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DOE OSTI2025

Machine learning-enabled multiscale modeling of mechanical deformation of aluminum and Al-SiC nanocomposites

A machine learning-enabled multiscale framework is developed for modeling the mechanical response of both pure metal and nanoparticle-reinforced metal matrix nanocomposites (MMNCs). Using aluminum–silicon carbide (Al-SiC) as an example MMNC, atomistic simulations reveal three distinct deformation mechanisms (i.e., defect-free, dislocation-based, and interface separation) governed by the interfaces between the Al matrix and SiC nanoparticles. As compared with single crystal Al, the lattice undergoes a more abrupt failure once the dislocation network becomes extensive and void nucleation initiates, whereas in Al-SiC, nanoparticle interfaces enable a more gradual progression of damage. These mechanisms are captured through a combined classification-regression neural network surrogate model that bridges atomic-scale insights with continuum-scale finite element analysis. Machine learning-enabled multiscale modeling of pure Al accurately predicted strain localization and confirmed by in-situ scanning electron microscopic tensile testing on perforated Al specimens. This study underscores the promise of integrating physics-informed machine learning with hierarchical modeling to capture the interface dominated phenomena and guide the design of advanced MMNCs.

Al-SiC↗

DOE OSTI2026

Spatial Optimization of Multiscale Biorefinery Deployment for a Diversified Bioeconomy in the United States

Strategic biorefinery siting is critical for a diversified bioeconomy, yet industry, policy, and research often focus on either large-scale biofuel plants or smaller-scale specialty bioproduct facilities, with limited coordination across scales. We address this gap by modeling biorefinery deployment spanning a 28-fold difference in capacity. We developed an open-source, spatially explicit framework integrating techno-economic analysis with logistics and refinery cost surrogate models to evaluate multiscale miscanthus-derived biorefineries across the rainfed U.S. for the production of ethanol, succinic acid, lactic acid, potassium sorbate, and acrylic acid. Overall costs change little as feedstock density increases, while transport distances decrease by ∼30 to 67% (∼100 km) and siting flexibility improves. Specifically, a 5-fold feedstock density increase (2% to 10% of suitable land) reduces minimum selling prices by <10% (e.g., 0.27 USD·gal –1 for ethanol). This limited economic sensitivity suggests dense planting is not required for competitive deployment, particularly for smaller-scale facilities. Representing collection areas as irregular rather than circular expands the feasible space under low-density scenarios. While large-scale refineries anchor regional supply chains, smaller facilities retain spatial flexibility even when large refineries are established. These findings highlight the importance of spatial representation and multiscale coordination for robust, regionally tailored biomanufacturing networks to advance renewable carbon integration without extensive land conversion.

biorefinery siting↗

DOE OSTI2025

Data-Driven Closures and Assimilation for Stiff Multiscale Random Dynamics

Here, we introduce a data-driven and physics-informed framework for propagating uncertainty in stiff, multiscale random ordinary differential equations (RODEs) driven by correlated (colored) noise. Unlike systems subjected to Gaussian white noise, a deterministic equation for the joint probability density function (PDF) of RODE state variables does not exist in closed form. Moreover, such an equation would require as many phase-space variables as there are states in the RODE system. To alleviate this curse of dimensionality, we instead derive exact, albeit unclosed, reduced-order PDF (RoPDF) equations for low-dimensional observables/quantities of interest. The unclosed terms take the form of state-dependent conditional expectations, which are directly estimated from data at sparse observation times. However, for systems exhibiting stiff, multiscale dynamics, data sparsity introduces regression discrepancies that compound during RoPDF evolution. This is overcome by introducing a kinetic-like defect term to the RoPDF equation, which is learned by assimilating in sparse, low-fidelity RoPDF estimates. Two assimilation methods are considered, namely nudging and deep neural networks, which are successfully tested against Monte Carlo simulations.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2013

A Parameter Estimation Scheme for Multiscale Kalman Smoother (MKS) Algorithm Used in Precipitation Data Fusion

A new approach is presented in this paper to effectively obtain parameter estimations for the Multiscale Kalman Smoother (MKS) algorithm. This new approach has demonstrated promising potentials in deriving better data products based on data of different spatial scales and precisions. Our new approach employs a multi-objective (MO) parameter estimation scheme (called MO scheme hereafter), rather than using the conventional maximum likelihood scheme (called ML scheme) to estimate the MKS parameters. Unlike the ML scheme, the MO scheme is not simply built on strict statistical assumptions related to prediction errors and observation errors, rather, it directly associates the fused data of multiple scales with multiple objective functions in searching best parameter estimations for MKS through optimization. In the MO scheme, objective functions are defined to facilitate consistency among the fused data at multiscales and the input data at their original scales in terms of spatial patterns and magnitudes. The new approach is evaluated through a Monte Carlo experiment and a series of comparison analyses using synthetic precipitation data. Our results show that the MKS fused precipitation performs better using the MO scheme than that using the ML scheme. Particularly, improvements are significant compared to that using the ML scheme for the fused precipitation associated with fine spatial resolutions. This is mainly due to having more criteria and constraints involved in the MO scheme than those included in the ML scheme. The weakness of the original ML scheme that blindly puts more weights onto the data associated with finer resolutions is overcome in our new approach.

multiscale↗

NASA NTRS2012

Multiscale Dynamics of Solar Magnetic Structures

Multiscale topological complexity of the solar magnetic field is among the primary factors controlling energy release in the corona, including associated processes in the photospheric and chromospheric boundaries.We present a new approach for analyzing multiscale behavior of the photospheric magnetic flux underlying these dynamics as depicted by a sequence of high-resolution solar magnetograms. The approach involves two basic processing steps: (1) identification of timing and location of magnetic flux origin and demise events (as defined by DeForest et al.) by tracking spatiotemporal evolution of unipolar and bipolar photospheric regions, and (2) analysis of collective behavior of the detected magnetic events using a generalized version of the Grassberger-Procaccia correlation integral algorithm. The scale-free nature of the developed algorithms makes it possible to characterize the dynamics of the photospheric network across a wide range of distances and relaxation times. Three types of photospheric conditions are considered to test the method: a quiet photosphere, a solar active region (NOAA 10365) in a quiescent non-flaring state, and the same active region during a period of M-class flares. The results obtained show (1) the presence of a topologically complex asymmetrically fragmented magnetic network in the quiet photosphere driven by meso- and supergranulation, (2) the formation of non-potential magnetic structures with complex polarity separation lines inside the active region, and (3) statistical signatures of canceling bipolar magnetic structures coinciding with flaring activity in the active region. Each of these effects can represent an unstable magnetic configuration acting as an energy source for coronal dissipation and heating.

Magnetic fields↗

NASA NTRS2016

Multiscale Modeling of Carbon/Phenolic Composite Thermal Protection Materials: Atomistic to Effective Properties

Next generation ablative thermal protection systems are expected to consist of 3D woven composite architectures. It is well known that composites can be tailored to achieve desired mechanical and thermal properties in various directions and thus can be made fit-for-purpose if the proper combination of constituent materials and microstructures can be realized. In the present work, the first, multiscale, atomistically-informed, computational analysis of mechanical and thermal properties of a present day - Carbon/Phenolic composite Thermal Protection System (TPS) material is conducted. Model results are compared to measured in-plane and out-of-plane mechanical and thermal properties to validate the computational approach. Results indicate that given sufficient microstructural fidelity, along with lowerscale, constituent properties derived from molecular dynamics simulations, accurate composite level (effective) thermo-elastic properties can be obtained. This suggests that next generation TPS properties can be accurately estimated via atomistically informed multiscale analysis.

Materials Science↗

NASA NTRS2016

Information Management Workflow and Tools Enabling Multiscale Modeling Within ICME Paradigm

With the increased emphasis on reducing the cost and time to market of new materials, the need for analytical tools that enable the virtual design and optimization of materials throughout their processing - internal structure - property - performance envelope, along with the capturing and storing of the associated material and model information across its lifecycle, has become critical. This need is also fueled by the demands for higher efficiency in material testing; consistency, quality and traceability of data; product design; engineering analysis; as well as control of access to proprietary or sensitive information. Fortunately, material information management systems and physics-based multiscale modeling methods have kept pace with the growing user demands. Herein, recent efforts to establish workflow for and demonstrate a unique set of web application tools for linking NASA GRC's Integrated Computational Materials Engineering (ICME) Granta MI database schema and NASA GRC's Integrated multiscale Micromechanics Analysis Code (ImMAC) software toolset are presented. The goal is to enable seamless coupling between both test data and simulation data, which is captured and tracked automatically within Granta MI®, with full model pedigree information. These tools, and this type of linkage, are foundational to realizing the full potential of ICME, in which materials processing, microstructure, properties, and performance are coupled to enable application-driven design and optimization of materials and structures.

Materials Engineering↗

NASA NTRS2016

Multiscale Static Analysis of Notched and Unnotched Laminates Using the Generalized Method of Cells

The generalized method of cells (GMC) is demonstrated to be a viable micromechanics tool for predicting the deformation and failure response of laminated composites, with and without notches, subjected to tensile and compressive static loading. Given the axial [0], transverse [90], and shear [+45/-45] response of a carbon/epoxy (IM7/977-3) system, the unnotched and notched behavior of three multidirectional layups (Layup 1: [0,45,90,-45](sub 2S), Layup 2: [0,60,0](sub 3S), and Layup 3: [30,60,90,-30, -60](sub 2S)) are predicted under both tensile and compressive static loading. Matrix nonlinearity is modeled in two ways. The first assumes all nonlinearity is due to anisotropic progressive damage of the matrix only, which is modeled, using the multiaxial mixed-mode continuum damage model (MMCDM) within GMC. The second utilizes matrix plasticity coupled with brittle final failure based on the maximum principle strain criteria to account for matrix nonlinearity and failure within the Finite Element Analysis--Micromechanics Analysis Code (FEAMAC) software multiscale framework. Both MMCDM and plasticity models incorporate brittle strain- and stress-based failure criteria for the fiber. Upon satisfaction of these criteria, the fiber properties are immediately reduced to a nominal value. The constitutive response for each constituent (fiber and matrix) is characterized using a combination of vendor data and the axial, transverse, and shear responses of unnotched laminates. Then, the capability of the multiscale methodology is assessed by performing blind predictions of the mentioned notched and unnotched composite laminates response under tensile and compressive loading. Tabulated data along with the detailed results (i.e., stress-strain curves as well as damage evolution states at various ratios of strain to failure) for all laminates are presented.

GMC↗

NASA NTRS2014

A Technique for Mapping Characteristic Lengths to Preserve Energy Dissipated via Strain Softening in a Multiscale Analysis

It is often advantageous to account for the microstructure of the material directly using multiscale modeling. For computational tractability, an idealized repeating unit cell (RUC) is used to capture all of the pertinent features of the microstructure. Typically, the RUC is dimensionless and depends only on the relative volume fractions of the different phases in the material. This works well for non-linear and inelastic behavior exhibiting a positive-definite constitutive response. Although, once the material exhibits strain softening, or localization, a mesh objective failure theories, such as smeared fracture theories, nodal and element enrichment theories (XFEM), cohesive elements or virtual crack closure technique (VCCT), can be utilized at the microscale, but the dimensions of the RUC must then be defined. One major challenge in multiscale progressive damage modeling is relating the characteristic lengths across the scales in order to preserve the energy that is dissipated via localization at the microscale. If there is no effort to relate the size of the macroscale element to the microscale RUC, then the energy that is dissipated will remain mesh dependent at the macroscale, even if it is regularized at the microscale. Here, a technique for mapping characteristic lengths across the scales is proposed. The RUC will be modeled using the generalized method of cells (GMC) micromechanics theory, and local failure in the matrix constituent subcells will be modeled using the crack band theory. The subcell characteristic lengths used in the crack band calculations will be mapped to the macroscale finite element in order to regularize the local energy in a manner consistent with the global length scale. Examples will be provided with and without the regularization, and they will be compared to a baseline case where the size and shape of the element and RUC are coincident (ensuring energy is preserved across the scales).

softening↗

NASA NTRS2018

Integration of Information Management System, Workflow and Computational Tools Enabling Multiscale Modeling Within an ICME Paradigm

With the increased emphasis on reducing the cost and time to market of new materials, the need for analytical tools that enable the virtual design and optimization of materials throughout their processing - internal structure - property - performance envelope, along with the capturing and storing of the associated material and model information across its lifecycle, has become critical. This need is also fueled by the demands for higher efficiency in material testing; consistency, quality and traceability of data; product design; engineering analysis; as well as control of access to proprietary or sensitive information. Fortunately, material information management systems and physics-based multiscale modeling methods have kept pace with the growing user demands. Herein, recent efforts to develop a set of Python functions that exchange information between NASA GRC's Integrated multiscale Micromechanics Analysis Code (ImMAC) software toolset and its Integrated Computational Materials Engineering (ICME), Granta MI® database schema is presented. The goal is to enable seamless coupling between both test data and simulation data, which is captured and tracked automatically within Granta MI®, with full model pedigree information. These tools, and this type of linkage, are foundational to realizing the full potential of ICME, in which materials processing, microstructure, properties, and performance are coupled to enable application-driven design and optimization of materials and structures.

multiscale modeling; Micromechanics; Computational↗

NASA NTRS2018

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

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 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 talk will describe the findings of this 2040 Vision study (e.g., the 2040 vision state; the required interdependent core technical work areas, Key Element (KE); associated critical gaps and actions to close those gaps; and major recommendations). This roadmap is a community consensus document and is a result of over 450 professionals input obtain via: i) four society workshops (AIAA, NAFEMS, and two TMS), ii) community-wide survey, and iii) the establishment of 9 expert panels (one per key element) consisting on average 10 non-team members from academia, government and industry to review, update content, and prioritize gaps and actions. It is NASA's hope and desire that this roadmap 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.

Multiscale Modeling↗

NASA NTRSDate not supplied

An Integrated Recursive Framework for Arbitrarily Multiscale and Multi-fidelity Modeling

The NASA Multiscale Analysis Tool (NAMSAT) serves as a state-of-the-art, “plug and play,” massively multiscale modeling (M3) platform for hierarchical materials and structures. The development of NASMAT has focused on modularity, upgradability and maintainability, interoperability, and utility. Application Program Interfaces (APIs) have been developed to facilitate the integration NASMAT into other programs (commercial, research, and user-defined) as well as the integration of other codes into NASMAT. NASMAT is an integrated, recursive platform that seamlessly allows for an arbitrary number of scales, and a variety of modeling fidelity, in a single, non-linear analysis. Thus, the macroscopic response of a material can be directly linked to the behavior of the microstructure(s), including subscale defects, making it a suitable tool for integrated computational materials engineering (ICME) because . Examples using NASMAT for simulation of polycrystalline metals at elevated temperatures will be presented.

Multiscale Modeling↗

NASA NTRSDate not supplied

Multiscale Modeling of the Uptake of Hydrogen Chloride on Anodized Aluminum in Relevance to Spacecraft Fire Safety

Fire safety is a critical component of space missions. An electrical fire within the spacecraft often produces gaseous hydrogen chloride (HCl) from the smoldering of wire insulation. These gases tend to stick to the interior materials of the spacecraft, which is often comprised of treated aluminum. Determining the rate of uptake for HCl by aluminum helps the safe design of the spacecraft to reduce catastrophic mission risk. Our previous studies showed that a one-step global reaction model for adsorption of HCl on aluminum is incapable of predicting the experimentally measured HCl uptake of anodized aluminum, compared to other treatments with thinner oxide layers. X-ray photoelectron spectroscopy revealed that aluminum chloride is found deep in the oxide layer of the anodized aluminum, implying that the transport of HCl within the oxide layer covering the aluminum surface must be considered. This work uses a multiscale modeling approach to predict the uptake of HCl. A pore model is developed wherein the HCl reacts with the aluminum oxide pore walls to create an aluminum chloride layer. The HCl then diffuses through that layer for further reaction, until the diffusion resistance grows too large, and the surface is said to be saturated. The pore model is then coupled with the reactor-scale model to predict overall HCl uptake. Results show that this new multiscale approach predicts the uptake of HCl far more accurately than previously used single-scale models.

Modeling↗

NASA NTRSDate not supplied

Estimation of 3D Woven Design Sensitivities Using a Rapid Multiscale Analysis Technique

Highly-refined finite element models of three-dimension (3D) woven composite systems currently require excessive computational demands that limit their use in sensitivity analysis, uncertainty quantification, and optimization. An alternative analysis methodology was developed using the NASA Multiscale Analysis Tool (NASMAT) where multiscale models of a 3D woven composite (including inter-tow matrix voids and constituent failure) can be completed on a single central processing unit(CPU)on the order of ~30 s. To develop inputs and validation data for the NASMAT model, coupon and acid-digesting testing and x-ray computed tomography were performed. The NASMAT inputs were parameterized using a set of 25 input variables and distributions. These inputs were randomly sampled to generate a total of 100,000 NASMAT analyses that could be used to understand the influence of different material and geometric properties on the warp and weft-direction stiffness and strength. These analyses (including pre/post-processing) were performed in less than eight hours on a 120 CPU cluster. The computational efficiency of the NASMAT model enabled a sensitivity analysis to be performed, and dominant input variables were able to be identified. Key results were consistent with theoretical and experimental observations for the specific 3D woven system studied in this work.

NASMAT↗

NASA NTRSDate not supplied

A Partitioned - Task Parallel Implementation of the NASA Multiscale Analysis Tool for High Performance Computing

The NASA Multiscale Analysis Tool (NASMAT) is a platform for multiscale modeling of composites which can perform analysis of materials with any arbitrary number of length scales. The platform supports modularity, scalability, and interoperability using recursive procedures and data structures. A Macro solver driven parallelization scheme often limits the capability of NASMAT to scale as it has access to limited memory and number of cores (often one core/thread) and often forces to implement macro solver specific changes to the platform. In this work, a partitioned task-parallel approach is adopted, where the parallelization strategy adopted for NASMAT is independent of the macro solver and the computational resources are managed independently. The programming architecture takes into account the hierarchy of multiple scales (task-dependence) and the heterogeneous nature (dynamic load balancing) of computation through implementation of a hierarchy-informed task parallel model. The partitioned nature of the framework further extends the “plug and play” capability of NASMAT. preCICE, an open-source library for coupling multiphysics solver in a partitioned manner, is adopted to integrate NASMAT with an external macro solver by implementing a NASMAT adapter for preCICE. Speedup and scalability of the framework is studied for micromechanical models of varying size.

task-parallel↗

NASA NTRSDate not supplied

Estimation of 3D Woven Design Sensitivities Using a Rapid Multiscale Analysis Technique

Highly-refined finite element models of three-dimension (3D) woven composite systems currently require excessive computational demands that limit their use in sensitivity analysis, uncertainty quantification, and optimization. An alternative analysis methodology was developed using the NASA Multiscale Analysis Tool (NASMAT) where multiscale models of a 3D woven composite (including inter-tow matrix voids and constituent failure) can be completed on a single central processing unit (CPU) on the order of ~30s. To develop inputs and validation data for the NASMAT model, coupon and acid-digesting testing and x-ray computed tomography were performed. The NASMAT inputs were parameterized using a set of 25 input variables and distributions. These inputs were randomly sampled to generate a total of 100,000 NASMAT analyses that could be used to understand the influence of different material and geometric properties on the warp and weft-direction stiffness and strength. These analyses (including pre/post-processing) were performed in less than eight hours on a 120 CPU cluster. The computational efficiency of the NASMAT model enabled a sensitivity analysis to be performed, and dominant input variables were able to be identified. Key results were consistent with theoretical and experimental observations for the specific 3D woven system studied in this work.

NASMAT↗

NASA NTRS2022

Multiscale Progressive Failure Analysis of 3D Woven Composites

Application of three-dimensional (3D) woven composites is growing as an alternative to the use of ply-based composite materials. However, the design, analysis, modeling, and optimization of these materials is more challenging due to their complex and inherently multiscale geometries. Herein, a multiscale modeling procedure, based on efficient, semi-analytical micromechanical theories rather than the traditional finite element approach, is presented and applied to a 3D woven carbon–epoxy composite. A crack-band progressive damage model was employed for the matrix constituent to capture the globally observed nonlinear response. Realistic microstructural dimensions and tow-fiber volume fractions were determined from detailed X-ray computed tomography (CT) and scanning electron microscopy data. Pre-existing binder-tow disbonds and weft-tow waviness, observed in X-ray CT scans of the composite, were also included in the model. The results were compared with experimental data for the in-plane tensile and shear behavior of the composite. The tensile predictions exhibited good correlations with the test data. While the model was able to capture the less brittle nature of the in-plane shear response, quantitative measures were underpredicted to some degree.

3D woven composites↗

NASA NTRS2026

Thermoplastic Matrix Composite Design for Cryotanks Using Multiscale Modeling and Bayesian Optimization

Designing lightweight, robust cryogenic storage tanks is critical for future launch vehicles, in-space propellant storage, and hydrogen powered aircraft. This work presents a multiscale modeling and Bayesian optimization framework for the design of thermoplastic matrix composite cryotanks. Molecular dynamics simulations are first used to determine temperature-dependent constituent properties for candidate thermoplastic matrices, which are homogenized to the lamina scale using NASA’s Multiscale Analysis Tool (NASMAT). These lamina properties, in combination with laminate family generation rules, are evaluated in HyperX structural optimization software to identify stacking sequences that meet all cryogenic load requirements. A Bayesian optimization framework is applied, with HyperX in the loop (via the HyperX API) to efficiently search across material and laminate design variables, yielding an optimized cryotank configuration with significant reductions in design cycle time compared to exhaustive search approaches.

thermoplastics↗