Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “local minimum”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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

At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS2003

Evidence for Tropopause Layer Moistening by Convection During CRYSTAL-FACE

Measurements and analysis of the impact of deep convection on tropopause layer moisture are easily confounded by difficulties making precise observations with sufficient spatial coverage before and after convective events and difficulties distinguishing between changes due to local convection versus large-scale advection. The interactions between cloud microphysics and dynamics in the convective transport of moisture into the tropopause layer also result in a sufficiently complex and poorly characterized system to allow for considerable freedom in theoretical models of stratosphere-troposphere exchange. In this work we perform detailed large-eddy simulations with an explicit cloud microphysics model to study the impact of deep convection on tropopause layer moisture profiles observed over southern Florida during CRYSTALFACE. For four days during the campaign (July 11, 16, 28, and 29) we initialize a 100-km square domain with temperature and moisture profiles measured prior to convection at the PARSL ground site, and initiate convection with a warm bubble that produces an anvil at peak elevations in agreement with lidar and radar observations on that day. Comparing the moisture field after the anvils decay with the initial state, we find that convection predominantly moistens the tropopause layer (as defined by minimum temperature and minimum potential temperature lapse rate), although some drying is also predicted in localized layers. We will also present results of sensitivity tests designed to separate the roles of cloud microphysics and dynamics.

Ackerman, A.↗
NASA NTRS1990

A class of systolizable IIR digital filters and its design for proper scaling and minimum output roundoff noise

A class of infinite impulse response (IIR) digital filters with a systolizable structure is proposed and its synthesis is investigated. The systolizable structure consists of pipelineable regular modules with local connections and is suitable for VLSI implementation. It is capable of achieving high performance as well as high throughput. This class of filter structure provides certain degrees of freedom that can be used to obtain some desirable properties for the filter. Techniques of evaluating the internal signal powers and the output roundoff noise of the proposed filter structure are developed. Based upon these techniques, a well-scaled IIR digital filter with minimum output roundoff noise is designed using a local optimization approach. The internal signals of all the modes of this filter are scaled to unity in the l2-norm sense. Compared to the Rao-Kailath (1984) orthogonal digital filter and the Gray-Markel (1973) normalized-lattice digital filter, this filter has better scaling properties and lower output roundoff noise.

Lei, Shaw-Min↗
DOE OSTI2025

Nondegenerate Noise-Resilient Superconducting Qubit

We propose a superconducting qubit based on engineering the first and second harmonics of the Josephson energy and phase relation 𝐸 𝐽⁢1 ⁢cos 𝜑 and 𝐸 𝐽⁢2 ⁢cos 2⁢𝜑. By constructing a circuit such that 𝐸 𝐽⁢2 is negative and |𝐸 𝐽⁢1 | ≪ |𝐸 𝐽⁢2 |, we create a periodic potential with two nondegenerate minima. The qubit, which we dub “harmonium,” is formed from the lowest-energy states of each minimum. Bit-flip protection of the qubit arises due to the localization of each qubit state to their respective minima, while phase-flip protection can be understood by considering the circuit within the Born-Oppenheimer approximation. We demonstrate with time-domain simulations that single- and two-qubit gates can be performed in approximately 100 ns. Finally, we compute the qubit coherence times using numerical diagonalization of the complete circuit in conjunction with state-of-the-art noise models. We estimate out-of-manifold heating times on the order of milliseconds, which can be treated as erasure errors using conventional dispersive readout. We estimate pure-dephasing times on the order of many tens of milliseconds, and bit-flip times on the order of seconds.

quantum error correction↗
NASA NTRS1978

Minimization of transmission cost in decentralized control systems

This paper considers the problem of stabilizing a linear time-invariant multivariable system by using local feedback controllers and some limited information exchange among local stations. The problem of achieving a given degree of stability with minimum transmission cost is solved.

Wang, S.-H.↗
NASA NTRS1992

Diurnal variation of overdense meteor echo duration and ozone

The diurnal variation of the median duration of overdense sporadic radar meteor echoes is examined. The meteors recorded in August, December, and January by the Ondrejov meteor radar during the period 1958-1990 were used for the analysis. A maximum median echo duration 1-3 hours after the time of local sunrise in the meteor region confirms the already known sunrise effect. Minimum echo duration occurring at the time of sunset seems to be the most important point of diurnal variation of the echo duration, when ozone is no longer dissociated by solar UV radiation. The effect of diurnal changes of the echo duration should be considered when the mass distribution of meteor showers is analyzed.

Simek, Milos↗
NASA NTRS1992

Nested-hierarchical scene models and image segmentation

An improved model of scenes for image analysis purposes, a nested-hierarchical approach which explicitly acknowledges multiple scales of objects or categories of objects, is presented. A multiple-pass, region-based segmentation algorithm improves the segmentation of images from scenes better modeled as a nested hierarchy. A multiple-pass approach allows slow and careful growth of regions while interregion distances are below a global threshold. Past the global threshold, a minimum region size parameter forces development of regions in areas of high local variance. Maximum and viable region size parameters limit the development of undesirably large regions. Application of the segmentation algorithm for forest stand delineation in TM imagery yields regions corresponding to identifiable features in the landscape. The use of a local variance, adaptive-window texture channel in conjunction with spectral bands improves the ability to define regions corresponding to sparsely stocked forest stands which have high internal variance.

Woodcock, C.↗
NASA NTRS2011

Design, Optimization and Evaluation of Integrally Stiffened Al 7050 Panel with Curved Stiffeners

A curvilinear stiffened panel was designed, manufactured, and tested in the Combined Load Test Fixture at NASA Langley Research Center. The panel was optimized for minimum mass subjected to constraints on buckling load, yielding, and crippling or local stiffener failure using a new analysis tool named EBF3PanelOpt. The panel was designed for a combined compression-shear loading configuration that is a realistic load case for a typical aircraft wing panel. The panel was loaded beyond buckling and strains and out-of-plane displacements were measured. The experimental data were compared with the strains and out-of-plane deflections from a high fidelity nonlinear finite element analysis and linear elastic finite element analysis of the panel/test-fixture assembly. The numerical results indicated that the panel buckled at the linearly elastic buckling eigenvalue predicted for the panel/test-fixture assembly. The experimental strains prior to buckling compared well with both the linear and nonlinear finite element model.

Slemp, Wesley C. H.↗
NASA NTRS2012

Design, Optimization, and Evaluation of A1-2139 Compression Panel with Integral T-Stiffeners

A T-stiffened panel was designed and optimized for minimum mass subjected to constraints on buckling load, yielding, and crippling or local stiffener failure using a new analysis and design tool named EBF3PanelOpt. The panel was designed for a compression loading configuration, a realistic load case for a typical aircraft skin-stiffened panel. The panel was integrally machined from 2139 aluminum alloy plate and was tested in compression. The panel was loaded beyond buckling and strains and out-of-plane displacements were extracted from 36 strain gages and one linear variable displacement transducer. A digital photogrammetric system was used to obtain full field displacements and strains on the smooth (unstiffened) side of the panel. The experimental data were compared with the strains and out-of-plane deflections from a high-fidelity nonlinear finite element analysis.

Mulani, Sameer B.↗
NASA NTRS2021

GRACE Fast Mascons from Spherical Harmonics and a Regularization Design Trade Study

Mass concentration (mascon) solutions have become a prominent medium for investigating time-variable gravity recovered by GRACE and GRACE Follow-On. While GRACE Level-2 spherical harmonic products require various post-processing techniques to eliminate correlated noise, mascon formulations employ spatial regularization strategies during the estimation step to improve signal recovery. However, mascon estimation has traditionally required large computing resources and GRACE Level-1B processing capabilities. In this study, we show that a typical mascon estimation system can be reformulated to allow for the estimation of regularized mascons from Level-2 spherical harmonics. Provided that spherical harmonic solution covariances are available, the computed mascons will be mathematically equivalent to similar mascons estimated from Level-1B observations. This method is computationally efficient, better leverages GRACE spherical harmonics than past methods, and matches the performance of typical mascon solutions without locking scientists into pre-determined regularization designs. We develop a proof-of-concept solution using ITSG-Grace2018 and compare results with traditional mascons from JPL and NASA GSFC. We then assess the effects of spherical harmonic truncation and use of regularization correlations on basin signal recovery. We find that spherical expansions to degree and order 60 provide the minimum expansion necessary to study most basins, while larger expansions help further localize signals. We also find that diagonal regularizations (i.e., regularizations that do not contain inter-mascon correlations) are adversely affected by leakage, especially across boundaries such as coastlines where signals are not highly correlated, whereas including inter-mascon correlations and regional boundaries in the regularization greatly improves signal recovery.

M. J. Croteau↗
DOE OSTI2024

Learning from metastable symmetric-tilt grain boundaries using physics-based descriptors

Grain boundaries (GBs) govern critical properties of polycrystalline materials. Although significant advancements have been made in characterizing minimum energy and ordered GBs, real GBs are seldom found in such well-defined states. This diversity of atomic arrangements in metastable states makes it challenging to establish structure-property relationships with physical insights. Here, to address this challenge, we use data-driven methods to explore these relationships and examine the underlying physics. In this study, we utilize a large atomistic database (~5000) of minimum energy and metastable states of symmetric-tilt copper GBs, combined with physically motivated local atomic environment (LAE) descriptors [strain functional descriptors (SFDs)], to predict GB properties and gain physical insights. Our regression models exhibit robust predictive capabilities using only 19 descriptors, generalizing to atomic environments in nanocrystals. A significant highlight of our work is the integration of an unsupervised method with SFDs to elucidate LAEs at GBs and their role in determining properties. The model, trained on these minimum energy and metastable GBs using SFDs, predicts the properties of unseen nanocrystals with good accuracy. Our research underscores the role of a physics-based representation of LAEs and the efficacy of data-driven methods in establishing GB structure-property relationships.

36 MATERIALS SCIENCE↗
NASA NTRS1992

Computational structures technology at Grumman: Current practice/future needs

The current practice for the design analysis of new airframe structural systems is to construct a master finite element model of the vehicle in order to develop internal load distributions. The inputs to this model include the geometry which is taken directly from CADAM and CATIA structural layout and aerodynamic loads and mass distribution computer models. This master model is sufficiently detailed to define major load paths and for the computation of dynamic mode shapes and structural frequencies, but not detailed enough to define local stress gradients and notch stresses. This master model is then used to perform structural optimization studies that will provide minimum weights for major structural members. The post-processed output from the master model, load, stress, and strain analysis is then used by structural analysts to perform detailed stress analysis of local regions in order to design local structure with all its required details. This local analysis consists of hand stress analysis and life prediction analysis with the assistance of manuals, design charts, computer stress and structural life analysis and sometimes finite element or boundary element analysis. The resulting design is verified by fatigue tests.

Pifko, Allan B.↗
DOE OSTI2023

Molecular Cage Reports on Its Contents: Spectroscopic Signatures of Cryo-Cooled K + - and Ba 2+ -Benzocryptand Complexes

UV photofragment spectroscopy and IR–UV double resonance methods are used to determine the structure and spectroscopic responses of a three-dimensional [2.2.2]-benzocryptand cage to the incorporation of a single K + or Ba 2+ imbedded inside it (labeled as K + -BzCrypt, Ba 2+ -BzCrypt). We studied the isolated ion-cryptand complex under cryo-cooled conditions, brought into the gas phase by nano-electrospray ionization. Incorporation of a phenyl ring in place of the central ethyl group in one of the three N-CH 2 -CH 2 -O-CH 2 -CH 2 -O-CH 2 -CH 2 -N chains provides a UV chromophore whose S 0 –S 1 transition we probe. K + -BzCrypt and Ba 2+ -BzCrypt have their S 0 –S 1 origin transitions at 35,925 and 36,446 cm –1 , respectively, blue-shifted by 174 and 695 cm –1 from that of 1,2-dimethoxybenzene. These origins are used to excite a single conformation of each complex selectively and record their IR spectra using IR–UV dip spectroscopy. The alkyl CH stretch region (2800–3000 cm –1 ) is surprisingly sensitive to the presence and nature of the encapsulated ion. We carried out an exhaustive conformational search of cage conformations for K + -BzCrypt and Ba 2+ -BzCrypt, identifying two conformations (A and B) that lie below all others in energy. Here, we extend our local mode anharmonic model of the CH stretch region to these strongly bound ion-cage complexes to predict conformation-specific alkyl CH stretch spectra, obtaining quantitative agreement with experiment for conformer A, the gas-phase global minimum. The large electrostatic effect of the charge on the O- and N-lone pairs affects the local mode frequencies of the CH 2 groups adjacent to these atoms. The localized CH 2 scissors modes are pushed up in frequency by the adjacent O/N-atoms so that their overtones have little effect on the alkyl CH stretch region. However, the localized CH 2 wags are nearly degenerate and strongly coupled to one another, producing an array of delocalized wag normal modes, whose highest frequency members reach up above 1400 cm –1 . As such, their overtones mix significantly with the CH stretch modes, most notably involving the CH 2 symmetric stretch fundamentals of the central ethyl groups in the all-alkyl chains and the CH stretches adjacent to the N-atoms and antiperiplanar to the nitrogen lone pair.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2011

Solar Drivers of 11-yr and Long-Term Cosmic Ray Modulation

In the current paradigm for the modulation of galactic cosmic rays (GCRs), diffusion is taken to be the dominant process during solar maxima while drift dominates at minima. Observations during the recent solar minimum challenge the pre-eminence of drift: at such times. In 2009, the approx.2 GV GCR intensity measured by the Newark neutron monitor increased by approx.5% relative to its maximum value two cycles earlier even though the average tilt angle in 2009 was slightly larger than that in 1986 (approx.20deg vs. approx.14deg), while solar wind B was significantly lower (approx.3.9 nT vs. approx.5.4 nT). A decomposition of the solar wind into high-speed streams, slow solar wind, and coronal mass ejections (CMEs; including postshock flows) reveals that the Sun transmits its message of changing magnetic field (diffusion coefficient) to the heliosphere primarily through CMEs at solar maximum and high-speed streams at solar minimum. Long-term reconstructions of solar wind B are in general agreement for the approx. 1900-present interval and can be used to reliably estimate GCR intensity over this period. For earlier epochs, however, a recent Be-10-based reconstruction covering the past approx. 10(exp 4) years shows nine abrupt and relatively short-lived drops of B to < or approx.= 0 nT, with the first of these corresponding to the Sporer minimum. Such dips are at variance with the recent suggestion that B has a minimum or floor value of approx.2.8 nT. A floor in solar wind B implies a ceiling in the GCR intensity (a permanent modulation of the local interstellar spectrum) at a given energy/rigidity. The 30-40% increase in the intensity of 2.5 GV electrons observed by Ulysses during the recent solar minimum raises an interesting paradox that will need to be resolved.

Cliver, E. W.↗
DOE OSTI2021

Refinement of Salt Dissolution Inhibitor Requirements (Final Report)

At Savannah River Site (SRS), High-Level Waste is stored in below-grade carbon steel tanks. This waste in part consists of sludge, salt cake, and/or supernate. Preparation of this waste for future processing involves dissolution of the salt cake layer. The salt dissolution process can create conditions that leave the carbon steel tanks susceptible to localized corrosion. The salt to be dissolved contains high concentrations of nitrate, that once released, create an environment that may be conducive to pitting corrosion and/or stress corrosion cracking (SCC) of carbon steel. The salt dissolution process also liberates interstitial liquid trapped between the salt crystals. This liquid is initially high in nitrite and hydroxide concentration. High pH and greater ratios of nitrite to nitrate act as inhibitors to minimize corrosion of carbon steel in high nitrate environments. However, as dissolution proceeds, the concentration of nitrate will increase, while the hydroxide and nitrite concentration of the interstitial liquid will deplete and become insufficient to prevent the onset of corrosion attack. Tank blending and addition of inhibitors are used to ensure adequate concentrations of hydroxide and nitrite. However, this is not desirable during salt dissolution as it can reduce process efficiency and increase the amount of waste that needs processing. It has been proposed that these corrosion control limits be revisited to evaluate the corrosion susceptibility of carbon steel in environments that more closely resemble current operating conditions at SRS. An experimental matrix was designed to evaluate the use of the pitting factor for supernate chemistries characteristic to SRS, particularly during the salt dissolution process. Two electrochemical methods were identified to determine the susceptibility of A537 and A285 low-carbon steels to pitting corrosion with this chemistry envelope at temperatures up to 75 °C. The predominant electrochemical test method was Cyclic Potentiodynamic Polarization (CPP) studies. Through CPP, the pitting factor was used, based on Hanford Site corrosion studies, to accurately identify pitting susceptibility within the compositional range studied with some conservatism. Additionally, sulfate was determined to have no statistically significant influence, at concentrations up to 0.6 M, on pitting behavior in more concentrated solutions where other aggressive species govern pitting susceptibility. Where CPP was inconclusive, Modified ASTM G192 was successfully used to evaluate pitting susceptibility conditions and allowed for a pass/fail result to be determined. In all cases, the pitting factor was determined to be applicable to the simulants tested, with this metric accurately predicting incidences in which pitting occurred. Based upon the findings in this work, a pitting factor of 1.2 is being proposed to build in a safety factor and remain consistent with the Hanford Site approach. Additionally, a minimum pH limit of 12 is proposed to ensure carbon steel passivity and localized corrosion the primary degradation mechanism. Susceptibility to SCC was evaluated using a reduced matrix of tests at 75 °C. No failures due SCC were observed at open circuit. In addition, tests polarized anodically by 200 mV only resulted in failures for trials with pitting factors less than 0.86. However, a test with a passing condition based upon the pitting factor metric (pitting factor = 1.40) did exhibit a failure with an applied potential of +300 mV vs. OCP. This result is contrary to the prediction based upon the pitting factor, however, a polarization of 300 mV, or even 200 mV, from open circuit is substantial. The relationship between these testing parameters and service environment/conditions and the desired level of conservatism in the metric should be further evaluated in the determination of the significance of this result. While the pitting factor accurately predicted susceptibility to SCC at temperatures up to 75 °C and with positive overpotentials up to 200 mV, the relatively small sample matrix and failure of a passing pitting factor with a 300 mV polarization resulted in an inconclusive determination of whether the pitting factor may be used for predicting susceptibility to SCC at temperatures between 50 °C and 75 °C. As such, additional testing is recommended to evaluate the validity of the pitting factor for SCC susceptibility prediction at temperatures between 50 °C and 75 °C.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

Evaluating Material Design Principles for Calcium-Ion Mobility in Intercalation Cathodes

Multivalent-ion batteries offer an alternative to Li-based technologies, with the potential for greater sustainability, improved safety, and higher energy density, primarily due to their rechargeable system featuring a passivating metal anode. Although a system based on the Ca 2+ /Ca couple is particularly attractive given the low electrochemical plating potential of Ca 2+ , the remaining challenge for a viable rechargeable Ca battery is to identify Ca cathodes with fast ion transport. In this work, a high-throughput computational pipeline is adapted to (1) discover novel Ca cathodes in a largely unexplored space of empty intercalation hosts and (2) develop material design rules for Ca-ion mobility. One candidate from the screening, W 2 O 3 (PO 4 ) 2 , is confirmed to have a low Nudged Elastic Band (NEB) barrier of 168 meV within a one-dimensional (1D) ion percolation topology. This candidate is subsequently synthesized and electrochemically tested, achieving reversible Ca cycling with a capacity of 25 mA h/g. To further accelerate the screening for promising Ca intercalation electrodes, machine learning (ML) Random Forest (RF) and Extreme Gradient Boosting (XGB) classification models are created with local environment descriptors based on a large, structurally and chemically diverse dataset of minimum energy pathways, spanning over 5,000 density functional theory (DFT) site energy calculations. Accuracies of 92% are achieved, material design metrics are quantified, ML force-fields are leveraged in an accelerated iteration of the screening, and a total of 27 novel Ca cathode materials are highlighted for further investigation.

25 ENERGY STORAGE↗
DOE OSTI2022

Giant resonances in topological spin Hall effect due to electron-skyrmion scattering in two-dimensional Rashba spin-orbit ferromagnets

Here we study a topological spin Hall effect where conduction electrons are scattered by Néel-type skyrmions in two-dimensional Rashba spin-orbit ferromagnets. We find the resonance structures in direct and Hall electric conductivities. The resonances strongly depend on the skyrmion size, the Rashba spin-orbit coupling vector value, and the relative direction between magnetization and Rashba vectors. The antiparallel arrangement of the Rashba spin-orbit coupling vector with respect to the magnetization determines the resonance structure and increases the direct conductivity by about two orders of magnitude. For the parallel arrangement the electric conductivities decrease by one to three orders of magnitude and the Hall conductivity changes the sign. The Rashba spin-orbit coupling also modifies electron bands depending on the ratio ε R /J, where ε R is Rashba energy and J is an exchange integral between conduction and localized electrons. If ε R /J ≤ 1, each energy band has the single minimum while for ε R /J > 1 the lower band has the “Mexican-hat” shape with the maximum at k = 0. We focus on the dependencies of direct and Hall electric conductivities on Fermi energy, ε F , skyrmion sizes, and Rashba spin-orbit coupling constant values and its relative direction with the magnetization. Analyzing both types of the energy bands, in general, we find two types of resonances: at the minimum of the upper band and behaviors, we employ the scattering pattern analysis. The resonance dependencies on skyrmion sizes and Rashba, a spin-orbit coupling contestant, can be qualitatively explained in terms of the Ramsauer-Townsend scattering of the upper band electrons by the skyrmion quantum well. The resonance properties can be used in spin transistors. To discover the resonances it is necessary to know the specific range of the parameters. At some values of the parameters the electric conductivity changes by about two orders of magnitude in the narrow range of ε F (< 0.01 eV). To detect the resonances it is also important to identify the relative direction of the Rashba spin-orbit coupling vector with respect to the magnetization.

36 MATERIALS SCIENCE↗
NASA NTRS1989

Stress distribution and topography of Tellus Regio, Venus

The Tellus Regio area of Venus represents a subset of a narrow latitude band where Pioneer Venus Orbiter (PVO) altimetry data, line-of-sight (LOS) gravity data, and Venera 15/16 radar images have all been obtained with good resolution. Tellus Regio also has a wide variety of surface morphologic features, elevations ranging up to 2.5 km, and a relatively low LOS gravity anomaly. This area was therefore chosen in order to examine the theoretical stress distributions resulting from various models of compensation of the observed topography. These surface stress distributions are then compared with the surface morphology revealed in the Venera 15/16 radar images. Conclusions drawn from these comparisons will enable constraints to be put on various tectonic parameters relevant to Tellus Regio. The stress distribution is calculated as a function of the topography, the equipotential anomaly, and the assumed model parameters. The topography data is obtained from the PVO altimetry. The equipotential anomaly is estimated from the PVO LOS gravity data. The PVO LOS gravity represents the spacecraft accelerations due to mass anomalies within the planet. These accelerations are measured at various altitudes and angles to the local vertical and therefore do not lend themselves to a straightforward conversion. A minimum variance estimator of the LOS gravity data is calculated, taking into account the various spacecraft altitudes and LOS angles and using the measured PVO topography as an a priori constraint. This results in an estimated equivalent surface mass distribution, from which the equipotential anomaly is determined.

Williams, David R.↗
NASA NTRS1992

An approximate solution for interlaminar stresses in laminated composites: Applied mechanics program

An approximate solution for interlaminar stresses in finite width, laminated composites subjected to uniform extensional, and bending loads is presented. The solution is based upon the principle of minimum complementary energy and an assumed, statically admissible stress state, derived by considering local material mismatch effects and global equilibrium requirements. The stresses in each layer are approximated by polynomial functions of the thickness coordinate, multiplied by combinations of exponential functions of the in-plane coordinate, expressed in terms of fourteen unknown decay parameters. Imposing the stationary condition of the laminate complementary energy with respect to the unknown variables yields a system of fourteen non-linear algebraic equations for the parameters. Newton's method is implemented to solve this system. Once the parameters are known, the stresses can be easily determined at any point in the laminate. Results are presented for through-thickness and interlaminar stress distributions for angle-ply, cross-ply (symmetric and unsymmetric laminates), and quasi-isotropic laminates subjected to uniform extension and bending. It is shown that the solution compares well with existing finite element solutions and represents an improved approximate solution for interlaminar stresses, primarily at interfaces where global equilibrium is satisfied by the in-plane stresses, but large local mismatch in properties requires the presence of interlaminar stresses.

Rose, Cheryl A.↗