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At least 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Time-reversed nonlinear acoustic downhole pore pressure measurements

Apparatus (10) and methods for measurement of pore pressure in rock formations through a metal borehole casing (32) after a well is cased and cemented, are described. Such measurements may be accomplished by using the Dynamic Acoustic Elasticity (DAE) method for characterizing nonlinear parameters by perturbing a selected rock formation region with a High Amplitude, Low Frequency (HALF) acoustic strain wave, and probing this region using a Low Amplitude, High Frequency (LAHF) acoustic wave (18), (22). Time reversal techniques (36) may be employed for focusing acoustic energy into the formation in the vicinity of the pipe or open hole. The change in wave speed of the probe pulses as the HALF induced strain wave oscillation propagates through the formation, as a function of the induced strain, may be used to determine the nonlinear elastic parameters α, β, δ, and A of the pore pressure, from which the pore pressure may be determined in the region of the HALF wave.

Goodman, Harvey E.↗
DOE OSTI2021

Downhole nonlinear acoustics measurements in rock formations using dynamic acoustic elasticity and time reversal

Apparatus and methods for measurement of pore pressure in rock formations through an open, or cemented and/or cased, borehole are described. Such measurements are achieved using the Dynamic Acoustic Elasticity (DAE) method for characterizing nonlinear parameters by perturbing a selected rock formation volume with a High Amplitude, Low Frequency (HALF) acoustic strain wave, and probing this volume using a Low Amplitude, High Frequency (LAHF) acoustic wave. Time reversal techniques may be employed for focusing acoustic energy Into the formation in the vicinity of the pipe or open hole.

Goodman, Harvey Edwin↗
DOE OSTI2025

Hyperelastic nature of the Hoek–Brown criterion

In this article, we propose a nonlinear elasto-plastic model, for which a specific class of hyperbolic elasticity arises as a straight consequence of the yield criterion invariance on the plasticity level. We superimpose this nonlinear elastic (or hyperelastic) behavior with plasticity obeying the associated flow rule. Interestingly, we find that a linear yield criterion on the thermodynamical force associated with plasticity results in a quadratic yield criterion in the stress space. This suggests a specific hyperelastic connection between Mohr–Coulomb and Hoek–Brown (or alternatively between Drucker–Prager and Pan–Hudson) yield criteria. We compare the elasto-plastic responses of standard tests for the Drucker–Prager yield criterion using either linear or the suggested hyperbolic elasticity. Notably, the nonlinear case stands out due to dilatancy saturation observed during cyclic loading in the triaxial compression test. We conclude this study with structural finite element simulations that clearly demonstrate the numerical applicability of the proposed model.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1974

Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades

The equations of motion are developed by two complementary methods, Hamilton's principle and the Newtonian method. The resulting equations are valid to second order for long, straight, slender, homogeneous, isotropic beams undergoing moderate displacements. The ordering scheme is based on the restriction that squares of the bending slopes, the torsion deformation, and the chord/radius and thickness/radius ratios are negligible with respect to unity. All remaining nonlinear terms are retained. The equations are valid for beams with mass centroid axis and area centroid (tension) axis offsets from the elastic axis, nonuniform mass and stiffness section properties, variable pretwist, and a small precone angle. The strain-displacement relations are developed from an exact transformation between the deformed and undeformed coordinate systems. These nonlinear relations form an important contribution to the final equations. Several nonlinear structural and inertial terms in the final equations are identified that can substantially influence the aeroelastic stability and response of hingeless helicopter rotor blades.

Hodges, D. H.↗
DOE OSTI2022

Elastic Solutions to 2D Plane Strain Problems: Nonlinear Contact and Settlement Analysis for Shallow Foundations

The classical Neumann boundary value problem of an isotropic, homogeneous elastic half-plane under plane strain conditions is readdressed as the limiting case of the fully three-dimensional problem. Analytical solutions of the stress and strain tensors are obtained by taking the limit from known three-dimensional solutions. It is shown that the displacement fields for the plane strain problem are not well defined. A small number of simple expressions are developed, which provide a general solution for linearly-varying traction over arbitrary regions on the boundary. A simple, efficient, and rapidly convergent algorithm is developed which uses these solutions as analytic elements and provides a solution approach to the general boundary value problem. The method is verified against known solutions for Hertzian contact between parallel cylinders. Two numerical examples are presented for the analysis of shallow foundation systems. In the first, the boundary conditions are informed by analytical elastoplastic calculations and a strain influence analysis is performed and compared with the Schmertmann method. Subsequently, empirical laboratory contact traction distributions measured by Bauer et al., in both the normal and tangential directions are employed as boundary conditions for an analysis of the underlying stress field.

42 ENGINEERING↗
NASA NTRS1982

Materials constitutive models for nonlinear analysis of thermally cycled structures

Effects of inelastic materials models on computed stress-strain solutions for thermally loaded structures were studied by performing nonlinear (elastoplastic creep) and elastic structural analyses on a prismatic, double edge wedge specimen of IN 100 alloy that was subjected to thermal cycling in fluidized beds. Four incremental plasticity creep models (isotropic, kinematic, combined isotropic kinematic, and combined plus transient creep) were exercised for the problem by using the MARC nonlinear, finite element computer program. Maximum total strain ranges computed from the elastic and nonlinear analyses agreed within 5 percent. Mean cyclic stresses, inelastic strain ranges, and inelastic work were significantly affected by the choice of inelastic constitutive model. The computing time per cycle for the nonlinear analyses was more than five times that required for the elastic analysis.

Kaufman, A.↗
NASA NTRS1990

Application of the operator spline technique to nonlinear estimation and control of moving elastic systems

A bilinear model of the vibrational dynamics of a deformable maneuvering body is described. Estimates of the deformation state are generated through a low dimensional operator spline interpolator of bilinear systems combined with a feedback linearized based observer. Upper bounds on error estimates are also generated through the operator spline, and potential application to shaping control purposes is highlighted.

Karray, Fakhreddine↗
DOE OSTI2021

Observations of modal coupling due to bolted joints in an experimental benchmark structure

The goal of this paper is to present a set of measurements from a benchmark structure containing two bolted joints to support future efforts to predict the damping due to the joints and to model nonlinear coupling between the first two elastic modes. Bolted joints introduce nonlinearities in structures, typically causing a softening in the natural frequency and an increase in damping because of frictional slip between the contact interfaces within the joint. These nonlinearities pose significant challenges when characterizing the response of the structure under a large range of load amplitudes, especially when the modal responses become coupled, causing the effective damping and natural frequency to not only depend on the excitation amplitude of the targeted mode, but also the relative amplitudes of other modes. In this work, two nominally identical benchmark structures, known in some prior works as the S4 beam, are tested to characterize their nonlinear properties for the first two elastic modes. Detailed surface measurements are presented and validated through finite element analysis and reveal distinct contact interactions between the two sets of beams. The free-free test structures are excited with an impact hammer and the transient response is analyzed to extract the damping and frequency backbone curves. A range of impact amplitudes and drive points are used to isolate a single mode or to excite both modes simultaneously. Differences in the nonlinear response correlate with the relative strength of the modes that are excited, allowing one to characterize mode coupling. Each of the beams shows different nonlinear properties for each mode, which is attributed to the different contact pressure distributions between the parts, although the mode coupling relationship is found to be consistent between the two. Lastly, the test data key finding are presented in this paper and the supporting data is available on a public repository for interested researchers.

42 ENGINEERING↗
NASA NTRS1972

Finite elements of nonlinear continua.

The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.

Oden, J. T.↗
NASA NTRS1971

Hard tissue as a composite material. I - Bounds on the elastic behavior.

Recent determination of the elastic moduli of hydroxyapatite by ultrasonic methods permits a re-examination of the Voigt or parallel model of the elastic behavior of bone, as a two phase composite material. It is shown that such a model alone cannot be used to describe the behavior of bone. Correlative data on the elastic moduli of dentin, enamel and various bone samples indicate the existence of a nonlinear dependence of elastic moduli on composition of hard tissue. Several composite models are used to calculate the bounds on the elastic behavior of these tissues. The limitations of these models are described, and experiments to obtain additional critical data are discussed.

Katz, J. L.↗
DOE OSTI2025

Thermal modulation of nonlinear ultrasonic waves for nondestructive evaluation of elastic materials

Temperature variation is often considered an undesirable factor in ultrasonic testing, as wave velocity is highly sensitive to thermal fluctuations. However, completely eliminating the temperature effect is difficult, particularly in tests requiring precise velocity measurements. Recently, a method called Thermal Modulation of Nonlinear Ultrasonics (TMNL) has been developed. Instead of eliminating the thermal effect, the TMNL method leverages the temperature variation as a driving force to stimulate the nonlinear response of the medium and modulate the ultrasonic waves propagating in it. These modulated waves can then be used to evaluate the nonlinear behaviours of the test medium. This paper presents a focused review of the TMNL technique, including its theoretical foundations, particularly the conceptual challenges in integrating thermal effects into classical acoustoelastic theory, and recent applications in non-destructive evaluation (NDE). Three case studies are presented to demonstrate TMNL’s application in detecting microcracking in concrete, assessing ageing in polymer materials, and enabling temperature compensation in acoustoelastic tests. In conclusion, the review also summarises related studies, including photothermal crack modulation, and discusses current limitations and future directions of TMNL in elastic media.

NDE↗
DOE OSTI2021

Experimental Investigation of Elastodynamic Nonlinear Response of Dry Intact, Fractured and Saturated Rock

Nonlinear elastodynamic response of fractured rocks carries crucial information on fracture features that can be exploited to forecast flow properties, friction constitutive behavior and poromechanical response. Well-controlled laboratory experiments are designed to measure the nonlinear elastodynamic response of Westerly granite in three states: dry intact, dry fractured and saturated fractured. We study the effect of fracturing and saturation in modifying the elastodynamic response of the rock. Each sample is tested at a normal stress level of 15 MPa. We measure the elastodynamic response of an intact L-shaped sample of Westerly Granite subjected to normal stress oscillations of prescribed amplitudes (0.2–1 MPa) and frequencies (0.1, 1, 10 Hz). Ultrasonic waves transmitted across the sample are used to monitor the evolution of wave velocity before, during and after dynamic stressing. Furthermore, the nonlinearity of the elastodynamic response is measured in terms of: (1) the offset in normalized wave velocity; (2) the amplitude of wave velocity fluctuation during the oscillations; and (3) recovery rate of the wave velocity post-oscillation. We observe that the three nonlinearity parameters show a similar trend. Irrespective of the parameter, the nonlinearity measures higher for sample in dry-intact condition than that for dry-fractured and the saturated-fractured sample exhibits smaller nonlinearity than the dry-fractured sample. As expected, the saturated sample exhibits less nonlinearity than the dry intact and fractured samples due to the presence of interstitial fluid and the resulting increased interface stiffness. Conversely, the dry intact rock shows a higher nonlinearity than the dry fractured. We use numerical simulations to show that the presence of fracture significantly alters the strain distribution across the bulk of the sample and only the contacting asperities are highly strained, thus resulting in a decrease in the measured elastodynamic nonlinearity.

58 GEOSCIENCES↗
DOE OSTI2024

Identifying Heterogeneous Micromechanical Properties of Biological Tissues via Physics–Informed Neural Networks

The heterogeneous micromechanical properties of biological tissues have profound implications across diverse medical and engineering domains. However, identifying full-field heterogeneous elastic properties of soft materials using traditional engineering approaches is fundamentally challenging due to difficulties in estimating local stress fields. Recently, there has been a growing interest in data-driven models for learning full-field mechanical responses, such as displacement and strain, from experimental or synthetic data. However, research studies on inferring full-field elastic properties of materials, a more challenging problem, are scarce, particularly for large deformation, hyperelastic materials. Here, a physics-informed machine learning approach is proposed to identify the elasticity map in nonlinear, large deformation hyperelastic materials. This study reports the prediction accuracies and computational efficiency of physics-informed neural networks (PINNs) in inferring the heterogeneous elasticity maps across materials with structural complexity that closely resemble real tissue microstructure, such as brain, tricuspid valve, and breast cancer tissues. Further, the improved architecture is applied to three hyperelastic constitutive models: Neo-Hookean, Mooney Rivlin, and Gent. Furthermore, the improved network architecture consistently produces accurate estimations of heterogeneous elasticity maps, even when there is up to 10% noise present in the training data.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS2014

Spacecraft Stabilization and Control for Capture of Non-Cooperative Space Objects

This paper addresses stabilization and control issues in autonomous capture and manipulation of non-cooperative space objects such as asteroids, space debris, and orbital spacecraft in need of servicing. Such objects are characterized by unknown mass-inertia properties, unknown rotational motion, and irregular shapes, which makes it a challenging control problem. The problem is further compounded by the presence of inherent nonlinearities, signi cant elastic modes with low damping, and parameter uncertainties in the spacecraft. Robust dissipativity-based control laws are presented and are shown to provide global asymptotic stability in spite of model uncertainties and nonlinearities. It is shown that robust stabilization can be accomplished via model-independent dissipativity-based controllers using thrusters alone, while stabilization with attitude and position control can be accomplished using thrusters and torque actuators.

Joshi, Suresh↗
NASA NTRS1990

Effect of stress on energy flux deviation of ultrasonic waves in GR/EP composites

Ultrasonic waves suffer energy flux deviation in graphite/epoxy because of the large anisotropy. The angle of deviation is a function of the elastic coefficients. For nonlinear solids, these coefficients and thus the angle of deviation is a function of stress. Acoustoelastic theory was used to model the effect of stress on flux deviation for unidirectional T300/5208 using previously measured elastic coefficients. Computations were made for uniaxial stress along the x3 axis (fiber axis) and the x1 for waves propagating in the x1x3 plane. These results predict a shift as large as three degrees for the quasi-transverse wave. The shift in energy flux offers a new nondestructive technique of evaluating stress in composites.

Prosser, William H.↗
NASA NTRS1990

Effect of Stress on Energy Flux Deviation of Ultrasonic Waves in Ultrasonic Waves in GR/EP Composites

Ultrasonic waves suffer energy flux deviation in graphite/epoxy because of the large anisotropy. The angle of deviation is a function of the elastic coefficients. For nonlinear solids, these coefficients and thus the angle of deviation is a function of stress. Acoustoelastic theory was used to model the effect of stress on flux deviation for unidirectional T300/5208 using previously measured elastic coefficients. Computations were made for uniaxial stress along the x3 axis fiber axis) and the x1 axis for waves propagating in the x1x3 plane. These results predict a shift as large as three degrees for the quasi-transverse wave. The shift in energy flux offers new nondestructive technique of evaluating stress in composites.

Prosser, William H.↗
NASA NTRS1985

Decomposition and state variable feedback control of elastic robotic systems

Energy-efficient, lightweight robot arms for space applications have considerable structural flexibility. An approach to control of a class of flexible robotic systems is presented. A control law is derived which decouples the joint-angle motion from the flexible motion and, in addition, asymptotically decomposes the elastic dynamics into two subsystems. This allows the design of an elastic mode stabilizer independently based on lower order models representing structural flexibility. The closed-loop system is shown to be globally asymptotically stable and robust to uncertaintly in system parameters. Simulation results show that the combination of nonlinear decoupling and elastic stabilization permits rapid, accurate tracking of large joint angle commands with well damped elastic response, in spite of space vehicle motion and payload uncertainty.

Singh, S. N.↗