Search NASA⌕ Search

SEARCH · Search NASA

Results for “computational homogenization”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

A nonlinear data-driven reduced order model for computational homogenization with physics/pattern-guided sampling

Developing an accurate nonlinear reduced order model from simulation data has been an outstanding research topic for many years. For many physical systems, data collection is very expensive and the optimal data distribution is not known in advance. Thus, maximizing the information gain remains a grand challenge. In a recent paper, Bhattacharjee and Matouš (2016) proposed a manifold-based nonlinear reduced order model for multiscale problems in mechanics of materials. Expanding this work here, we develop a novel sampling strategy based on the physics/pattern-guided data distribution. Our adaptive sampling strategy relies on enrichment of sub-manifolds based on the principal stretches and rotational sensitivity analysis. This novel sampling strategy substantially decreases the number of snapshots needed for accurate reduced order model construction (i.e., ~5 x reduction of snapshots over Bhattacharjee and Matouš (2016)). Moreover, we build the nonlinear manifold using the displacement rather than deformation gradient data. We provide rigorous verification and error assessment. We demonstrate both localization and homogenization of the multiscale solution on a large particulate composite unit cell.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

MIPS: The good, the bad and the useful

Many authors are critical of the use of MIPS (Millions of Instructions per Second) as a measure of computer power. Some feel that MIPS are meaningless. While there is justification for some of the criticism of MIPS, sometimes the criticism is carried too far. MIPS can be a useful number for planning and estimating purposes when used in a homogeneous computer environmnet. Comparisons between published MIPS ratings and benchmark results reveal that there does exist a high positive correlation between MIPS and tested performance, given a homogeneous computer environment. MIPS should be understood so as not to be misused. It is not correct that the use of MIPS is always inappropriate or inaccurate

Richardson, Jerry K.↗
DOE OSTI2025

Micrometer: Micromechanics transformer for predicting full field mechanical responses of heterogeneous materials

Predicting mechanical responses of heterogeneous materials across scales remains a significant challenge. Traditional computational methods often struggle with complex and multiscale nature of these materials, limiting their effectiveness in real-world applications. Here, in this paper, we introduce Micrometer, a vision transformer based deep learning model designed to predict full field mechanical responses of heterogeneous materials, bridging the gap between computer vision and solid mechanics problems. We show that Micrometer, trained on a large-scale high-resolution dataset of 2D fiber-reinforced composites, can achieve state-of-the-art performance in predicting microscale strain fields across a wide range of material properties and loading conditions. Our model demonstrates accuracy and computational efficiency in applications such as computational homogenization and multiscale modeling, reducing computational time by up to two orders of magnitude compared to conventional numerical solvers while maintaining less than 1 % errors in predicting macroscale stress fields. Furthermore, we showcase Micrometer’s adaptability through transfer learning experiments on new materials with limited data, highlighting its potential to tackle diverse scenarios in computational solid mechanics. These results represent a significant step towards AI-driven innovation in materials science, addressing the limitations of traditional numerical methods and paving the way for more efficient simulations of heterogeneous materials across various industrial applications.

Composite materials↗
DOE OSTI2020

Computational thermomechanics for crystalline rock. Part II: Chemo-damage-plasticity and healing in strongly anisotropic polycrystals

We present a thermal–mechanical–chemical-phase field model that captures the multi-physical coupling effects of precipitation creeping, crystal plasticity, anisotropic fracture, and crack healing in polycrystalline rock at various temperature and strain-rate regimes. This model is solved via a fast Fourier transfer solver with an operator-split algorithm to update displacement, temperature and phase field, and chemical concentration incrementally. In nuclear waste disposal in salt formation, brine inside the crystal salt may migrate along the grain boundary and cracks due to the gradient of interfacial energy and pressure. This migration has a significant implication on the permeability evolution, creep deformation, and crack healing within rock salt but is difficult to incorporate implicitly via effective medium theories compared with computational homogenization. As such, we introduce a thermodynamic framework and a corresponding computational implementation that explicitly captures the brine diffusion along the grain boundary and crack at the grain scale. Meanwhile, the anisotropic fracture and healing are captured via a high-order phase field that represents the regularized crack region in which a newly derived non-monotonic driving force is used to capture the fracture and healing due to the solution–precipitation. Numerical examples are presented to demonstrate the capacity of the thermodynamic framework to capture the multiphysics material behaviors of rock salt.

42 ENGINEERING↗
DOE OSTI2021

Mechanical analysis of heterogeneous materials with higher-order parameters

Abstract Even though heterogeneous porous materials are widely used in a variety of engineering and scientific fields, such as aerospace, energy-storage technology, and bio-engineering, the relationship between effective material properties of porous materials and their underlying morphology is still not fully understood. To contribute to this knowledge gap, this paper adopts a higher-order asymptotic homogenization method to numerically investigate the effect of complex micropore morphology on the effective mechanical properties of a porous system. Specifically, we use the second-order scheme that is an extension of the first-order computational homogenization framework, where a generalized continuum enables us to introduce length scale into the material constitutive law and capture both pore size and pore distribution. Through several numerical case studies with different combinations of porosity, pore shapes, and distributions, we systematically studied the relationship between the underlying morphology and effective mechanical properties. The results highlight the necessity of higher-order homogenization in understanding the mechanical properties and reveal that higher-order parameters are required to capture the role of realistic pore morphologies on effective mechanical properties. Furthermore, for specific pore shapes, higher-order parameters exhibit dominant influence over the first-order continuum.

42 ENGINEERING↗
DOE OSTI2021

Methodology for Sensitivity Analysis of Homogenized Cross-Sections to Instantaneous and Historical Lattice Conditions with Application to AP1000® PWR Lattice

In the two-step method for nuclear reactor simulation, lattice physics calculations are performed to compute homogenized cross-sections for a variety of burnups and lattice configurations. A nodal code is then used to perform full-core analysis using the pre-calculated homogenized cross-sections. One source of uncertainty introduced in this method is that the lattice configuration or depletion conditions typically do not match a pre-calculated one from the lattice physics simulations. Therefore, some interpolation model must be used to estimate the homogenized cross-sections in the nodal code. This current study provides a methodology for sensitivity analysis to quantify the impact of state variables on the homogenized cross-sections. This methodology also allows for analyses of the historical effect that the state variables have on homogenized cross-sections. An application of this methodology on a lattice for the Westinghouse AP1000® reactor is presented where coolant density, fuel temperature, soluble boron concentration, and control rod insertion are the state variables of interest. The effects of considering the instantaneous values of the state variables, historical values of the state variables, and burnup-averaged values of the state variables are analyzed. Using these methods, it was found that a linear model that only considers the instantaneous and burnup-averaged values of state variables can fail to capture some variations in the homogenized cross-sections.

Price, Dean (ORCID:0000000309990111)↗
NASA NTRS1999

A Design Tool for Liquid Rocket Engine Injectors

A practical design tool for the analysis of flowfields near the injector face has been developed and used to analyze the Fastrac engine. The objective was to produce a computational design tool which was detailed enough to predict the interactive effects of injector element impingement angles and points and the momenta of the individual orifice flows. To obtain a model which could be used to simulate a significant number of individual orifices, a homogeneous computational fluid dynamics model was developed. To describe liquid and vapor sub- and super-critical flows, the model included thermal and caloric equations of state which were valid over a wide range of pressures and temperatures. A homogeneous model was constructed such that the local state of the flow was determined directly, i.e. the quality of the flow was calculated. Such a model does not identify drops or their distribution, but it does allow the flow along the injector face and into the acoustic cavity to be predicted. It also allows the film coolant flow to be accurately described. The initial evaluation of the injector code was made by simulating cold flow from an unlike injector element and from a like-on-like overlapping fan (LOL) injector element. The predicted mass flux distributions of these injector elements compared well to cold flow test results. These are the same cold flow tests which serve as the data base for the JANNAF performance prediction codes. The flux distributions 1 inch downstream of the injector face are very similar; the differences were somewhat larger at further distances from the faceplate. Since the cold flow testing did not achieve good mass balances when integrations across the entire fan were made, the CFD simulation appears to be reasonable alternative to future cold flow testing. To simulate the Fastrac, an RP-1/LOX combustion model must be chosen. This submodel must be relatively simple to accomplish three-dimensional, multiphase flow simulations. Single RP-1 pyrolysis and partial oxidation steps were chosen and the combustion was completed with the wet CO mechanism. Soot was also formed with a single global reaction. To validate the combustion submodel, global data from gas generator tests and from subscale motor test were used to predict qualitatively correct mean molecular weights, temperature, and soot levels. Because such tests do not provide general kinetics rates, the methodology is not necessarily appropriate for other than rocket type flows conditions. Soot predictions were made so that radiation heating to the motor walls can be made. These initial studies of the Fastrac were for a small region close to the injector face and chamber wall which included a segment of the acoustic cavity. The region analyzed includes 11 individual orifice holes to represent the LOL elements and the H2 film coolant holes. Typical results of this simulation are shown in Figure 1. At this point the only available test data to verify the predictions are temperatures measured in the acoustic cavity. These temperatures are in reasonable agreement at about 2000R (1111 K). Future work is expected to include improving the computational efficiency or the CFD model and/or using more computer capacity than the single Pentium PC with which these simulations were made.

Farmer, Richard C.↗
DOE OSTI2023

Simulation toolkit for digital material characterization of large image-based microstructures

In this paper, an efficient image-based simulation toolkit for material characterization is presented, which is scalable to work from personal computers to workstations. The effective thermal conductivity, elasticity, and permeability are evaluated employing a computational homogenization framework based on the Finite Element Method (FEM). Two complementary open-source packages are presented: one developed in Python, which can convert digital images into voxel meshes (pyTomoviewer); the other developed in Julia, that can run numerical simulations to compute effective material properties (chpack). Also, a CUDA C version of chpack is provided (chfem_gpu). They were designed to deal with large multi-phase models, so strategies were devised to minimize their memory footprint, while avoiding a high toll on execution time. The voxel-based approach significantly simplifies the FEM meshes and allows efficient matrix-free implementations. In that sense, to handle large linear systems of equations, the element-by-element (EBE) technique is adopted, in conjunction with a low-memory implementation of the Preconditioned Conjugate Gradient (PCG) method. Finally, the code was thoroughly tested on an artificial geometry made of a square array of cylinders, for which analytical solutions exist, as well as on a real micro-tomographic reconstruction of FiberForm TM , a carbon preform commonly used in thermal protection systems.

36 MATERIALS SCIENCE↗
NASA NTRS2000

A Design Tool for Liquid Rocket Engine Injectors

A practical design tool which emphasizes the analysis of flowfields near the injector face of liquid rocket engines has been developed and used to simulate preliminary configurations of NASA's Fastrac and vortex engines. This computational design tool is sufficiently detailed to predict the interactive effects of injector element impingement angles and points and the momenta of the individual orifice flows and the combusting flow which results. In order to simulate a significant number of individual orifices, a homogeneous computational fluid dynamics model was developed. To describe sub- and supercritical liquid and vapor flows, the model utilized thermal and caloric equations of state which were valid over a wide range of pressures and temperatures. The model was constructed such that the local quality of the flow was determined directly. Since both the Fastrac and vortex engines utilize RP-1/LOX propellants, a simplified hydrocarbon combustion model was devised in order to accomplish three-dimensional, multiphase flow simulations. Such a model does not identify drops or their distribution, but it does allow the recirculating flow along the injector face and into the acoustic cavity and the film coolant flow to be accurately predicted.

Farmer, R.↗
NASA NTRS1990

Effects of organized turbulence structures on the phase distortion in a coherent optical beam propagating through a turbulent shear flow

Phase distortion in a coherent optical beam propagating through a turbulent shear flow is studied. The instantaneous distribution of the index refraction is represented by a passive-scalar field in a computed homogeneous shear flow. The flow contains organized vortical structures (hairpin eddies), which are characteristic of turbulent shear flows. The phase distortion induced by turbulent fluctuations is calculated from the optical path difference through the flow. A conceptual model is proposed for the distribution of scalar fluctuations produced by the hairpin vortices in the shear flow. It is shown that the phase distortion of an optical beam can be minimized by propagating the beam at an angle approximately normal to the organized vortical structures in a turbulent shear flow.

Truman, C. Randall↗
NASA NTRS1996

Micromechanics for particulate reinforced composites

A set of micromechanics equations for the analysis of particulate reinforced composites is developed using the mechanics of materials approach. Simplified equations are used to compute homogenized or equivalent thermal and mechanical properties of particulate reinforced composites in terms of the properties of the constituent materials. The microstress equations are also presented here to decompose the applied stresses on the overall composite to the microstresses in the constituent materials. The properties of a 'generic' particulate composite as well as those of a particle reinforced metal matrix composite are predicted and compared with other theories as well as some experimental data. The micromechanics predictions are in excellent agreement with the measured values.

Murthy, Pappu L. N.↗
NASA NTRS1990

Materials with periodic internal structure: Computation based on homogenization and comparison with experiment

The combination of thermal and mechanical loading expected in practice means that constitutive equations of metal matrix composites must be developed which deal with time-independent and time-dependent irreversible deformation. Also, the internal state of composites is extremely complicated which underlines the need to formulate macroscopic constitutive equations with a limited number of state variables which represent the internal state at the micro level. One available method for calculating the macro properties of composites in terms of the distribution and properties of the constituent materials is the method of homogenization whose formulation is based on the periodicity of the substructure of the composite. A homogenization procedure was developed which lends itself to the use of the finite element procedure. The efficiency of these procedures, to determine the macroscopic properties of a composite system from its constituent properties, was demonstrated utilizing an aluminum plate perforated by directionally oriented slits. The selection of this problem is based on the fact that, extensive experimental results exist, the macroscopic response is highly anisotropic, and that the slits provide very high stress gradients which severely test the effectiveness of the computational procedures. Furthermore, both elastic and plastic properties were investigated so that the application to practical systems with inelastic deformation should be able to proceed without difficulty. The effectiveness of the procedures was rigorously checked against experimental results and with the predictions of approximate calculations. Using the computational results it is illustrated how macroscopic constitutive equations can be expressed in forms of the elastic and limit load behavior.

Jansson, S.↗
DOE OSTI2020

A numerical-homogenization based phase-field fracture modeling of linear elastic heterogeneous porous media

Most porous media, such as geomaterials and biomaterials are highly heterogeneous in nature, and they contain large variations of microscopic pore structures, such as pore sizes, pore distribution, and pore shapes. The oscillation of microscopic structures is a substantial challenge in theoretical characterization and is usually ignored in continuous modeling. However, mechanical behavior of porous media such as deformation and failure, are essentially impacted by the microscopic heterogeneity which needs to be considered in modeling a porous media. Here, this research proposes a numerical modeling framework with a capability to investigate the effect of microscopic heterogeneity on the macroscopic fracture behavior in porous media by using a numerical homogenization technique, combined with the phase-field fracture modeling method. This numerical modeling strategy computes a homogenized elasticity tensor based on microscopic heterogeneous pore structures heterogenous porous domain by solving boundary value problems at microscopic domain. The strain energy and subsequent propagation of macroscopic fractures will be updated using homogenized stiffness information. Using this numerical scheme, the microscopic pore structure’s impact on the fracture behavior through the homogenized elastic tensor will be taken into account. This multiscale technique is benchmarked against classical problems. Finally, the results highlight the importance of the underlying pore structure and reveal that both fracture strength and propagation path can be influenced by the microscopic heterogeneity.

36 MATERIALS SCIENCE↗
NASA NTRS1992

Reactant conversion in homogeneous turbulence - Mathematical modeling, computational validations, and practical applications

The presently obtained closed-form analytical expressions, which predict the limiting rate of mean reactant conversion in homogeneous turbulent flows under the influence of a binary reaction, are derived via the single-point pdf method based on amplitude mapping closure. With this model, the maximum rate of the mean reactant's decay can be conveniently expressed in terms of definite integrals of the parabolic cylinder functions. The results obtained are shown to be in good agreement with data generated by direct numerical simulations.

Madnia, C. K.↗
NASA NTRS1992

Reactant conversion in homogeneous turbulence: Mathematical modeling, computational validations and practical applications

Closed form analytical expressions are obtained for predicting the limited rate of reactant conversion in a binary reaction of the type F + rO yields (1 + r) Product in unpremixed homogeneous turbulence. These relations are obtained by means of a single point Probability Density Function (PDF) method based on the Amplitude Mapping Closure. It is demonstrated that with this model, the maximum rate of the reactants' decay can be conveniently expressed in terms of definite integrals of the Parabolic Cylinder Functions. For the cases with complete initial segregation, it is shown that the results agree very closely with those predicted by employing a Beta density of the first kind for an appropriately defined Shvab-Zeldovich scalar variable. With this assumption, the final results can also be expressed in terms of closed form analytical expressions which are based on the Incomplete Beta Functions. With both models, the dependence of the results on the stoichiometric coefficient and the equivalence ratio can be expressed in an explicit manner. For a stoichiometric mixture, the analytical results simplify significantly. In the mapping closure, these results are expressed in terms of simple trigonometric functions. For the Beta density model, they are in the form of Gamma Functions. In all the cases considered, the results are shown to agree well with data generated by Direct Numerical Simulations (DNS). Due to the simplicity of these expressions and because of nice mathematical features of the Parabolic Cylinder and the Incomplete Beta Functions, these models are recommended for estimating the limiting rate of reactant conversion in homogeneous reacting flows. These results also provide useful insights in assessing the extent of validity of turbulence closures in the modeling of unpremixed reacting flows. Some discussions are provided on the extension of the model for treating more complicated reacting systems including realistic kinetics schemes and multi-scalar mixing with finite rate chemical reactions in more complex configurations.

Madnia, C. K.↗
NASA NTRS1974

Computer program for thin-wire structures in a homogeneous conducting medium

A computer program is presented for thin-wire antennas and scatters in a homogeneous conducting medium. The anaylsis is performed in the real or complex frequency domain. The program handles insulated and bare wires with finite conductivity and lumped loads. The output data includes the current distribution, impedance, radiation efficiency, gain, absorption cross section, scattering cross section, echo area and the polarization scattering matrix. The program uses sinusoidal bases and Galerkin's method.

Richmond, J. H.↗
DOE OSTI2020

Computationally efficient evaluation of optimum homogeneous charge compression ignition operating range with accelerated multizone engine cycle simulation

The very intensive calculations necessary to define a performance map requiring evaluation of over a hundred individual operating points can be efficiently conducted with accelerated multizone for engine cycle simulation, leading to a definition of regions of acceptable and optimum homogeneous charge compression ignition operation. Accelerated multizone for engine cycle simulation has the virtue of enabling accurate evaluation of many operating conditions based on thermal stratification data from a single fluid mechanics run at motored conditions. This is possible because thermal stratification is more sensitive to engine geometry than to operating conditions. In this article, accuracy of accelerated multizone for engine cycle simulation is demonstrated by comparison with experimental data for iso-octane homogeneous charge compression ignition operation over a broad range of lean equivalence ratios (0.14–0.28). The validated accelerated multizone for engine cycle simulation model is then applied to generating a performance map for an engine controlled by appropriately adjusting equivalence ratio and internal exhaust gas recirculation. Regions of acceptable and optimum combustion are identified. It is finally demonstrated that while indicated mean effective pressure remains low for optimum homogeneous charge compression ignition operation (1–4 bar), this is sufficient for a large fraction of typical driving in light-duty vehicles. Much driving including idle can therefore be done in homogeneous charge compression ignition mode at high efficiency and low (essentially zero) NOx and particulate matter emissions.

30 DIRECT ENERGY CONVERSION↗