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At least 433 records · Page 24

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DOE OSTI2024

Ion-Depleted Microenvironments During Lithium Deposition Revealed by Operando Freezing Cryogenic Electron Microscopy

Local structures and chemistry at active electrochemical interfaces are critical to determining safety, lifetime, and energy density in lithium metal batteries and other devices, but they are challenging to characterize at the nanoscale. We address this issue by developing operando freezing cryogenic electron microscopy (cryo-EM) to preserve battery interfaces in an active state for subsequent high-resolution characterization. We find that ion-depleted microenvironments form locally in the electrolyte adjacent to the lithium deposition interface in lithium metal batteries and are linked to heterogenous growth morphologies. These depleted environments arise locally even under conditions for which ion depletion is not predicted at steady state; this provides a mechanistic explanation for why dangerous lithium morphologies can still propagate in such systems and lead to thermal runaway. Operando freezing cryo-EM thus provides a method to directly visualize nanoscale heterogeneities that arise locally at electrochemical interfaces and play key roles in device failure.

CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS,E↗

DOE OSTI2020

Gas Production from Hot Water Circulation through Hydraulic Fractures in Methane Hydrate-Bearing Sediments: THC-Coupled Simulation of Production Mechanisms

Methane hydrates, widely found in permafrost and deep marine sediments, have great potential as a future energy 6 source. Conventional production schemes perform poorly for challenging hydrate reservoirs with low permeability. We propose an 7 efficient production scheme by combining hydraulic fracturing from horizontal wells and hot water circulation through fractures. A 8 fully coupled thermo-hydro-chemical (THC) model is developed to simulate the key physical processes during gas production from 9 a hydrate reservoir representative of typical geological settings in Shenhu, South China Sea. We found that the gas production 10 process has two distinct stages divided by thermal breakthrough: a relatively short prebreakthrough stage and a postbreakthrough 11 stage yielding stable gas production. Heat advection along and near the hydraulic fracture dominates the prebreakthrough stage, 12 whereas conduction-driven thermal recovery in the volume around fractures dominates the postbreakthrough stage. We identified 13 that the steady-state injection temperature has a strong effect on the performance of the proposed scheme while the fluid mass 14 circulation rate has a moderate impact beyond a threshold. The proposed scheme proves to be efficient and robust over a range of 15 reservoir conditions with respect to initial hydrate saturation and intrinsic permeability, including their spatial heterogeneities, 16 thereby offering a promising solution for challenging reservoir conditions.

gas hydrate, fracture flow, gas production, numeri↗

DOE OSTI2024

Hourly dynamic line ratings for existing transmission across the contiguous United States (preliminary results) [Slides]

The thermal rating of a transmission line depends on the rate at which heat generated by current flow through the line can be dissipated into the environment by convective and radiative cooling, keeping the conductor below a maximum operating temperature. Static or seasonal line ratings assume nearly-worst-case weather conditions (high ambient air temperature, high solar irradiance, and low wind speed), resulting in a low risk of "overrating" a line (i.e., allowing more current to flow than the line is designed for) but a high fraction of time when the line is "underrated" (i.e., able to flow more current while staying below the maximum temperature). Dynamic transmission line ratings (DLR) use real-time measurements of weather conditions, line sag, or line temperature to determine the thermal rating of transmission lines at hourly or higher time resolution, allowing for increased ratings during some (cold, windy, and/or dark) periods and correcting for overrating during other (hot, calm, and/or sunny) periods. Many studies have explored the benefits of DLR, but typically for small collections of transmission lines under a limited sample of weather conditions, leaving open the question of how widely applicable the benefits of DLR might be over diverse geographies and weather conditions. Here, we combine geospatial data on tens of thousands of transmission line routes across the contiguous United States with high-resolution hourly historical weather data for 2007-2013 to estimate the impact of DLR and other weather-adjusted rating systems. We compare static and dynamic line ratings to intermediate ratings adjusted by ambient temperature, day/night irradiance, clear-sky irradiance, and/or measured irradiance, illustrating the benefits of incorporating progressively more detailed weather data into the calculated line ratings. Moving from nighttime-adjusted ratings to clear-sky-adjusted ratings provides more benefit than moving from clear-sky-adjusted ratings to measured-irradiance-adjusted ratings. Depending on the assumed static windspeed for irradiance-adjusted-ratings, DLR either corrects for overrated hours or provides substantially increased ratings in the majority of hours on the majority of lines.

14 SOLAR ENERGY↗

DOE OSTI2026

Ultra-clear Aerogels for Insulated Glass in Refrigeration Doors (CRADA Final Report)

Display refrigerators commonly employ glass doors to provide product visibility; however, these doors exhibit significantly poorer thermal insulation than solid doors, resulting in increased heat transfer and higher energy consumption. To address this limitation, this project investigated the use of silica aerogel as a transparent insulating medium for refrigerator glass doors, with the objective of enhancing thermal performance without compromising visual clarity. In Phase I of the project, we assessed the feasibility of silica aerogel insulation through laboratory and full-scale studies, including material characterization, durability testing, and heat transfer measurements, along with the development and performance evaluation of prototype glass doors under realistic operating conditions. In Phase II, the project focused on scaling the technology toward practical deployment. This included scaling up the manufacturing process to achieve a surface area roughly 20 times larger for commercial applications, developing full-scale prototypes that integrated silica aerogel into standard display refrigerator doors, and conducting field evaluations to assess thermal performance, energy savings, and operational durability under real-world conditions.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2025

From Theory to Practice: Feasibility Study of a Thermal Microgrid at a DoD Installation

Advanced district thermal energy systems, also known as thermal microgrids, can meet the energy needs of urban districts in a highly efficient way, but adoption of such systems, especially in the United States, has been slow. Thermal microgrids use a network circulating water at near-ambient (60-80 degrees F; 15-25 degrees C) temperatures, and water-source heat pumps at connected buildings are used to boost or lower the temperature for space conditioning and service hot water. Addressing challenges related to retrofits of existing buildings for integration with such systems, as well as quantifying the benefits of different configurations, will be key to accelerating their adoption. This paper aims to contribute to that by reporting preliminary results from a feasibility study of a thermal microgrid at a U.S. Department of Defense installation and illustrating the process of conceptual design to seek the best possible performance within the many constraints of existing buildings. The cluster of buildings under consideration in this study has much in common with commercial buildings in the United States. The process of and results from this feasibility study can inform assessment of the potential for thermal microgrids in other locations and help unlock the benefits of such systems for resilience and energy savings.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2021

Modeling Nanosecond-Pulsed Spark Discharge and Flame Kernel Evolution

Dilute combustion, either using exhaust gas recirculation or with excess air, is considered a promising strategy to improve the thermal efficiency of internal combustion engines. However, the dilute air-fuel mixture, especially under intensified turbulence and high-pressure conditions, poses significant challenges for ignitability and combustion stability, which may limit the attainable efficiency benefits. In-depth knowledge of the flame kernel evolution to stabilize ignition and combustion in a challenging environment is crucial for effective engine development and optimization. To date, a comprehensive understanding of ignition processes that result in the development of fully predictive ignition models usable by the automotive industry does not yet exist. Spark-ignition consists of a wide range of physics that includes electrical discharge, plasma evolution, joule-heating of gas, and flame kernel initiation and growth into a self-sustainable flame. In this study, an advanced approach is proposed to model spark-ignition energy deposition and flame kernel growth. To decouple the flame kernel growth from the electrical discharge, a nanosecond-pulsed high-voltage discharge is used to trigger spark-ignition in an optically accessible small ignition test vessel with a quiescent mixture of air and methane. Initial conditions for the flame kernel, including its thermodynamic state and species composition, are derived from a plasma-chemical equilibrium calculation. The geometric shape and dimension of the kernel are characterized using a multi-dimensional thermal plasma solver. Here, the proposed modeling approach is evaluated using a high-fidelity computational fluid dynamics procedure to compare the simulated flame kernel evolution against flame boundaries from companion Schlieren images.

42 ENGINEERING↗

NASA NTRS1998

Acquisition and Early Losses of Rare Gases from the Deep Earth

Direct observations show that the deep Earth contains rare gases of solar composition distinct from those in the atmosphere. We examine the implications of mantle rare gas characteristics on acquisition of rare gases from the solar nebula and subsequent losses due to a large impact. Deep mantle rare gas concentrations and isotopic compositions can be obtained from a model of transport and distribution of mantle rare gases. This model assumes the lower mantle closed early, while the upper mantle is open to subduction from the atmosphere and mass transfer from the lower mantle. Constraints are derived that can be incorporated into models for terrestrial volatile acquisition: (1) Calculated lower-mantle Xe-isotopic ratios indicate that the fraction of radiogenic Xe produced by I-129 and Pu-244 during the first about 10(exp 8) yr was lost, a conclusion also drawn for atmospheric Xe. Thus, either the Earth was made from materials that had lost >99% of rare gases about (0.7-2) x 10(exp 8) yr after the solar system formed, or gases were then lost from the fully formed Earth. (2) Concentrations of 3He and 20Ne in the lower mantle were established after these losses. (3) Neon-isotopic data indicates that mantle Ne has solar composition. The model allows for solar Ar/Ne and Xe/Ne in the lower mantle if a dominant fraction of upper mantle Ar and Xe are subduction-derived. If Earth formed in the presence of the solar nebula, it could have been melted by accretional energy and the blanketing effect of a massive, nebula-derived atmosphere. Gases from this atmosphere would have been sequestered within the molten Earth by dissolution at the surface and downward mixing. It was found that too much Ne would be dissolved in the Earth unless the atmosphere began to escape when the Earth was only partially assembled. Here we consider conditions required to initially dissolve sufficient rare gases to account for the present lower mantle concentrations after subsequent losses at 10(exp 8) yr. It is assumed that equilibration of the atmosphere with a thoroughly molten mantle was rapid, so that initial abundances of gases retained in any mantle layer reflected surface conditions when the layer solidified. For subsequent gas loss of 99.5% and typical solubility coefficients, a total pressure of 100 atm was required for an atmosphere of solar composition. Calculations of the pressure at the base of a primordial atmosphere indicate that this value might be exceeded by an order of magnitude or more for an atmosphere supported by accretional energy. Surface temperatures of about 4000 K would have been produced, probably high enough to melt the deep mantle. Initial distributions of retained rare gases would then be determined by the history of surface pressure and temperature during mantle cooling and solidification, i.e., the coupled cooling of Earth and atmosphere. The Earth's thermal state was determined by its surface temperature and the efficiency of convection in the molten mantle, estimated to be sufficient to maintain an adiabatic gradient. Because the melting curve is steeper than the adiabat, solidification of the mantle proceeded outward from the interior. Incorporation of atmospheric gases in the mantle therefore occurred over a range in surface temperature of a few thousand degrees Kelvin. The thermal state of the atmosphere was controlled by total luminosity of the Earth (energy) released by accreting planetesimals and the cooling Earth), nebular temperature and pressure, and atmospheric opacity. The energy released by accretion declined with time as did nebular pressure. Analytical solutions for an idealized (constant opacity radiative atmosphere show that declining energy sources under constant nebular conditions result in slowly diminishing surface temperature but dramatically increasing surface pressure. For such an atmosphere with declining nebular pressure but constant total luminosity, surface pressure decreases gradually with decreasing temperaure. A decline in accretion luminosity might be compensated by energy released as the mantle cools for about 10(exp 5) year, after which luminosity must decline. The total complement of dissolved rare gases will depend on the particular evolutionary path determined by the declining accretional luminosity, the Earth thermal history, removal of the nebula, and opacity variations of the atmosphere. Models for these coupled evolutionary histories for Earth's acquisition of nebular-derived noble gases are in progress. The later losses required at about 10(exp 8) yr (depleting the interior concentrations of the sequestered solar gases by a factor of > 100) were presumably related to the major impact in which the Moon formed.

Porcelli, D.↗

DOE OSTI2021

Quantifying Turbine-Level Risk to Golden Eagles Using a High-Fidelity Updraft Model and a Stochastic Behavioral Model

To minimize the effects of wind farms on Golden Eagle (Aquila chrysaetos) populations while enabling sustainable development of renewable energy resources, it is important to understand how eagles interact with atmospheric flows, terrain features, and anthropogenic structures. Models that predict migratory flight paths provide one tool that helps us grasp how the location of wind farms may influence interactions and impacts on migrating Golden Eagles. The current state-of-the-art in predicting migratory flight paths uses a deterministic fluid-flow analogy to predict eagle trajectory using only an orographic updraft potential computed from topographical features. This model does not take into account variables, such as thermal updrafts and time varying atmospheric conditions that are known to influence migratory behavior. In this work, we improve on the model with the objective of developing tools that advance our understanding of how atmospheric flows and terrain features affect migratory eagle behavior and their interactions with wind farms. Specifically, we 1) incorporate both orographic and thermal updraft information in simulating eagle flight paths; 2) incorporate stochasticity into eagle travel patterns to better capture the influence of exogenous factors on, and the inherent stochasticity of eagle behavior; 3) consider spatio-temporal atmospheric data at wind-farm-scale when computing updraft potential; and 4) account for how atmospheric conditions and the direction of migration change seasonally and how these changes affect eagle migratory flight behavior. We tested the model using a 50km by 50km region with 50 m resolution in the western United States. We simulated 900 independent, probabilistic eagle tracks during southerly and northerly migration, assuming eagles solely rely on orographic updrafts. The preliminary results indicate that the inclusion of finer resolution atmospheric data allows for the inclusion of realistic conditions that an eagle experiences. The stochasticity in eagle tracks provides a platform to include uncertainty in eagle decision making and help produce robust eagle presence maps. We will deploy updraft and downdraft velocities computed using a high-fidelity, wind farm scale, computational fluid dynamics solver under development at National Renewable Energy Laboratory. This work is a first step in the development of a predictive and generalizable eagle behavior model at the wind farm scale that does not rely on empirical data collection. Although the current model is intended for migratory eagles, we will extend and refine this model to inform the development of additional behavioral modes, including resident eagle behavior. This modeling approach improves our ability to understand eagle use of the landscape at a fine scale, and it is our hope that this work will ultimately help advance strategies that minimize the impact of wind development on Golden Eagle populations.

49 EE - Wind and Water Power Program - Wind (EE-4W↗

DOE OSTI2020

Steady-state off-design modeling of the supercritical carbon dioxide recompression cycle for concentrating solar power applications with two-tank sensible-heat storage

Concentrating solar power researchers are evaluating the potential of the supercritical carbon dioxide recompression cycle to improve the thermal efficiency and decrease the capital costs of next-generation systems. This analysis investigates the steady-state off-design performance of a recompression cycle integrated with two-tank sensible-heat thermal energy storage as the ambient temperature and heat-transfer fluid (HTF) inlet conditions to the cycle change. This paper presents off-design component models and then cycle convergence and control models to maximize net cycle power output while constraining the high-side pressure and air-cooler fan power to their respective design values and fixing the cycle HTF outlet temperature to its design value. Results show that inventory control and air-cooler fan power are important control parameters that can be optimized to maximize off-design power output as the ambient temperature and HTF mass flow rate diverge from design. The high-side pressure and fan power constraints cause the cycle net power to degrade when the ambient temperature is warmer than the design value, and this study calculates a maximum mass flow rate for hot days above which the cycle cannot achieve the design HTF outlet temperature. Finally, the analysis shows that optimizing compressor shaft speeds can improve cold-day performance by around 1.5 percentage points and part-load performance by up to 2.5 percentage points versus a baseline case with no active compressor control.

14 SOLAR ENERGY↗

DOE OSTI2026

Routes to high-performance operation in Wendelstein 7-X: turbulence suppression with shaping of the density profile

Steep density gradients generally lead to improved plasma performance in the neoclassically optimized stellarator W7-X. This is evident in the global energy confinement time as well as in the ion temperature and can be explained by a strong reduction of the ion temperature gradient turbulence. Such conditions can experimentally be realized by several methods: injection of cryogenic hydrogen pellets, appropriate combination of neutral beam and electron cyclotron resonance heating (ECRH) and, in some cases, with low power of ECRH after preconditioning of the first wall. The duration of the improved phases is determined by the ability to sustain the steep density gradient, by technical limitations of the involved systems and, eventually, by the plasma stability. This paper gives an overview of relevant experimental results and presents example discharges where the improved confinement conditions could be extended to multiple seconds: up to 4 s using neutral beam injection and from 14 to 40 s with steady state pellet injection. In these plasmas the turbulent thermal diffusivity is reduced by a factor of 3 to 4 in a broad radial range, which allows high ion temperatures of up to 3 keV at the densities of about 1.5 • 10 20 m −3 .

high performance plasma↗

DOE OSTI2024

Neural simulation-based inference of the neutron star equation of state directly from telescope spectra

Neutron stars provide a unique opportunity to study strongly interacting matter under extreme density conditions. The intricacies of matter inside neutron stars and their equation of state are not directly visible, but determine bulk properties, such as mass and radius, which affect the star's thermal X-ray emissions. However, the telescope spectra of these emissions are also affected by the stellar distance, hydrogen column, and effective surface temperature, which are not always well-constrained. Uncertainties on these nuisance parameters must be accounted for when making a robust estimation of the equation of state. In this study, we develop a novel methodology that, for the first time, can infer the full posterior distribution of both the equation of state and nuisance parameters directly from telescope observations. This method relies on the use of neural likelihood estimation, in which normalizing flows use samples of simulated telescope data to learn the likelihood of the neutron star spectra as a function of these parameters, coupled with Hamiltonian Monte Carlo methods to efficiently sample from the corresponding posterior distribution. Our approach surpasses the accuracy of previous methods, improves the interpretability of the results by providing access to the full posterior distribution, and naturally scales to a growing number of neutron star observations expected in the coming years.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Analysis of the inter-species power balance in JET plasmas

Most auxiliary heating methods provide heating to more than one particle species (electrons, ions, impurities) in a fusion plasma. This can lead to substantial temperature differences between species, depending on conditions such as heating power to the different species and collisionality, with temperature differences between species limited by inter-species thermal equipartition and transport. The analysis of the steady-state electron-ion and impurity-ion power balances presented in this paper are used for consistency-checking experimental ion and electron temperature measurements and for inferring the main ion temperature from measured impurity temperatures. As ion temperature measurements by charge exchange spectroscopy (CXS) based on impurity ions have become more difficult and time-consuming since the installation of the ITER-like wall (ILW) with Be and W PFC's, knowing the maximum sustainable temperature difference between ions and electrons, |T i -T e | allows rejecting erroneous measurements. It also obviates the need for an ion temperature measurement, if an electron temperature measurement is available and |T i - T e | cannot be larger than the combined errors of the underlying measurements. A power balance analysis is also required for estimating the errors of the ion and electron heat fluxes prior to any species-resolved transport analysis. The ion-impurity temperature differences are usually found to be small due to strong thermal equipartition between ion species. However, they can approach 10% in JET-ILW low density, high power discharges, such the ones under development for a future JET deuterium–tritium campaign (Joffrin et al 2019 Nucl. Fusion). This has a generally small, but not always negligible effect on the calculation of fusion reaction rates, which depend on main ion temperatures. An important outcome of this analysis is that temperature differences between impurity species are always much smaller than between the impurities and hydrogenic species and can usually be neglected. The article presents two methods for calculating the impurity-to-main ion temperature ratio. Finally, this analysis leads to a method for the reconstruction ion temperature profiles from ion temperature data available at only one or a small number of spatial locations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1984

Investigation of the relations between neat resin and advanced composite mechanical properties. Volume 1: Results

A detailed evaluation of one untoughened epoxy baseline resin and three toughened epoxy resin systems was performed. The Hercules 3502, 2220-1, and 2220-3, and Ciba-Geigy Fibredux 914 resin systems were supplied in the uncured state by NASA-Langley and cast into thin flat specimens and round dogbone specimens. Tensile and torsional shear measurements were performed at three temperatures and two moisture conditions. Coefficients of thermal expansion and moisture expansion were also measured. Extensive scanning electron microscopic examination of fracture surfaces was performed, to permit the correlation of observed failure modes with the environmental conditions under which the various specimens were tested. A micromechanics analysis was used to predict the unidirectional composite response under the various test conditions, using the neat resin experimental results as the required input data. Mechanical and physical test results, the scanning electron microscope observations, and the analytical predictions were then correlated.

Zimmerman, R. S.↗

NASA NTRS1984

Investigation of the relations between resin and advanced composite mechanical properties. Volume 2: Appendices

One untoughened epoxy baseline resin and three toughened epoxy resin systems were evaluated. The Hercules 3502, 2220-1, and 2220-3, and Ciba-Geigy Fibredux 914 resin systems were supplied in the uncured state by NASA-Langley and cast into thin flat specimens and round dogbone specimens. Tensile and torsional shear measurements were performed at three temperatures and two moisture conditions. Coefficients of thermal expansion and moisture expansion were also measured. Extensive scanning electron microscopic examination of fracture surfaces was performed to permit the correlation of observed failure modes with the environmental conditions under which the various specimens were tested. A micromechanics analysis was used to predict the unidirectional composite response under the various test conditions, incorporating the neat resin experimental results as the required input data. The mechanical and physical test results, the scanning electron microscope observations, and the analytical predictions were then correlated.

Zimmerman, R. S.↗

NASA NTRS1990

The steady state solutions of radiatively driven stellar winds for a non-Sobolev, pure absorption model

The steady state solution topology for absorption line-driven flows is investigated for the condition that the Sobolev approximation is not used to compute the line force. The solution topology near the sonic point is of the nodal type with two positive slope solutions. The shallower of these slopes applies to reasonable lower boundary conditions and realistic ion thermal speed v(th) and to the Sobolev limit of zero of the usual Castor, Abbott, and Klein model. At finite v(th), this solution consists of a family of very similar solutions converging on the sonic point. It is concluded that a non-Sobolev, absorption line-driven flow with a realistic values of v(th) has no uniquely defined steady state. To the extent that a pure absorption model of the outflow of stellar winds is applicable, radiatively driven winds should be intrinsically variable.

Poe, C. H.↗

NASA NTRS1993

Regional mantle upwelling on Venus: The Beta-Atla-Themis anomaly and correlation with global tectonic patterns

The morphology and global distribution of volcanic centers and their association with other geological characteristics offers significant insight into the global patterns of geology, tectonic style, thermal state, and interior dynamics of Venus. Magellan data permit the detailed geological interpretation necessary to address questions about interior dynamics of Venus particularly as they reflect relatively physical, chemical, and thermal conditions of the interior. This paper focuses on the distribution of anomalous concentrations of volcanic centers on Venus and regional patterns of tectonic deformation as it may relate to the identification of global internal anomalies, including mantle dynamic, petrological, or thermal patterns.

Crumpler, L. S.↗

NASA NTRS1996

Thermomechanical Multiaxial Fatigue Testing Capability Developed

Structural components in aeronautical gas turbine engines typically experience multiaxial states of stress under nonisothermal conditions. To estimate the durability of the various components in the engine, one must characterize the cyclic deformation and fatigue behavior of the materials used under thermal and complex mechanical loading conditions. To this end, a testing protocol and associated test control software were developed at the NASA Lewis Research Center for thermomechanical axial-torsional fatigue tests. These tests are to be performed on thin-walled, tubular specimens fabricated from the cobalt-based superalloy Haynes 188. The software is written in C and runs on an MS-DOS based microcomputer.

Source record↗

NASA NTRSDate not supplied

Effect of Boundary Conditions on Process-Induced Stresses in a Plain Weave Unit Cell

Woven polymer matrix composites (PMCs) are leveraged in aerospace applications for their desirable specific properties, yet they are vulnerable to high residual stresses during manufacturing and their complex geometry makes experimental results difficult to observe. Process modeling is needed to characterize the effects of the curing and predict end stress states. Finite element software can be used to model woven architectures, however accurate representation of processing conditions remains a challenge when it comes to selecting boundary conditions. The effect of BCs on process-induced stress within woven PMCs is studied. The commercial Finite Element Analysis (FEA) software Abaqus is coupled with user-written subroutines in a process modeling framework. A two-dimensionally (2D) woven PMC repeating unit cell (RUC) is modeled with TexGen and Abaqus. Virtual curing is imposed on the bulk matrix. The BC study is conducted with Free, Periodic, Flat, and Flat-Free configurations. Results show that the end stress state is sensitive to the boundary condition assumptions. Flat BC results show great agreement with Periodic BCs. Residual stress results from process modeling are then compared with a linear-elastic thermal cooldown analysis in Abaqus. Cooldown results indicate an overestimation in matrix stresses compared with process modeling.

micromechanics↗