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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A Micromorphic Length-Scale Coupling Framework for the Determination of Higher-Order Constitutive Models and the Multi-Scale Simulation of Heterogeneous Materials [Thesis]

Heterogeneous materials and materials with complex microstructures pose a unique challenge in the development of accurate models of their response to external stimuli. These difficulties principally arise due to the difficulty in characterizing and modeling the constituents and their interactions. It is usually possible, though non-trivial, to construct an explicit representation of the microstructure (a direct numeric simulation or DNS) but the method by which the complex modes of deformation and other processes can be homogenized to a reduced-order approximation is frequently unclear. Many homogenization approaches are ad-hoc and lack a strong justification beyond ease of computation. Furthermore, the homogenization approach can, in some cases, not utilize the full breadth of information available in the computation of the macro-scale stresses and deformation measures. It is also noteworthy that homogenization, by its very nature, will tend to obfuscate details of processes occurring at the lower length-scale. It is therefore of interest to include as much information as possible in the construction of the reduced-order model so as to be predictive in a variety of loading environments. We here present a length-scale bridging technique based upon the micromorphic continuum mechanics of Eringen which incorporates volume and surface area averages as a part of its construction. This approach enforces the balance equations at the micro-scale and then studies the effect of the spatially varying nature on the macro-scale. This leads, naturally, to further balance equations which are solved at the macro-scale. This work details a homogenization framework which arises naturally from the micromorphic construction of Eringen attempting to introduce no definitions beyond which are justifiable from micro-structural considerations. One of the results of this effort is the so-called “micromorphic filter” which has been developed and applied to several DNS to demonstrate its effectively. In order to determine the macroscopic degrees of freedom we utilize the special case of an overlap coupling technique where the macro-scale is fully constrained to the micro-scale. This enables us to study the resulting material properties as expected but also allows us to further study the boundary conditions on the additional degrees of freedom at the macro-scale.

42 ENGINEERING↗
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 OSTI2022

Nanoindentation mapping defects filtration for heterogeneous materials using generative adversarial networks

Advanced composite materials with multiple phases and heterogeneous microstructure necessitate spatial mapping characterization of elastic modulus to develop constitutive relations and overall mechanical response. Such modulus mapping can be obtained using the nanoindentation technique, where the indenter tip raster over the selected microstructure region. Typically, a surface preparation procedure is done in the specimens to ensure proper contact between the indenter tip and sample surface. However, a near-perfect surface finish is unachievable in heterogeneous materials, primarily with ceramic reinforcements, due to the differential material removal rate during polishing. Thus, the nanoindenter records localized erroneous measurements due to differences in surface roughness and corresponding force response. This study establishes a novel deep learning-based strategy to rectify incorrect experimental spatial measurements acquire during nanoindentation modulus mapping. Here, the integrated bicubic interpolation and generative adversarial networks (GANs) model was trained using 14 ceramic and 18 metallic data sets, each comprising 65,536 measurements. The developed algorithm was validated against experimental measurements on four unknown specimens. The standard deviation in measured elastic modulus reduces by ~50% in ceramics and ~72% in metallic samples. This computational framework proposes a novel approach to reducing uncertainty in materials’ properties using state-of-the-art computer vision techniques.

36 MATERIALS SCIENCE↗
DOE OSTI2025

A Green’s function fast multipole method for computation of micromechanical fields in heterogeneous materials

Computation of micromechanical fields in heterogeneous materials is usually performed using either the finite element method or the Green’s function method based on FFTs. The finite element method allows for accurate discretization and for non-periodic boundary conditions but is computationally expensive. On the other hand, the FFT-based method is computationally efficient but requires discretization on a regular grid of hexahedral voxels. In this paper, a Green’s function method allowing for accurate discretization using tetrahedral elements and for non-periodic boundary conditions is proposed. The convolution is computed using the fast multipole method, which provides good accuracy even for low-order expansion due to the fast decay of interactions between elements. The proposed Green’s function fast multipole method is verified by comparison with analytical and FFT-based solutions. Furthermore, the computational time is analyzed and compared to the FFT-based method for non-periodic convolution. Finally, effective properties of an elastic polycrystalline microstructure containing thin intergranular cracks are computed and analyzed.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Generalized thermo-mechanical framework for heterogeneous materials through asymptotic homogenization

Abstract A fundamental understanding of the interaction between microstructure and underlying physical mechanisms is essential, especially for developing more accurate multi-physics models for heterogeneous materials. Effects of microstructure on the material response at the macroscale are modeled by using the generalized thermomechanics. In this study, strain gradient theory is employed as a higher-order theory on the macroscale with thermodynamics modeled as a first-order theory on the microscale. Hence, energy depends only on the temperature such that we circumvent an extension of Fourier’s law and analyze the “simplest” thermo-mechanical model in strain gradient elasticity. Developing multiphysics models for heterogeneous materials is indeed a challenge and even this “simplest” model in generalized thermomechanics creates dozens of parameters to be determined. We develop a thermo-mechanical framework, in which microstructure is modeled as a periodic structure and through asymptotic homogenization approach, higher-order parameters at macroscopic scale are calculated. To illustrate the importance of higher-order parameters in overall thermo-mechanical response of a heterogeneous materials, finite element method (FEM) is employed with the aid of open-source codes (FEniCS). Verification example of a bulk system and several case studies of porous structures demonstrate how such numerical framework can be beneficial in the design of materials with tailored microstructures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

10-th order of accuracy for numerical solution of 3-D elasticity equations for heterogeneous materials on unfitted Cartesian meshes

We have developed the Optimal Local Truncation Error Method (OLTEM) with 10-th order of accuracy on unfitted Cartesian meshes for a system of 3-D elasticity equations with smooth irregular interfaces. 5 x 5 x 5 = 125-point stencils (similar to those for quadratic finite elements) for elastic heterogeneous materials are used for OLTEM. There are no unknowns at the interface points between different materials; the structure of the global discrete equations is the same for homogeneous and heterogeneous materials. The calculation of unknown stencil coefficients is based on the minimization of the local truncation error of the stencil equations and yields the optimal 10-th order of accuracy for OLTEM on unfitted Cartesian meshes, i.e., the increase by 7 orders in accuracy compared to quadratic finite elements on conformal meshes. A new post-processing procedure provides the 9-th order of accuracy for stresses in the 3-D case. Similar to basic computations it uses OLTEM with the 125-point stencils, the interface conditions and the elasticity equations. It was shown that the use of the elasticity equations for post-processing improves the accuracy of 0.1% stresses by 6 orders compared to post-processing without the use of PDEs. At an accuracy of for stresses, OLTEM with the new post-processing procedure reduces the number of degrees of freedom by 360 - 8000 times compared to quadratic finite elements with similar stencils. OLTEM with the 125-point stencils yields even more accurate results than high-order finite elements with much wider stencils. OLTEM provides accurate numerical results for compressible and nearly incompressible materials.

elasticity equations↗
DOE OSTI2024

Progress towards subsurface spectroscopy inside heterogeneous materials using four wave mixing phase conjugation

Herein, we report preliminary results on subsurface spectroscopy inside heterogeneous materials using four wave mixing phase conjugation. For our test material we use an inert plastic bonded explosive simulant that contains fluorescent guidestar particles. Using phase conjugation, we are able to obtain spectral enhancements approximately equal to the phase conjugate reflectivity. Additionally, we discuss future directions to improve this technique to obtain greater signal enhancements.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Derivation of heterogeneous material distributions and their sensitivity to HM-coupled two-phase flow models exemplified with the LASGIT experiment

Abstract Advective gas transport in bentonite, a possible buffer material in repositories for radioactive materials, is difficult to simulate in numerical continuum models, partly due to the complicated microstructure of bentonite. To generate reliable models of repositories nevertheless, spatially distributed heterogeneous material properties can be used to allow localization of gas flow. In this study, a pore-size-dependent stochastic approach of the gas entry pressure is derived from Mercury Intrusion Porosimetry, which is used to replicate measurements from the LASGIT experiment. In addition, three benchmark tests are simulated to investigate the dependence of heterogeneous distributions of material properties on the mesh discretization, the temporal dependence, and the coupling between the processes influenced by the heterogeneous parameters. The numerical modeling results of the LASGIT experiment show that the onset of gas flow into the system and the subsequent increase in pressure and stress can be well reproduced using heterogeneous distributions. Compared to a model with homogeneous material properties, heterogeneous distributions may allow the generation of dilatancy-controlled microfractures—an important feature with regard to the advective gas flow in bentonites. However, it can be observed that the heterogeneous distributions in LASGIT are less significant, as technical gaps or differences in material types could have a greater impact.

Environmental Sciences & Ecology↗
DOE OSTI2024

Subsurface Spectroscopy in Heterogeneous Materials Using Self-Healing Laser Beams

Self-healing optical beams are a class of propagation modes that can recover their beam shapes after distortion or partial blockage. This self-healing property makes them attractive for use in applications involving turbid media as they can—in theory—penetrate further into these materials than standard Gaussian beams. In this paper, we characterize the propagation of two different self-healing beams (Bessel and Airy) through a solid scattering material with different scatterer concentrations and find that both beams do recover after scattering for samples below a threshold scatterer concentration. Additionally, we test the applicability of both beam shapes for improved sub-surface spectroscopy in heterogeneous materials using fluorescent particles and find that there is an average fluorescence intensity enhancement of 1.3× using self-healing beams versus a standard Gaussian beam.

47 OTHER INSTRUMENTATION↗
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 OSTI2022

Continuous conditional generative adversarial networks for data-driven solutions of poroelasticity with heterogeneous material properties

Machine learning-based data-driven modeling can allow computationally efficient time-dependent solutions of PDEs, such as those that describe subsurface multiphysical problems. In this work, our previous approach (Kadeethum et al., 2021d) of conditional generative adversarial networks (cGAN) developed for the solution of steady-state problems involving highly heterogeneous material properties is extended to time-dependent problems by adopting the concept of continuous cGAN (CcGAN). The CcGAN that can condition continuous variables is developed to incorporate the time domain through either element-wise addition or conditional batch normalization. Moreover, this framework can handle training data that contain different timestamps and then predict timestamps that do not exist in the training data. As a numerical example, the transient response of the coupled poroelastic process is studied in two different permeability fields: Zinn & Harvey transformation and a bimodal transformation. The proposed CcGAN uses heterogeneous permeability fields as input parameters while pressure and displacement fields over time are model output. Our results show that the model provides sufficient accuracy with computational speed-up. This robust framework will enable us to perform real-time reservoir management and robust uncertainty quantification in poroelastic problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Data for: Ultrasonic characterization of material heterogeneities in stainless steel parts fabricated by powder bed fusion

These are the raw ultrasonic waveform files and nanoindentation measurements for three additively manufactured 316L stainless steel components with different fabrication parameters. Each part's length is divided into four segmented regions where their fabrication energy densities change. Part V+ begins at 33 J/mm^3 and increases in energy density by 3 J/mm^3 with each segment. Part C remains at a constant 33 J/mm^3 throughout the part. Part V- begins at 33 J/mm^3 and decreases in energy density by 3 J/mm^3 with each segment. We have found that the ultrasonic waves in regions with higher energy densities will traverse more quickly, as shown by the shorter time of flight, and vice versa. Similarly, nanoindentation measurements of reduced modulus and hardness follow this trend. We have measured the direction in which the parts were fabricated (build direction) and the segmented regions that are perpendicular to the build direction (transverse directions). The build direction longitudinal wave velocity measurements are considerably lower than their transverse direction counterparts, indicating anisotropy between the two directions. In Part C, we have removed material from one of its surfaces and recorded its ultrasonic and nanoindentation measurements with each material removal iteration. Changes in the material properties are more prominent by nanoindentation, suggesting material heterogeneity between the part's surface and interior. The README.txt file has information on how to navigate the files and process the data.

Anisotropy↗
DOE OSTI2023

Subsurface spectroscopy of heterogeneous materials using optical wavefront shaping

Plastic-bonded explosives and propellants consist of energetic molecular crystals embedded in a polymer matrix that also includes additives, such as taggants, plasticizers, grit, antioxidants, etc. Furthermore, this heterogeneous composition renders these materials optically opaque, limiting optical characterization techniques (e.g., Raman spectroscopy) to probing chemical reactions at the sur-face. However, many reactions of interest are believed to occur inside the material where current optical techniques can not probe. To address this challenge, we have developed a new optical technique that utilizes feedback assisted wavefront shaping (using spatial light modulators) to focus probe light inside a heterogeneous material, such that we can perform subsurface spectroscopy. Recently, we demonstrated this technique by monitoring subsurface photodegradation and thermal degradation of Eu-doped molecular crystals using both fluorescence and Raman spectroscopy. Based off these successes we are now looking into improvements to this technique to allow for greater time resolution, including replacing our spatial light modulators with fast digital mirror devices, using ns optical phase conjugation, and self-healing optical beams.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Ultrasonic characterization of material heterogeneities in stainless steel components produced by laser powder bed fusion

We introduce pulse-echo ultrasound as a method for characterizing the impact of powder bed fusion parameters on the properties of additively manufactured stainless-steel components, their material anisotropy, and location-dependent heterogeneity. Our results indicate that accurate characterization requires careful selection of ultrasonic propagation paths, which must consider the direction of additive layering, variations in processing parameters, and the component's geometry. We employed two distinct methods to estimate material properties from ultrasonic data: One assumes isotropy, while the other accounts for anisotropic interactions during the propagation of elastic waves. When applied to samples fabricated with laser energy densities ranging from 24 to 42 J/mm³ , these methods revealed transverse isotropy and weak anisotropy (quantified by small Thomsen parameters, ε = 0.0651 and γ = 0.0092) and less than a ∼6 % change in acoustic impedance. The assumption of isotropy, in this case, leads to small errors (less than 4 % or 1 % for Young's modulus in the build or transverse directions) when estimating orthotropic material properties using ultrasonic data measured along just two orthogonal directions, one of which must align with the build direction. By comparing ultrasonic measurements — which aggregate the spatial variability in material properties along the length of elastic wave propagation into a single value — with localized measurements obtained from surface nanoindentation, we uncovered and spatially profiled significant differences between the surface and interior properties. Specifically, the surface Young's modulus decreased from approximately 210 GPa to 180 GPa within a depth of about 3 mm. We attribute this surface-localized heterogeneity in PBF-fabricated components to distinct thermal histories experienced by the surface and interior regions. Collectively, the results of this study establish a framework for the ultrasonic characterization of material heterogeneity and anisotropy in material properties and demonstrate its application in additively manufactured metal components.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Sub-10 nm Probing of Ferroelectricity in Heterogeneous Materials by Machine Learning Enabled Contact Kelvin Probe Force Microscopy

Reducing the dimensions of ferroelectric materials down to the nanoscale has strong implications on the ferroelectric polarization pattern and on the ability to switch the polarization. As the size of ferroelectric domains shrinks to the nanometer scale, the heterogeneity of the polarization pattern becomes increasingly pronounced, enabling a large variety of possible polar textures in nanocrystalline and nanocomposite materials. Critical to the understanding of fundamental physics of such materials and hence their applications in electronic nanodevices is the ability to investigate their ferroelectric polarization at the nanoscale in a nondestructive way. We show that contact Kelvin probe force microscopy (cKPFM) combined with a k-means response clustering algorithm enables to measure the ferroelectric response at a mapping resolution of 8 nm. In a BaTiO 3 thin film on silicon composed of tetragonal and hexagonal nanocrystals, we determine a nanoscale lateral distribution of discrete ferroelectric response clusters, fully consistent with the nanostructure determined by transmission electron microscopy. Moreover, we apply this data clustering method to the cKPFM responses measured at different temperatures, which allows us to follow the corresponding change in the polarization pattern as the Curie temperature is approached and across the phase transition. This work opens up perspectives for mapping complex ferroelectric polarization textures such as curled/swirled polar textures that can be stabilized in epitaxial heterostructures and more generally for mapping the polar domain distribution of any spatially highly heterogeneous ferroelectric materials.

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

An adjoint-based optimization method for jointly inverting heterogeneous material properties and fault slip from earthquake surface deformation data

SUMMARY Analysis of tectonic and earthquake-cycle associated deformation of the crust can provide valuable insights into the underlying deformation processes including fault slip. How those processes are expressed at the surface depends on the lateral and depth variations of rock properties. The effect of such variations is often tested by forward models based on a priori geological or geophysical information. Here, we first develop a novel technique based on an open-source finite-element computational framework to invert geodetic constraints directly for heterogeneous media properties. We focus on the elastic, coseismic problem and seek to constrain variations in shear modulus and Poisson’s ratio, proxies for the effects of lithology and/or temperature and porous flow, respectively. The corresponding nonlinear inversion is implemented using adjoint-based optimization that efficiently reduces the cost function that includes the misfit between the calculated and observed displacements and a penalty term. We then extend our theoretical and numerical framework to simultaneously infer both heterogeneous Earth’s structure and fault slip from surface deformation. Based on a range of 2-D synthetic cases, we find that both model parameters can be satisfactorily estimated for the megathrust setting-inspired test problems considered. Within limits, this is the case even in the presence of noise and if the fault geometry is not perfectly known. Our method lays the foundation for a future reassessment of the information contained in increasingly data-rich settings, for example, geodetic GNSS constraints for large earthquakes such as the 2011 Tohoku-oki M9 event, or distributed deformation along plate boundaries as constrained from InSAR.

Geochemistry & Geophysics↗
DOE OSTI2022

Optical emissivity dataset of multi-material heterogeneous designs generated with automated figure extraction

Optical device design is typically an iterative optimization process based on a good initial guess from prior reports. Optical properties databases are useful in this process but difficult to compile because their parsing requires finding relevant papers and manually converting graphical emissivity curves to data tables. Here, we present two contributions: one is a dataset of thermal emissivity records with design-related parameters, and the other is a software tool for automated colored curve data extraction from scientific plots. We manually collected 64 papers with 176 figures reporting thermal emissivity and automatically retrieved 153 colored curve data records. The automated figure analysis software pipeline uses Faster R-CNN for axes and legend object detection, EasyOCR for axes numbering recognition, and k-means clustering for colored curve retrieval. Additionally, we manually extracted geometry, materials, and method information from the text to add necessary metadata to each emissivity curve. Finally, we analyzed the dataset to determine the dominant classes of emissivity curves and determine the underlying design parameters leading to a type of emissivity profile.

47 OTHER INSTRUMENTATION↗