (3) Design of nanotechnology systems based on biology. (4) Characterization of diamonoid mechanosynthetic pathways. (5) Studies of the laplacian of the electronic charge density to understand molecular structure and reactivity. (6) Studies of entropic effects during self-assembly. Characterization of properties of matter for clusters up to sizes exhibiting bulk properties. In addition, the NAS (NASA Advanced Supercomputing) supercomputer division sponsored a workshop on computational molecular nanotechnology on March 4-5, 1996 held at NASA Ames Research Center. Finally, collaborations with Bill Goddard at CalTech, Ralph Merkle at Xerox Parc, Don Brenner at NCSU (North Carolina State University), Tom McKendree at Hughes, and Todd Wipke at UCSC are underway.

Globus, Al↗

A brief overview of computational structures technology related activities at NASA Lewis Research Center

The presentation gives a partial overview of research and development underway in the Structures Division of LeRC, which collectively is referred to as the Computational Structures Technology Program. The activities in the program are diverse and encompass four major categories: (1) composite materials and structures; (2) probabilistic analysis and reliability; (3) design optimization and expert systems; and (4) computational methods and simulation. The approach of the program is comprehensive and entails exploration of fundamental theories of structural mechanics to accurately represent the complex physics governing engine structural performance, formulation, and implementation of computational techniques and integrated simulation strategies to provide accurate and efficient solutions of the governing theoretical models by exploiting the emerging advances in computer technology, and validation and verification through numerical and experimental tests to establish confidence and define the qualities and limitations of the resulting theoretical models and computational solutions. The program comprises both in-house and sponsored research activities. The remainder of the presentation provides a sample of activities to illustrate the breadth and depth of the program and to demonstrate the accomplishments and benefits that have resulted.

Hopkins, Dale A.↗

Predictive Modeling of Carbon Ablators

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↗

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↗

Vision 2040: A Roadmap for Integrated, Multiscale Modeling and Simulation of Materials and Systems

Over the last few decades, advances in high-performance computing, new materials characterization methods, and, more recently, an emphasis on integrated computational materials engineering (ICME) and additive manufacturing have been a catalyst for multiscale modeling and simulation-based design of materials and structures in the aerospace industry. While these advances have driven significant progress in the development of aerospace components and systems, that progress has been limited by persistent technology and infrastructure challenges that must be overcome to realize the full potential of integrated materials and systems design and simulation modeling throughout the supply chain. As a result, NASA's Transformational Tools and Technology (TTT) Project sponsored a study (performed by a diverse team led by Pratt & Whitney) to define the potential 25-year future state required for integrated multiscale modeling of materials and systems (e.g., load-bearing structures) to accelerate the pace and reduce the expense of innovation in future aerospace and aeronautical systems. This report describes the findings of this 2040 Vision study (e.g., the 2040 vision state; the required interdependent core technical work areas, Key Element (KE); identified gaps and actions to close those gaps; and major recommendations) which constitutes a community consensus document as it is a result of over 450 professionals input obtain via: 1) four society workshops (AIAA, NAFEMS, and two TMS), 2) community-wide survey, and 3) the establishment of 9 expert panels (one per KE) consisting on average of 10 non-team members from academia, government and industry to review, update content, and prioritize gaps and actions. The study envisions the development of a cyber-physical-social ecosystem comprised of experimentally verified and validated computational models, tools, and techniques, along with the associated digital tapestry, that impacts the entire supply chain to enable cost-effective, rapid, and revolutionary design of fit-for-purpose materials, components, and systems. Although the vision focused on aeronautics and space applications, it is believed that other engineering communities (e.g., automotive, biomedical, etc.) can benefit as well from the proposed framework with only minor modifications. Finally, it is TTT's hope and desire that this vision provides the strategic guidance to both public and private research and development decision makers to make the proposed 2040 vision state a reality and thereby provide a significant advancement in the United States global competitiveness.

multi-scale modeling↗

Analytical modeling of intumescent coating thermal protection system in a JP-5 fuel fire environment

The thermochemical response of Coating 313 when exposed to a fuel fire environment was studied to provide a tool for predicting the reaction time. The existing Aerotherm Charring Material Thermal Response and Ablation (CMA) computer program was modified to treat swelling materials. The modified code is now designated Aerotherm Transient Response of Intumescing Materials (TRIM) code. In addition, thermophysical property data for Coating 313 were analyzed and reduced for use in the TRIM code. An input data sensitivity study was performed, and performance tests of Coating 313/steel substrate models were carried out. The end product is a reliable computational model, the TRIM code, which was thoroughly validated for Coating 313. The tasks reported include: generation of input data, development of swell model and implementation in TRIM code, sensitivity study, acquisition of experimental data, comparisons of predictions with data, and predictions with intermediate insulation.

Clark, K. J.↗

Quantum Mechanical Simulations of Dynamics of Electronic Excitations in Low-Dimensional Photovoltaics Materials

Dynamics of electronically excited states including exciton generation and relaxation, exciton-exciton interaction, and charge/energy transfer and transport, are critical to understanding and optimizing photovoltaic materials. Although considerable progress has been made, accurate experimental characterization of such crucial dynamics remains extremely challenging, especially in low-dimensional materials. In this talk, I will discuss how the advancement of quantum mechanical simulations of the dynamics of electronic excitations can reveal the physical mechanisms hindering or improving solar energy harvest. Specifically, we find that surface dangling-bond defects on silicon quantum dots cause rapid charge recombination and low carrier mobility in the inorganic-organic PV cells. Although small quantum dots are essentially free of defects, their optical gaps are too large. To solve this issue, a full-spectrum-light-absorption scheme is computationally designed, taking advantage of complexity and flexibility of low-dimensional materials consisting of different characteristics and dimensions. In this scheme the multifunctional ligands are used to (1) passivate against oxidation, (2) facilitate interfacial charge transfer, and (3) improve both charge transport and optical absorption. A joint theoretical and experimental study has demonstrated the feasibility of this approach. Finally, I will briefly talk about how this scheme and the well-tested quantum mechanical simulations can be employed to help improve energy-conversion efficiency in perovskite photovoltaics including perovskite-based tandem cells.

Zhigang Wu↗

The LARSYS Educational Package: Instructor's Notes for Use with the Data 100

The LARSYS Educational Package is a set of instructional materials developed to train people to analyze remotely sensed multispectral data using LARSYS, a computer software system. The materials included in this volume have been designed to assist LARSYS instructors as they guide students through the LARSYS Educational Package. All of the materials have been updated from the previous version to reflect the use of a Data 100 Remote Terminal.

Lindenlaub, J. C.↗

Atoms to Aircraft to Spacecraft

The next generation of aerospace systems requires materials and structures that combine high performance at high utilization in short missions with the possibility of high rate production, without excessive non-recurring cost, to allow for rate flexibility and shorter structural life cycles. The development of materials and structures that offer this flexibility in rate without negatively influencing performance and economic viability will require a matching and overlapping experimental and computational design approach. The objective is to go from Atom to Airframe to Spaceframe for thermoplastic unidirectional tape based fastener-free assemblies. Thermoplastic composites are chosen as the focus because these materials allow for reversible fusion bonding in every stage of their life cycle after synthesis. Our strategy is to combine multi-scale computational approaches with multi-scale experimental activities to develop an understanding of and capabilities to manufacture custom unidirectional thermoplastic tape. This tape will be the basis for our high-rate multiple-technology manufacturing approach validated by the production of two representative demonstrators for urban air mobility vehicle structures. The multi-disciplinary team will work in an integrated manner to effectively combine computational approaches with experimental approaches at each stage of characteristic manufacturing flows. The team aims for tools and technology to quantify the thermo-rheological aspects of unidirectional tape-based production and assembly of aerospace quality thermoplastic components as well as for validated tools for unidirectional tape-based thermoplastic preform and part design and manufacture. The work will be used to design and build two demonstration structural parts characteristic for urban air mobility vehicles.

Paul Ziehl↗

Challenges in Qualification of Thermal Protection Systems for Extreme Entry Environments

Planetary entry vehicles employ ablative TPS materials to shield the aeroshell from entry aeroheating environments. To ensure mission success, it must be demonstrated that the heatshield system, including local features such as seams, does not fail at conditions that are suitably margined beyond those expected in flight. Furthermore, its thermal response must be predictable, with acceptable fidelity, by computational tools used in heatshield design. Mission assurance is accomplished through a combination of ground testing and material response modelling. A material's robustness to failure is verified through arcjet testing while its thermal response is predicted by analytical tools that are verified against experimental data. Due to limitations in flight-like ground testing capability and lack of validated high-fidelity computational models, qualification of heatshield materials is often achieved by piecing together evidence from multiple ground tests and analytical simulations, none of which fully bound the flight conditions and vehicle configuration. Extreme heating environments (>2000 W/cm2 heat flux and >2 atm pressure), experienced during entries at Venus, Saturn and Ice Giants, further stretch the current testing and modelling capabilities for applicable TPS materials. Fully-dense Carbon Phenolic was the material of choice for these applications; however, since heritage raw materials are no longer available, future uses of re-created Carbon Phenolic will require re-qualification. To address this sustainability challenge, NASA is developing a new dual-layer material based on 3D weaving technology called Heatshield for Extreme Entry Environments (HEEET) [1]. Regardless of TPS material, extreme environments pose additional certification challenges beyond what has been typical in recent NASA missions.Scope of this presentation: This presentation will give an overview of challenges faced in verifying TPS performance at extreme heating conditions.

Mahzari, Milad↗

Computer-aided analysis and design of the shape rolling process for producing turbine engine airfoils

Mild steel (AISI 1018) was selected as model cold rolling material and Ti-6A1-4V and Inconel 718 were selected as typical hot rolling and cold rolling alloys, respectively. The flow stress and workability of these alloys were characterized and friction factor at the roll/workpiece interface was determined at their respective working conditions by conducting ring tests. Computer-aided mathematical models for predicting metal flow and stresses, and for simulating the shape rolling process were developed. These models utilized the upper bound and the slab methods of analysis, and were capable of predicting the lateral spread, roll separating force, roll torque, and local stresses, strains and strain rates. This computer-aided design system was also capable of simulating the actual rolling process, and thereby designing the roll pass schedule in rolling of an airfoil or a similar shape.

Lahoti, G. D.↗

Shielding materials for highly penetrating space radiations

Interplanetary travel involves the transfer from an Earth orbit to a solar orbit. Once outside the Earth's magnetosphere, the major sources of particulate radiation are solar cosmic rays (SCR's) and galactic cosmic rays (GCR's). Intense fluxes of SCR's come from solar flares and consist primarily of protons with energies up to 1 GeV. The GCR consists of a low flux of nuclei with energies up to 10(exp 10) GeV. About 70 percent of the GCR are protons, but a small amount (0.6 percent) are nuclei with atomic numbers greater than 10. High energy charged particles (HZE) interact with matter by transferring energy to atomic electrons in a Coulomb process and by reacting with an atomic nucleus. Energy transferred in the first process increases with the square of the atomic number, so particles with high atomic numbers would be expected to lose large amounts of energy by this process. Nuclear reactions produced by (HZE) particles produce high-energy secondary particles which in turn lose energy to the material. The HZE nuclei are a major concern for radiation protection of humans during interplanetary missions because of the very high specific ionization of both primary and secondary particles. Computer codes have been developed to calculate the deposition of energy by very energetic charged particles in various materials. Calculations show that there is a significant buildup of secondary particles from nuclear fragmentation and Coulomb dissociation processes. A large portion of these particles are neutrons. Since neutrons carry no charge, they only lose energy by collision or reaction with a nucleus. Neutrons with high energies transfer large amounts of energy by inelastic collisions with nuclei. However, as the neutron energy decreases, elastic collisions become much more effective for energy loss. The lighter the nucleus, the greater the fraction of the neutron's kinetic energy that can be lost in an elastic collision. Thus, hydrogen-containing materials such as polymers are most effective in reducing the energy of neutrons. Once neutrons are reduced to very low energies, the probability for undergoing a reaction with a nucleus (the cross section) becomes very high. The product of such a reaction is often radioactive and can involve the release of a significant amount of energy. Thus, it is important to provide protection from low energy neutrons during a long duration space flight. Among the light elements, lithium and boron each have an isotope with a large thermal neutron capture cross section, Li-6 and B-10. However, B-10 is more abundant in the naturally-occurring element than Li-6, has a thermal neutron capture cross section four times that of Li-6, and produces the stable products, He-4 and Li-7 in the interaction while Li-6 produces radioactive tritium (H-3). Thus, boron is the best light-weight material for thermal neutron absorption in spacecraft. The work on this project was focused in two areas: computer design where existing computer codes were used, and in some cases modified, to calculate the propagation and interactions of high energy charged particles through various media, and materials development where boron was incorporated into high performance materials.

Kiefer, Richard L.↗

Simulating the Gradually Deteriorating Performance of an RTG

Degra (now in version 3) is a computer program that simulates the performance of a radioisotope thermoelectric generator (RTG) over its lifetime. Degra is provided with a graphical user interface that is used to edit input parameters that describe the initial state of the RTG and the time-varying loads and environment to which it will be exposed. Performance is computed by modeling the flows of heat from the radioactive source and through the thermocouples, also allowing for losses, to determine the temperature drop across the thermocouples. This temperature drop is used to determine the open-circuit voltage, electrical resistance, and thermal conductance of the thermocouples. Output power can then be computed by relating the open-circuit voltage and the electrical resistance of the thermocouples to a specified time-varying load voltage. Degra accounts for the gradual deterioration of performance attributable primarily to decay of the radioactive source and secondarily to gradual deterioration of the thermoelectric material. To provide guidance to an RTG designer, given a minimum of input, Degra computes the dimensions, masses, and thermal conductances of important internal structures as well as the overall external dimensions and total mass.

Wood, Eric G.↗

Higher-Order Theory for Functionally Graded Materials

Functionally graded materials (FGM's) are a new generation of engineered materials wherein the microstructural details are spatially varied through nonuniform distribution of the reinforcement phase(s). Engineers accomplish this by using reinforcements with different properties, sizes, and shapes, as well as by interchanging the roles of the reinforcement and matrix phases in a continuous manner (ref. 1). The result is a microstructure that produces continuously or discretely changing thermal and mechanical properties at the macroscopic or continuum scale. This new concept of engineering the material's microstructure marks the beginning of a revolution both in the materials science and mechanics of materials areas since it allows one, for the first time, to fully integrate the material and structural considerations into the final design of structural components. Functionally graded materials are ideal candidates for applications involving severe thermal gradients, ranging from thermal structures in advanced aircraft and aerospace engines to computer circuit boards. Owing to the many variables that control the design of functionally graded microstructures, full exploitation of the FGM's potential requires the development of appropriate modeling strategies for their response to combined thermomechanical loads. Previously, most computational strategies for the response of FGM's did not explicitly couple the material's heterogeneous microstructure with the structural global analysis. Rather, local effective or macroscopic properties at a given point within the FGM were first obtained through homogenization based on a chosen micromechanics scheme and then subsequently used in a global thermomechanical analysis.

Aboudi, J.↗