Search NASA⌕ Search

SEARCH · Search NASA

Results for “strain tensor”

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 145 records · Page 8

A magnetic analog of pressure–strain interaction

We study the evolution equation for magnetic energy density for a non-relativistic magnetized plasma in the (Lagrangian) reference frame comoving with the electron bulk velocity. Analyzing the terms that arise due to the ideal electric field, namely, perpendicular electron compression and magnetic field line bending, we recast them to reveal a quantity with a functional form analogous to the often-studied pressure–strain interaction term that describes one piece of internal energy density evolution of the species in a plasma, except with the species pressure tensor replaced by the magnetic stress tensor. We dub it the “magnetic stress–strain interaction.” We discuss decompositions of the magnetic stress–strain interaction analogous to those used for pressure–strain interaction. These analogies facilitate the interpretation of the evolution of the various forms of energy in magnetized plasmas and should be useful for a wide array of applications, including magnetic reconnection, turbulence, collisionless shocks, and wave–particle interactions. We display and analyze all the terms that can change magnetic energy density in the Lagrangian reference frame of the electrons using a particle-in-cell simulation of magnetic reconnection.

Barbhuiya, M. Hasan (ORCID:0000000163301650)↗

Determination of single crystal thermal expansion in Uranium-6wt%Niobium shape memory alloy using in-situ diffraction and modeling of textured polycrystalline samples

In-situ neutron diffraction and ex-situ dilatometry experiments were performed on a chemically banded, quenched uranium-6wt% niobium shape memory alloy to study the impact of deformation-(detwinning-) induced texture on the evolution of thermally induced strains (and associated stresses). Thermal heating and cooling cycles between 5K and 473K were performed in-situ with neutron diffraction, and the lattice strain evolution is reported for the observed monoclinic α" phase. Comparisons between the measured diffraction strains and macroscopic dilatometry experiments reveal relationships between micro- and macro-level thermal expansion. Softening of the texture during heating suggests that twin boundary motion can accommodate the large internal thermal strains which are approximately 2% greater than that typically observed during the 175K heating interval used to age more randomly oriented polycrystalline material. Assuming weak constraint of neighboring grains in randomly textured polycrystals, the single crystal thermal expansion tensor is extracted from measurements of lattice strains over the range 5K to 473K. Predictions of polycrystalline thermal expansion, based upon this single crystal thermal expansion tensor, are shown to compare favorably with bulk thermal expansion observations of the as quenched microstructure. However, such a lower-bound estimate is insufficient to explain all aspects of the behavior of the textured material, where the matrix is not isotropic. In conclusion, it is hypothesized that relaxation processes which occur within the quenched microstructure during heating are responsible for the distinct thermal expansion behavior observed during the initial heating cycle compared to cooling and subsequent cycling.

36 MATERIALS SCIENCE↗

Adaptor for Measuring Principal Strains with Tuckerman Strain Gage

An adapter is described which uses three Tuckerman optical strain gages to measure the displacement of the three vortices of an equilateral triangle along lines 120 degrees apart. These displacements are substituted in well-known equations in order to compute the magnitude and direction of the principal strains. Tests of the adaptor indicate that principal strains over a gage length of 1.42 inch may be measured with a systematic error not exceeding 4 percent and a mean observational error of the order of + or minus 0.000006. The maximum observed error in strain was of the order of 0.00006. The directions of principal strains for unidirectional stress were measured with the adaptor with an average error of the order of 1 degree.

INSTRUMENTS-STRAIN GAUGES-RUGE & DE FOREST↗

Implicit Large-Eddy Simulations of Compressible Mixing Layers

Implicit large-eddy simulations of the self-similar regions of two compressible mixing layers at high Reynolds number and convective Mach numbers of 0.381 and 0.690 were carried out. Experimental data was used as the input into a synthetic eddy method turbulent inflow boundary condition to initiate simulations. Computational grids with nearly isotropic cells were used and the grid counts ranged from 24 to 270 million points. Agreement with experimental velocity and Reynolds stress data was good given the simplifications of the simulation. The decrease in mixing layer growth rate with increasing compressibility compares well with the literature. Budgets for the Reynolds stress transport equation were extracted from the simulations. It was demonstrated that the grids used did not resolve the dissipation term at the experimental Reynolds number. However, low Reynolds number simulations indicate that the numerical dissipation replaces the physical dissipation and the dissipation term in the transport equation can be represented by the summation term that quantifies the imbalance in the budget. The budgets for the high Reynolds number mixing layers agree well with previous low Reynolds number studies; indicating that the primary mechanism for the reduced growth rate and increased anistropy of the Reynolds stress tensor due to compressibility is a reduction in the pressure-strain and production terms. A new scaling based on the magnitude of the Reynolds stress tensor is proposed. This scaling provides better relative comparisons between the data and shows that the decrease in pressure-strain in the shear component is the primary driver in reducing the transverse normal stress.

turbulence↗

A study of tectonic activity in the Basin-Range Province and on the San Andreas Fault. No. 1: Kinematics of Basin-Range intraplate extension

Strain rates assessed from brittle fracture and total brittle-ductile deformation measured from geodetic data were compared to estimates of paleo-strain from Quaternary geology for the intraplate Great Basin part of the Basin-Range, western United States. These data provide an assessment of the kinematics and mode of lithospheric extension that the western U.S. Cordillera has experienced from the past few million years to the present. Strain and deformation rates were determined by the seismic moment tensor method using historic seismicity and fault plane solutions for sub-regions of homogeneous strain. Contemporary deformation in the Great Basin occurs principally along the active seismic zones. The integrated opening rate across the entire Great Basin is accommodated by E-E extension at 8 to 10 mm/a in the north that diminishes to NW-SE extension of 3.5 mm/a in the south. Zones of maximum lithospheric extension correspond to belts of thin crust, high heat flow, and Quaternary basaltic volcanism, suggesting that these parameters are related through mechanism of extension such as a stress relaxation, allowing bouyant uplift and ascension of magmas.

Eddington, P. K.↗

Predicting crack growth direction in unidirectional composites

The purpose of this study is to gain a better understanding of the parameters affecting crack growth direction in unidirectional composite materials. To achieve this, the effect of anisotropy and biaxial, far field, loading on the direction of crack growth in unidirectional off-axis composite materials is investigated. Specific emphasis is placed on defining the crack-tip-stress field and finding a consistent criterion for predicting the direction of crack growth. An anisotropic crack-tip-stress analysis was implemented using three criteria (the normal stress ratio theory, the tensor polynomial failure criterion, and the strain energy density theory) to predict the direction of crack extension in unidirectional off-axis graphite-epoxy. The theoretically predicted crack extension directions were then compared with experimental results. It was determined that only the normal stress-ratio criterion correctly predicts the direction of crack extension.

Gregory, M. A.↗

Direct numerical simulations and modeling of a spatially-evolving turbulent wake

Understanding of turbulent free shear flows (wakes, jets, and mixing layers) is important, not only for scientific interest, but also because of their appearance in numerous practical applications. Turbulent wakes, in particular, have recently received increased attention by researchers at NASA Langley. The turbulent wake generated by a two-dimensional airfoil has been selected as the test-case for detailed high-resolution particle image velocimetry (PIV) experiments. This same wake has also been chosen to enhance NASA's turbulence modeling efforts. Over the past year, the author has completed several wake computations, while visiting NASA through the 1993 and 1994 ASEE summer programs, and also while on sabbatical leave during the 1993-94 academic year. These calculations have included two-equation (K-omega and K-epsilon) models, algebraic stress models (ASM), full Reynolds stress closure models, and direct numerical simulations (DNS). Recently, there has been mutually beneficial collaboration of the experimental and computational efforts. In fact, these projects have been chosen for joint presentation at the NASA Turbulence Peer Review, scheduled for September 1994. DNS calculations are presently underway for a turbulent wake at Re(sub theta) = 1000 and at a Mach number of 0.20. (Theta is the momentum thickness, which remains constant in the wake of a two dimensional body.) These calculations utilize a compressible DNS code written by M. M. Rai of NASA Ames, and modified for the wake by J. Cimbala. The code employs fifth-order accurate upwind-biased finite differencing for the convective terms, fourth-order accurate central differencing for the viscous terms, and an iterative-implicit time-integration scheme. The computational domain for these calculations starts at x/theta = 10, and extends to x/theta = 610. Fully developed turbulent wake profiles, obtained from experimental data from several wake generators, are supplied at the computational inlet, along with appropriate noise. After some adjustment period, the flow downstream of the inlet develops into a fully three-dimensional turbulent wake. Of particular interest in the present study is the far wake spreading rate and the self-similar mean and turbulence profiles. At the time of this writing, grid resolution studies are underway, and a code is being written to calculate turbulence statistics from these wake calculations; the statistics will be compared to those from the ongoing PIV wake measurements, those of previous experiments, and those predicted by the various turbulence models. These calculations will lead to significant long-term benefits for the turbulence modeling effort. In particular, quantities such as the pressure-strain correlation and the dissipation rate tensor can be easily calculated from the DNS results, whereas these quantities are nearly impossible to measure experimentally. Improvements to existing turbulence models (and development of new models) require knowledge about flow quantities such as these. Present turbulence models do a very good job at prediction of the shape of the mean velocity and Reynolds stress profiles in a turbulent wake, but significantly underpredict the magnitude of the stresses and the spreading rate of the wake. Thus, the turbulent wake is an ideal flow for turbulence modeling research. By careful comparison and analysis of each term in the modeled Reynolds stress equations, the DNS data can show where deficiencies in the models exist; improvements to the models can then be attempted.

Cimbala, John M.↗

Molecular Modeling for Calculation of Mechanical Properties of Epoxies with Moisture Ingress

Atomistic models of epoxy structures were built in order to assess the effect of crosslink degree, moisture content and temperature on the calculated properties of a typical representative generic epoxy. Each atomistic model had approximately 7000 atoms and was contained within a periodic boundary condition cell with edge lengths of about 4 nm. Four atomistic models were built with a range of crosslink degree and moisture content. Each of these structures was simulated at three temperatures: 300 K, 350 K, and 400 K. Elastic constants were calculated for these structures by monitoring the stress tensor as a function of applied strain deformations to the periodic boundary conditions. The mechanical properties showed reasonably consistent behavior with respect to these parameters. The moduli decreased with decreasing crosslink degree with increasing temperature. The moduli generally decreased with increasing moisture content, although this effect was not as consistent as that seen for temperature and crosslink degree.

Clancy, Thomas C.↗

Density Functional Theory Study of Epitaxially Strained Monolayer Transition Metal Chalcogenides for Piezoelectricity Generation

Two-dimensional transition metal chalcogenides (2D TMCs) are known for their wide range of bandgaps, flexibility, and high strength. Recent synthesis and data mining efforts indicate that 56 2D TMCs have low exfoliation energies and are relatively stable in monolayer form. Under epitaxial strain, we predict using density functional theory (DFT) calculations that the majority of these 2D TMCs can accommodate ±10% strain without breaking their crystal symmetry. The elastic and piezoelectric tensors indicate that 22 of 56 candidates are piezoelectric, and we derive their in-plane piezoelectric coefficient d 11 . The epitaxial strain is further predicted to enhance the d 11 by over 100% at 10% tensile epitaxial strain for most of these piezoelectric 2D TMCs. ReSe 2 at pristine state and Au 2 Se 2 at +5% epitaxial strain are predicted to obtain the extreme d 11 coefficients at -120 and 326 pm/V, respectively. Lastly, these findings have implications for the use of high-performance 2D piezoelectric materials in devices.

2D materials↗

Effective drift velocity from turbulent transport by vorticity

Here, we highlight the differing roles of vorticity and strain in the transport of coarse-grained scalars at length scales larger than ℓ by smaller scale (subscale) turbulence. We use the first term in a multiscale gradient expansion due to which exhibits excellent correlation with the exact subscale physics when the partitioning length ℓ is any scale smaller than that of the spectral peak. We show that unlike subscale strain, which acts as an anisotropic diffusion/antidiffusion tensor, subscale vorticity's contribution is solely a conservative advection of coarse-grained quantities by an eddy-induced nondivergent velocity, v * , that is proportional to the curl of vorticity. Therefore, material (Lagrangian) advection of coarse-grained quantities is accomplished not by the coarse-grained flow velocity, u¯ ℓ , but by the effective velocity, u¯ ℓ + v * , the physics of which may improve commonly used LES models.

42 ENGINEERING↗

Shear Is Not Always Simple: Rate-Dependent Effects of Flow Type on Granular Rheology

we report that despite there being an infinite variety of types of flow, most rheological studies focus on a single type such as simple shear. Using discrete element simulations, we explore bulk granular systems in a wide range of flow types at large strains and characterize invariants of the stress tensor for different inertial numbers and interparticle friction coefficients. We identify a strong dependence on the type of flow, which grows with increasing inertial number or friction. Standard models of yielding, repurposed to describe the dependence of the stress on flow type in steady-state flow and at finite rates, are compared with data.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The nature and origins of decametre-scale porosity in Ordovician carbonate rocks, Halahatang oilfield, Tarim Basin, China

At >7 km depths in the Tarim Basin, hydrocarbon reservoirs in Ordovician rocks of the Yijianfang Formation contain large cavities ( c . 10 m or more), vugs, fractures and porous fault rocks. Although some Yijianfang Formation outcrops contain shallow (formed near surface) palaeokarst features, cores from the Halahatang oilfield lack penetrative palaeokarst evidence. Outcrop palaeokarst cavities and opening-mode fractures are mostly mineral filled but some show evidence of secondary dissolution and fault rocks are locally highly ( c . 30%) porous. Cores contain textural evidence of repeated formation of dissolution cavities and subsequent filling by cement. Calcite isotopic analyses indicate depths between c . 220 and 2000 m. Correlation of core and image logs shows abundant cement-filled vugs associated with decametre-scale fractured zones with open cavities that host hydrocarbons. A Sm–Nd isochron age of 400 ± 37 Ma for fracture-filling fluorite indicates that cavities in core formed and were partially cemented prior to the Carboniferous, predating Permian oil emplacement. Repeated creation and filling of vugs, timing constraints and the association of vugs with large cavities suggest dissolution related to fractures and faults. In the current high-strain-rate regime, corroborated by velocity gradient tensor analysis of global positioning system (GPS) data, rapid horizontal extension could promote connection of porous and/or solution-enlarged fault rock, fractures and cavities. Supplementary material: Stable isotopic analyses and the velocity gradient tensor and principal direction and magnitude calculation are available at https://doi.org/10.6084/m9.figshare.c.4946046 Thematic collection: This article is part of the The Geology of Fractured Reservoirs collection available at: https://www.lyellcollection.org/cc/the-geology-of-fractured-reservoirs

Geology↗

Turbulence energy redistributive model

A study is made to improve the predictions of turbulent flows through modifications of the pressure-strain correlation of the Reynolds stress equations. The mean-strain term of the pressure-strain correlation is formulated by incorporating the tensor with the Reynolds stresses that account for a non-isotropic turbulence effect in the flows which are accompanied by a turbulent separating flow. This model is compared with other existing models and results are verified with existing experimental results for turbulent shear flows.

Amano, R. S.↗

A study of tectonic activity in the Basin-Range Province and on the San Andreas Fault. No. 3: Kinematics of Great Basin intraplate extension from earthquake, geodetic and geologic information

Strain rates assessed from brittle fracture, associated with earthquakes, and total brittle-ductile deformation measured from geodetic data were compared to paleostrain from Quaternary geology for the intraplate Great Basin of the western United States. These data provide an assessment of the kinematics and mode of lithospheric extension that the western U.S. Cordillera has experienced in the last 5 to 10 million years. Strain and deformation rates were determined by the seismic moment tensor method using historic seismicity and fault plane solutions. Contemporary deformation of the Great Basin occurs principally along the active seismic zones. The earthquake related strain shows that the Great Basin is characterized by regional E-W extension at 8.4 mm/a in the north that diminishes to NW-SE extension of 3.5 mm/a in the south. Zones of maximum extension correspond to belts of shallow crust, high heat flow, and Quaternary basaltic volcanism, suggesting that these parameters are related through an effect such as a stress relaxation allowing bouyant uplift and ascension of magmas.

Eddington, P. K.↗

An extended structure-based model based on a stochastic eddy-axis evolution equation

We have proposed and implemented an extension of the structure-based model for weak deformations. It was shown that the extended model will correctly reduce to the form of standard k-e models for the case of equilibrium under weak mean strain. The realizability of the extended model is guaranteed by the method of its construction. The predictions of the proposed model were very good for rotating homogeneous shear flows and for irrotational axisymmetric contraction, but were seriously deficient in the case of plane strain and axisymmetric expansion. We have concluded that the problem behind these difficulties lies in the algebraic constitutive equation relating the Reynolds stresses to the structure parameters rather than in the slow model developed here. In its present form, this equation assumes that under irrotational strain the principal axes of the Reynolds stresses remain locked onto those of the eddy-axis tensor. This is correct in the RDT limit, but inappropriate under weaker mean strains, when the non-linear eddy-eddy interactions tend to misalign the two sets of principal axes and create some non-zero theta and gamma.

Kassinos, S. C.↗

Rheological Properties of Small-Molecular Liquids at High Shear Strain Rates

Molecular-scale understanding of rheological properties of small-molecular liquids and polymers is critical to optimizing their performance in practical applications such as lubrication and hydraulic fracking. We combine nonequilibrium molecular dynamics simulations with two unsupervised machine learning methods: principal component analysis (PCA) and t-distributed stochastic neighbor embedding (t-SNE), to extract the correlation between the rheological properties and molecular structure of squalane sheared at high strain rates (10 6 –10 10 s -1 ) for which substantial shear thinning is observed under pressures P ϵ 0.1–955 MPa at 293 K. Intramolecular atom pair orientation tensors of 435 × 6 dimensions and the intermolecular atom pair orientation tensors of 61 × 6 dimensions are reduced and visualized using PCA and t-SNE to assess the changes in the orientation order during the shear thinning of squalane. Dimension reduction of intramolecular orientation tensors at low pressures P = 0.1,100 MPa reveals a strong correlation between changes in strain rate and the orientation of the side-backbone atom pairs, end-backbone atom pairs, short backbone-backbone atom pairs, and long backbone-backbone atom pairs associated with a squalane molecule. At high pressures P ≥ 400 MPa, the orientation tensors are better classified by these different pair types rather than strain rate, signaling an overall limited evolution of intramolecular orientation with changes in strain rate. Dimension reduction also finds no clear evidence of the link between shear thinning at high pressures and changes in the intermolecular orientation. The alignment of squalane molecules is found to be saturated over the entire range of rates during which squalane exhibits substantial shear thinning at high pressures.

36 MATERIALS SCIENCE↗

Theory of nonlinear terahertz susceptibility in ferroelectrics

An analytical theory is developed for predicting the nonlinear susceptibility of ionic polarization to continuous electromagnetic waves in both bulk and strained thin film ferroelectrics. Using a perturbation method for solving the nonlinear equation of motion for ionic polarization within the framework of Landau-Ginzburg-Devonshire theory, the full second-order nonlinear susceptibility tensor is derived as a function of frequency, temperature, and strain. Here, the theory predicts the coexistence of a significantly enhanced second-order dielectric susceptibility and a relatively low dielectric loss in BaTiO 3 films with a strain-stabilized monoclinic ferroelectric phase and in a strained SrTiO 3 film near its temperature-driven second-order ferroelectric-to-paraelectric phase transition. In this paper, we establish a theoretical framework for predicting and exploiting nonlinear interactions between terahertz waves and ferroelectric materials and, more generally, suggest exciting opportunities to strain-engineer nonlinear dynamical properties of ferroelectrics beyond the static and quasistatic limits.

36 MATERIALS SCIENCE↗

Derivation of the Navier-Stokes equation

The proposed approach to the derivation of the Navier-Stokes equation is thought to be more plausible and easier to understand than other derivations that can be found in works on fluid mechanics. The tensor character of the stress is central to the derivation. In particular, a linear relation between stress and strain rate is assumed only for the shear, rather than for the full stress tensor as is done in most other derivations. An assumption for the shear is naturally simpler and easier to verify experimentally. The use of tensor analysis is shown to greatly simplify the derivation.

Deissler, R. G.↗