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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Parametrizations of the spin density matrix

Highlights: • Proposed two methods for parametrizing the SDM of spinning, unstable particles. • All non-negativity conditions fulfilled; adaptability to various constraints. • First method: based on a theorem; applicable in a simple and flexible way. • Second method: particularly suitable for especial conditions. • Applications: two of them interesting in the search for new physics. We propose for the spin density matrix two parametrizations which automatically fulfill the non-negativity conditions, without setting any bound on the parameters. The first one relies on a theorem, that we prove, and it is rather simple and easily adaptable to some specific reactions, where, for example, parity is conserved or angular momentum conservation entails selection rules. Moreover, in the case when the rank is less than the order of the density matrix, we show how to improve the fits to the data, either by implementing previous suggestions, or by elaborating an alternative method, for which we prove a second theorem. Our second parametrization is a variant of previous treatments, it appears suitable for some particular processes. Moreover, we discuss about the possibility of inferring the elements of the density matrix from the differential decay width. Last, we illustrate various examples of current interest, both in strong and weak decays; some of them may be helpful in the investigation of physics beyond the standard model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A mean field homogenization model for the mechanical response of ceramic matrix composites

SiC/SiC composites offer exceptional mechanical stability at high temperatures and under irradiation. These ceramic matrix composites are therefore strong candidate materials for future nuclear energy applications. Their mechanical response, which exhibits pseudo-plasticity, is mediated by matrix cracking, fiber debonding, and fiber pull-out due to slip. Here, this study introduces a mechanistic model for the behavior of unidirectionally reinforced SiC/SiC composites. Specifically a mean field homogenization approach is proposed to account for all deformation and degradation modes during mechanical deformation. The homogenization scheme relies on a Mori Tanaka method that is extended to consider the effects of the coating’s elasto-plastic response on the development of micromechanical fields. Further, the model proposed introduces a method to effectively account for the role of localized damage (i.e., cracks) on mechanical fields within both the fiber and the matrix. Upon validating the model against experimental data, the roles of interface sliding, coating dimensions and intrinsic elastic response, as well as of microstructure (e.g. porosity, fiber volume fraction) are discussed.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

On the interactions between molten aluminum and high entropy alloy particles during aluminum matrix composite processing

The feasibility of adding AlCrTiV high entropy alloy (HEA) particles to molten aluminum to make metal matrix composites was studied. Equiatomic AlCrTiV HEA particles, produced by a solid state reduction process, were dispersed into pure aluminum and 7075 alloy (Al-5.8Zn-2.3Mg-1.4Cu, all weight %) melt and by a ultrasonic dispenser. It was found that the AlCrTiV particles reacted with molten aluminum, leading to the formation of Al 45 (Cr,V) 7 and Al 3 Ti intermetallic phases in the aluminum matrix composites. Although the AlCrTiV HEA particles did not survive in molten aluminum during composite processing, the final composite materials showed significantly improved mechanical properties, due to grain refinement and dispersion strengthening. Finally, the research suggests that the interactions between matrix aluminum alloys and the particles are key in controlling the final microstructure and properties of the composites.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Flow and transport in three-dimensional discrete fracture matrix models using mimetic finite difference on a conforming multi-dimensional mesh

Here, we present a comprehensive workflow to simulate single-phase flow and transport in fractured porous media using the discrete fracture matrix approach. The workflow has three primary parts: (1) a method for conforming mesh generation of and around a three-dimensional fracture network, (2) the discretization of the governing equations using a second-order mimetic finite difference method, and (3) implementation of numerical methods for high-performance computing environments. A method to create a conforming Delaunay tetrahedralization of the volume surrounding the fracture network, where the triangular cells of the fracture mesh are faces in the volume mesh, that addresses pathological cases which commonly arise and degrade mesh quality is also provided. Our open-source subsurface simulator uses a hierarchy of process kernels (one kernel per physical process) that allows for both strong and weak coupling of the fracture and matrix domains. We provide verification tests based on analytic solutions for flow and transport, as well as numerical convergence. We also provide multiple expositions of the method in complex fracture networks. In the first example, we demonstrate that the method is robust by considering two scenarios where the fracture network acts as a barrier to flow, as the primary pathway, or offers the same resistance as the surrounding matrix. In the second test, flow and transport through a three-dimensional stochastically generated network containing 257 fractures is presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Determination of preferential binder oxidation in HTGR matrix material subjected to high temperature steam

Graphitic matrix material encapsulates tristructural isotropic (TRISO) coated fuel particles and is a structural component for both pebble and cylindrical fuel compacts in high temperature gas reactor (HTGR) designs. In an off-normal event involving steam exposure, the matrix material is exposed to oxidants, leading to degradation of the fuel compact and subsequent exposure of the TRISO particle fuel to oxidizing species. This study presents microstructural characterization of matrix material after exposure to high temperature (1200°C), 48 kPa steam in which the evolved microstructure demonstrated nonuniform degradation. Subsequent Raman spectroscopy determined the nature of the remaining material post-exposure. Finally, the electron microscopy characterization suggests and Raman spectroscopic analysis confirms, under off-normal conditions, the carbonized phenolic resin binder is preferentially oxidized ahead of the graphite flake filler and is responsible for the nonuniform degradation and enhanced depth of attack.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Organic Matrix Derived from Host–Microbe Interplay Contributes to Pathological Renal Biomineralization

Matrix stones are a rare form of kidney stones. They feature a high percentage of hydrogel-like organic matter, and their formation is closely associated with urinary tract infections. Herein, comprehensive materials and biochemical approaches were taken to map the organic-inorganic interface and gather insights into the host-microbe interplay in pathological renal biomineralization. Surgically extracted soft and slimy matrix stones were examined using micro-X-ray computed tomography and various microspectroscopy techniques. Higher-mineral-density laminae were positive for calcium-bound Alizarin red. Lower-mineral-density laminae revealed periodic acid-Schiff-positive organic filamentous networks of varied thickness. These organic filamentous networks, which featured a high polysaccharide content, were enriched with zinc, carbon, and sulfur elements. Neutrophil extracellular traps (NETs) along with immune response-related proteins, including calprotectin, myeloperoxidase, CD63, and CD86, also were identified in the filamentous networks. Expressions of NETs and upregulation of polysaccharide-rich mucin secretion are proposed as a part of the host immune defense to "trap" pathogens. These host-microbe derived organic matrices can facilitate heterogeneous nucleation and precipitation of inorganic particulates, resulting in macroscale aggregates known as "matrix stones". These insights into the plausible aggregation of constituents through host-microbe interplay underscore the unique "double-edged sword" effect of the host immune response to pathogens and the resulting renal biominerals.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Ceramic Composite Inert Matrix Fuel Forms in High-Temperature Gas-Cooled Microreactors

Here, this work optimizes micro-prismatic high-temperature gas reactor (HTGR) designs to reduce the energy-normalized mass of spent nuclear fuel (SNF) and high-level waste (HLW) produced. The optimization was performed for the current graphite moderator and an inert matrix fuel (IMF) concept employing different composite moderators in a prismatic design architecture. The fuel matrix is magnesium oxide (MgO) with entrained tristructural-isotropic (TRISO) fuel. The moderator materials, including beryllium oxide (MgO-BeO) and beryllium (MgO-Be) at 40 vol % loading and yttrium hydride (MgO-YH x=1.9 ) and zirconium hydride (MgO-ZrH x=1.9 ) at 15 vol % loading, were entrained within the MgO host matrix. A generic graphite micro-prismatic HTGR is used as the baseline point design where the external dimensions are held constant. The composite moderator designs use 19.9% enriched uranium nitride TRISO fuel and hexagonal assemblies. For each IMF concept, an optimization study was performed to maximize the discharge burnup of the fuel by varying the TRISO packing fraction and the lattice pitch of the assemblies. The mass of SNF and HLW, other waste metrics, fuel cost, environmental impact metrics, and the activity of the SNF and HLW at 100 years and 100 000 years were calculated for the optimized IMF and graphite reference designs. The IMF results were subsequently compared to those of the graphite reference and the values for a light water reactor (LWR) and a small modular LWR. For the SNF and HLW, all the IMF concepts and the graphite reference produced less waste compared to the traditional LWR designs. However, the IMF concepts outperformed the graphite reference regarding the mass of SNF and HLW. For the other waste metrics, the IMF concepts showed reductions in fuel cost with improved environmental metrics relative to the graphite reference. Overall, the IMF concepts significantly reduced the SNF and HLW produced per unit of energy generated compared to traditional LWR designs.

TRISO↗
DOE OSTI2022

Dynamic Matrix Completion Based State Estimation in Distribution Grids

The power distribution network is undergoing tremendous transformation due to an increase in the penetration of renewable energy resources and electric vehicles. These changes have resulted in greater uncertainty and dynamics in the distribution grid states. Therefore, the ability to track and monitor system states has become a critical need for accurate and timely control actions. In this paper, we propose two dynamic sparsity-based state estimation approaches for distribution systems: (1) locally weighted matrix completion (LW-MC) and (2) Bayesian matrix completion with Kalman filter prediction (BMC-KF). The performance of the proposed dynamic state estimation strategies is compared with the classic/static matrix completion (static-MC) approach using the IEEE 37 and IEEE 123 bus test systems. Finally, results indicate that BMC-KF approach outperforms both LW-MC as well as static-MC even when 30% of the measurement data is available. Computational complexity associated with both approaches is quantified.

42 ENGINEERING↗
DOE OSTI2022

Probing for the Trace Estimation of a Permuted Matrix Inverse Corresponding to a Lattice Displacement

We report thatpProbing is a general technique that is used to reduce the variance of the Hutchinson stochastic estimator for the trace of the inverse of a large, sparse matrix A. The variance of the estimator is the sum of the squares of the off-diagonal elements of A -1 . Therefore, this technique computes probing vectors that when used in the estimator annihilate the largest off-diagonal elements. For matrices that display decay of the magnitude of |A$^{-1}_{ij}$| with the graph distance between nodes i and j, this is achieved through graph coloring of increasing powers A k . Equivalently, when a matrix stems from a lattice discretization, it is computationally beneficial to find a distance-k coloring of the lattice. Previously, a hierarchical coloring was proposed so that k can be increased at runtime as needed without discarding previous work. In this work, we study probing for the more general problem of computing the trace of a permutation of A -1 , say PA -1 . The motivation comes from lattice quantum chromodynamics (QCD), where we need to construct “disconnected diagrams” to extract flavor-separated generalized parton functions. In lattice QCD, where the matrix has a four-dimensional toroidal lattice structure, these nonlocal operators correspond to a PA -1 , where P is the permutation relating to some displacement $\vec{p}$ in one or more dimensions. We focus on a single dimension displacement (p), but our methods are general. We show that probing on A k or (PA) k does not annihilate the largest magnitude elements. To resolve this issue, our displacement-based probing works on PA k using a new coloring scheme that works directly on appropriately displaced neighborhoods on the lattice. We prove lower bounds on the number of colors needed and study the effect of this scheme on variance reduction, both theoretically and experimentally on a real-world lattice QCD calculation. We achieve orders of magnitude speedup over the unprobed or the naively probed methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Matrix-Free High-Performance Saddle-Point Solvers for High-Order Problems in \(\boldsymbol{H}(\operatorname{\textbf{div}})\)

Here, this work describes the development of matrix-free GPU-accelerated solvers for high-order finite element problems in H(div). The solvers are applicable to grad-div and Darcy problems in saddle-point formulation, and have applications in radiation diffusion and porous media flow problems, among others. Using the interpolation–histopolation basis, efficient matrix-free preconditioners can be constructed for the (1, 1)-block and Schur complement of the block system. With these approximations, block-preconditioned MINRES converges in a number of iterations that is independent of the mesh size and polynomial degree. The approximate Schur complement takes the form of an M-matrix graph Laplacian and therefore can be well-preconditioned by highly scalable algebraic multigrid methods. High-performance GPU-accelerated algorithms for all components of the solution algorithm are developed, discussed, and benchmarked. Numerical results are presented on a number of challenging test cases, including the “crooked pipe” grad-div problem, the SPE10 reservoir modeling benchmark problem, and a nonlinear radiation diffusion test case.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

T -matrix analysis of static Wilson line correlators from lattice QCD at finite temperature

Here, we utilize a previously constructed thermodynamic T -matrix approach to the quark-gluon plasma (QGP) to derive constaints on its input by using results on Wilson line correlators (WLCs) of a static quark-antiquark pair from 2 + 1-flavor lattice-QCD (lQCD) computations with realistic pion mass. The self-consistent T -matrix results, which include previous constraints from the lQCD equation of state in the light-parton sector, can describe the lQCD data for WLCs fairly well once refinements of its driving kernel are applied. In particular, the input potential requires less screening than what has been inferred from previous T-matrix analyses. Pertinent predictions for the spectral and transport properties of the QGP are discussed, including the spatial diffusion coefficient for heavy quarks; the latter turns out to have a rather weak temperature dependence, in approximate agreement with recent unquenched lQCD results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Particle interspacing effects on the mechanical behavior of a Fe–TiB 2 metal matrix composite using FFT-based mesoscopic field dislocation mechanics

This paper presents an application to metal matrix composites (MMCs) of an enhanced elasto-viscoplastic Fast Fourier Transform (EVP-FFT) formulation coupled with a phenomenological continuum Mesoscale Field Dislocation Mechanics (MFDM) theory. Contrary to conventional crystal plasticity, which only accounts for plastic flow and hardening induced by statistically stored dislocations (SSDs), MFDM-EVP-FFT also describes the evolution of polarized geometrically necessary dislocation (GND) density and its effect on both plastic flow and hardening. Numerical results for a Fe–TiB 2 MMC made of a ferrite matrix (α-Fe) and elastic ceramic particles (TiB 2 ) are presented. Full-field simulations are performed using synthetic periodic unit cells representative of the MMC, with single-crystalline and polycrystalline matrix, for different particle interspacing distances. A strong dependence of the predicted equivalent stress, cumulated plastic strain and GND density fields with particle interspacing distance is observed, in contrast with conventional crystal plasticity. Correlations between these mechanical fields and microstructural features, and their influence on local and global mechanical behavior are examined for the different MMC microstructures.

42 ENGINEERING↗
DOE OSTI2025

Sempervirens: A Fast Reconstruction Algorithm for Noisy and Incomplete Binary Matrix Representations of Trees

Applications such as reconstructing cell lineage trees (represented as phylogenetic trees) from single-cell sequencing data require reconstructing a {0,1}-matrix that has many errors and missing entries. We introduce Sempervirens, a very fast matrix reconstruction algorithm for noisy and incomplete matrix representations of phylogenetic trees. Sempervirens uses an iterative maximum-likelihood approach to determine the topology tree represented by the corrupted data. We show that Sempervirens is at least three orders of magnitude faster than other methods on thousand by thousand matrices, with the speed gap widening with larger matrices. We also show that Sempervirens matches state-of-the-art methods in reconstruction accuracy. The speed of Sempervirens enables it to be tractably applied to reconstructing much larger matrices than those that other methods can reconstruct. In addition to experimental results, we justify the algorithm with a mathematical treatment of its subprocedures.

algorithms↗
DOE OSTI2021

Measurement of Fission Product Concentration Profiles in AGR-3/4 TRISO Fuel Graphitic Matrix and Nuclear Graphites

The third Advanced Gas Reactor (AGR) irradiation experiment, AGR-3/4, was designed to investigate the migration of fission products in fuel compact graphitic matrix and reactor graphite components. Using destructive methods, radial fission product concentration profiles were measured for gamma-emitting fission products (e.g., Ag-110m, Cs-134, and Eu-154) and beta-emitting Sr-90 in irradiated graphitic and graphite components from six different AGR-3/4 irradiation capsules. These new measured concentration profiles can now be compared to non-destructive measurements and fission product transport simulations and will be used to derive new diffusivities and sorptivities to support refinement of fission product transport models and high-temperature gas-cooled reactor (HTGR) source-term analyses. Each capsule in the AGR-3/4 experiment had four fuel compacts in the middle of two concentric rings of graphitic matrix material, PCEA graphite, or IG-110 graphite. In addition to the approximately 1898 tristructural isotropic (TRISO) coated particles in each compact, there were 20 designed to fail (DTF) particles coated only in pyrocarbon so that they released fission products into the surrounding cylindrical rings of carbonaceous materials. Destructive sampling of the rings involved machining/milling material from around the circumference of the rings, collecting that material, and performing radiochemical analyses on it. Milling operations were performed in multiple steps or segments, and each segment was generally 0.508 mm (0.020 in) thick. Knowing the radial position at which each segment was milled, the volume of the milled material at each segment, and the fission product content in each segment, the radial fission product concentrations were constructed for select isotopes in each ring. Ag-110m profiles had the most variation. Some profiles were peaked at an inner or outer surface. Some were peaked at the middle of the ring wall thickness. Some increased radially outward, and some decreased radially outward. These types of variations and the fact that the measured profiles do not generally compare favorably with the transport model employed for AGR-3/4 may adversely impact the ability to extract reasonable transport parameters for this isotope. In many cases, the Cs-134 profiles decreased somewhat linearly in the outward radial direction, and in cursory comparisons, the shapes of these profiles appeared similar to those from model predictions. The step changes in concentration across the inner-outer ring gap were generally consistent with the model predictions as well. In some cases, there were local maxima in concentration at the outer surface of the rings. This suggests that fission products could have transported in the small gaps between the inner ring and the outer ring and between the outer ring and the sink ring such that some portion of a given fission product can bypass diffusion through the ring itself. The analysis of the small nubs on the outer surfaces of some of the outer rings revealed fission product concentrations in the nubs that were often higher than in the outermost segments of the rings. This further supports the hypothesis that short-circuit, gap transport occurred, causing relatively high surface concentrations on the outer surfaces of the rings. Eu-154 and Sr-90 profiles tend to have very similar shapes, suggesting that they transport via the same mechanisms. The observed profiles were indicative of a transport process where the isotopes are sorbed on the inner surface of the ring, but diffusion into the ring from that surface is quite slow. Some elevated concentrations of Sr-90 (relative to Eu-154) on the outer surface of a ring suggested that rapid, gas-gap transport of gaseous precursor Kr-90 and volatile Rb-90 could have occurred prior to their decaying to Sr-90. Overall, the Eu 154 and Sr-90 profiles were still very similar, which indicates that the transport of short-lived Sr-90 precursors is not a major effect. In some capsules, the qualitative Sr-90 behavior across the ring gaps was consistent with the model (using the available legacy Sr-90 transport parameters), but in other capsules the model was inconsistent with the measurements and seems to underestimate the amount of Sr-90 in the outer rings. The total ring Sr-90 inventories were estimated for all the rings that were subject to physical sampling. These results will be used to adjust the predicted particle and/or compact releases used in the AGR-3/4 fission product transport model. Given the different irradiation temperatures among the capsules and the rings, it was not possible to discern fundamental differences in the transport of isotopes within the different carbon materials, i.e., graphitic matrix, IG-110, or PCEA. It may be possible to do this in the course of determining transport from the concentration profiles in future work.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

Guanidinium-Assisted Surface Matrix Engineering for Highly Efficient Perovskite Quantum Dot Photovoltaics

Metal halide perovskite quantum dots (Pe-QDs) are of great interest in new-generation photovoltaics (PVs). However, it remains challenging in the construction of conductive and intact Pe-QD films to maximize their functionality. Herein, a ligand-assisted surface matrix strategy to engineer the surface and packing states of Pe-QD solids is demonstrated by a mild thermal annealing treatment after ligand exchange processing (referred to as “LE-TA”) triggered by guanidinium thiocyanate. The “LE-TA” method induces the formation of surface matrix on CsPbI 3 QDs, which is dominated by the cationic guanidinium (GA+) rather than the SCN-, maintaining the intact cubic structure and facilitating interparticle electrical interaction of QD solids. Consequently, the GA-matrix-confined CsPbI 3 QDs exhibit remarkably enhanced charge mobility and carrier diffusion length compared to control ones, leading to a champion power conversion efficiency of 15.21% when assembled in PVs, which is one of the highest among all Pe-QD solar cells. Additionally, the “LE-TA” method shows similar effects when applied to other Pe-QD PV systems like CsPbBr 3 and FAPbI 3 (FA = formamidinium), indicating its versatility in regulating the surfaces of various Pe-QDs. This work may afford new guidelines to construct electrically conductive and structurally intact Pe-QD solids for efficient optoelectronic devices.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Control of Host-Matrix Morphology Enables Efficient Deep-Blue Organic Light-Emitting Devices

Mixing a sterically bulky, electron-transporting host material into a conventional single host–guest emissive layer is demonstrated to suppress phase separation of the host matrix while increasing the efficiency and operational lifetime of deep-blue phosphorescent organic light-emitting diodes (PHOLEDs) with chromaticity coordinates of (0.14, 0.15). Here, the bulky host enables homogenous mixing of the molecules comprising the emissive layer while suppressing single host aggregation; a significant loss channel of nonradiative recombination. By controlling the amorphous phase of the host-matrix morphology, the mixed-host device achieves a significant reduction in nonradiative exciton decay, resulting in 120 ± 6% increase in external quantum efficiency relative to an analogous, single-host device. In contrast to single host PHOLEDs where electrons are transported by the host and holes by the dopants, both charge carriers are conducted by the mixed host, reducing the probability of exciton annihilation, thereby doubling of the deep-blue PHOLED operational lifetime. These findings demonstrate that the host matrix morphology affects almost every aspect of PHOLED performance.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Changes in rock matrix compressibility during deep CO 2 storage

Geologic carbon storage projects aim to permanently trap large volumes of CO 2 in reservoir rock sealed with low permeability layers. As high-pressure supercritical or liquid CO 2 is injected, hydromechanical and chemical processes caused by the reaction between the rock and acidic mixture of brine and CO 2 are initiated. The compressibility of reservoir rock needs to be properly characterized in order to assess the deformation and stability of the host formations, and there are a number of factors to be considered, including the matrix structure, solid, pores, and fluid. Here this study triggers from a fundamental question whether CO 2 treatment affects the compressibility of the rock matrix and its dominant composing solid minerals. Three different reservoir representatives are selected: Berea sandstone for silica-rich rock, and Apulian limestone and Indiana limestone for calcite-rich rock. Quartz and calcite are the main composing minerals of the reservoir rock, and their crystals are separately examined. Experimental methods are introduced for high-pressure CO 2 treatment of water-saturated materials, and measurements of the unjacketed and solid compressibilities are conducted. No change in the solid compressibility of the sandstone and quartz after CO 2 treatment is observed, whereas it increases by 18–21% for the limestones and by 15% for calcite. The latter observation is inconsistent with the ultrasonic wave velocities measurements and is believed to be due to the local dissolution of the calcite crystal surface. Our results show that only the solid matrix of the limestones becomes more compressible after CO 2 treatment. Consequent microimaging and mercury intrusion porosimetry analyses allowed observations of dissolution and precipitation of calcite, and creation of new connected and non-connected pores. Finally, the changes in limestone solid compressibilities and pore structure could significantly affect the rock properties and behavior during and after CO 2 injection and should be accounted for in the reservoir models.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Accelerating structural dynamics simulations with localised phenomena through matrix compression and projection‐based model order reduction

In this work, a novel approach is introduced for accelerating the solution of structural dynamics problems in the presence of localised phenomena, such as cracks. For this category of problems, conventional projection-based Model Order Reduction (MOR) methods are either limited with respect to the range of system configurations that can be represented or require frequent solutions of the Full Order Model (FOM) to update the low-dimensional spaces, in which solutions are represented. In the proposed approach, low-dimensional spaces, constructed for the healthy structure, are enriched with appropriately selected columns of the flexibility matrix of the system. It can be shown that these spaces contain the solution to the original problem for the static case, while their dimension is much smaller. In order to allow their online construction for arbitrary localised features, the full flexibility matrix of the system should be available. To this end, a hierarchical representation is used for the matrices involved, allowing to compute the flexibility matrix efficiently and with reduced memory requirements. The resulting method offers significant speedups, without sacrificing the flexibility and accuracy of the full order model. The performance and limitations of the approach are studied through a series of examples in structural dynamics.

fracture mechanics↗