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Results for “HOOKE LAW”

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

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Galilean covariant harmonic oscillator

A Galilean covariant approach to classical mechanics of a single particle is described. Within the proposed formalism, all non-covariant force laws defining acting forces which become to be defined covariantly by some differential equations are rejected. Such an approach leads out of the standard classical mechanics and gives an example of non-Newtonian mechanics. It is shown that the exactly solvable linear system of differential equations defining forces contains the Galilean covariant description of harmonic oscillator as its particular case. Additionally, it is demonstrated that in Galilean covariant classical mechanics the validity of the second Newton law of dynamics implies the Hooke law and vice versa. It is shown that the kinetic and total energies transform differently with respect to the Galilean transformations.

Horzela, Andrzej↗
NASA NTRS1973

Finite element stress analysis of polymers at high strains

A numerical analysis is presented for the problem of a flat rectangular rubber membrane with a circular rigid inclusion undergoing high strains due to the action of an axial load. The neo-hookean constitutive equations are introduced into the general purpose TITUS program by means of equivalent hookean constants and initial strains. The convergence is achieved after a few iterations. The method is not limited to any specific program. The results are in good agreement with those of a company sponsored photoelastic stress analysis. The theoretical and experimental deformed shapes also agree very closely with one another. For high strains it is demonstrated that using the conventional HOOKE law the stress concentration factor obtained is unreliable in the case of rubberlike material.

Durand, M.↗
NASA NTRS2013

Stress-Dependent Voltage Offsets From Polymer Insulators Used in Rock Mechanics and Material Testing

Dielectric insulators are used in a variety of laboratory settings when performing experiments in rock mechanics, petrology, and electromagnetic studies of rocks in the fields of geophysics,material science, and civil engineering. These components may be used to electrically isolate geological samples from the experimental equipment, to perform a mechanical compliance function between brittle samples and the loading equipment, to match ultrasonic transducers, or perform other functions. In manyexperimental configurations the insulators bear the full brunt of force applied to the sample but do not need to withstand high voltages, therefore the insulators are often thin sheets of mechanically tough polymers. From an instrument perspective, transduction from various types of mechanical perturbation has beenqualitatively compared for a number of polymers [1, 2] and these error sources are readily apparent duringhigh-impedance measurements if not mitigated. However even when following best practices, a force dependent voltage signal still remains and its behavior is explored in this presentation. In this experimenttwo thin sheets (0.25 mm) of high-density polyethylene (HDPE) were set up in a stack, held alternatelybetween three aluminum bars; this stack was placed on the platen of a 60T capacity hydraulic testingmachine. The surface area, A, over which the force is applied to the PE sheets in this sandwich is roughly 40 square cm, each sheet forming a parallel-plate capacitor having roughly 320 pF [3], assuming therelative dielectric permittivity of PE is approximately 2.3. The outer two aluminum bars were connected to the LO input ofthe electrometer and the central aluminum bar was connected to the HI input of a Keithley model 617 electrometer. Once the stack is mechanically well-seated with no air gaps, the voltage offset is observed tobe a linear function of the baseline voltage for a given change in applied force. For a periodically appliedforce of 66.7 kN the voltage offsets were measured as a function of initial voltage, and these data were fitwith a linear function that was constrained to pass through the origin. The best fit solution had a correlation coefficient of R=0.85 and a slope of approximately -0.0228 volts/volt. The voltage offset when normalizedis demonstrated to be constant -2.28% for both positive and negative polarities over nearly 3 orders ofbaseline voltage magnitude. From this, the voltage-force coefficient is derived to be -0.34 ppm/N. Thiscorrelates well to a first-order parallel plate capacitor model that assumes constant area, and smalldeformation such that the polymer may be mechanically modeled by a spring that obeys Hookes law. Thissimple model predicts that the coefficient of proportionality is a function of Youngs modulus E= 0.8 GPaand surface area of the insulator, theoretically -1EA= -0.31 ppm/N. The outcome of this work is animproved insulator made from ultra-high molecular weight (UHMW) polyethylene and other approachestoward the minimization of and compensation for these experimental artifacts.

Electromagnetic Studies of Rocks↗
NASA NTRS1931

Experiments with airplane brakes

This report begins by examining the forces on the brake shoes. For the determination of the load distribution over the shoes it was assumed that the brake linings follow Hooke's law, are neatly fitted and bedded in by wear. The assumption of Hooke's law, that is, the proportionality between compression of the lining and the absorption of force, is fulfilled to a certain extent for the loading, as becomes apparent from the load tests described further on. But there is a material discrepancy at unloading. From the load distribution we merely defined the position of the normal force resultant, while for the rest, the effect of the distribution was disregarded in the comparison of the different shoe dispositions.

Michael, Franz↗
NASA NTRS2011

An In-Depth Tutorial on Constitutive Equations for Elastic Anisotropic Materials

An in-depth tutorial on the constitutive equations for elastic, anisotropic materials is presented. Basic concepts are introduced that are used to characterize materials, and notions about how anisotropic material deform are presented. Hooke s law and the Duhamel-Neuman law for isotropic materials are presented and discussed. Then, the most general form of Hooke s law for elastic anisotropic materials is presented and symmetry requirements are given. A similar presentation is also given for the generalized Duhamel-Neuman law for elastic, anisotropic materials that includes thermal effects. Transformation equations for stress and strains are presented and the most general form of the transformation equations for the constitutive matrices are given. Then, specialized transformation equations are presented for dextral rotations about the coordinate axes. Next, concepts of material symmetry are introduced and criteria for material symmetries are presented. Additionally, engineering constants of fully anisotropic, elastic materials are derived from first principles and the specialized to several cases of practical importance.

Nemeth, Michael P.↗
NASA NTRS2007

Mechanical Properties of Cells

Many physiologic and pathologic processes alter the biomechanical properties of the tissue they affect, and these changes may be manifest at the single cell level. The normal and abnormal mechanical properties of a given cell type can be established with the aid of an atomic force microscope (AFM), nonetheless, consistency in the area of the tip has been a mayor limitation of using the AFM for quantitative measurements of mechanical properties. This project attempts to overcome this limitation by using materials with a known elastic modulus, which resembles the one of the cell, to create force-deformation curves to calculate the area of indentation by means of Hooke s Law (sigma = E(epsilon)), which states that stress (sigma) is proportional to the strain (epsilon) where the constant of proportionality, E, is called the Young s modulus, also referred as the elastic modulus. Hook s Law can be rearranged to find the area of indentation (Area= Force/ E(epsilon)), where the indentation force is defined by the means of the added mass spring calibration method.

Bradley, Robert↗
NASA NTRS1972

Experimental investigation of strains in fabric under biaxial and shear forces.

The paper defines the experimental phase of an objective to obtain the mechanical characteristics and coefficients required by the generalized form of Hooke's law for nylon-polyurethane-coated fabric. Test specimens were cylindrical fabric sleeves and were loaded in axial tension by an Instron, in hoop tension by pressurizing, and in shear by a torquing fixture. An extensive amount of strain data is included for a wide combination of the three membrane loads. The tests indicate highly nonlinear stress-strain characteristics of the fabric and a strong dependency on all three membrane loads.

Alley, V. L., Jr.↗
NASA NTRS1972

Large amplitude flexural vibration of thin elastic flat plates and shells

The general equations governing the large amplitude flexural vibration of any thin elastic shell using curvilinear orthogonal coordinates are derived and consist of two coupled, nonlinear, partial differential equations in the normal displacement w and the stress function F. From these equations, the governing equations for the case of shells of revolution or flat plates can be readily obtained as special cases. The material of the shell or plate is isotropic and homogeneous and Hooke's law for the two-dimensional case is valid. It is suggested that the difference between the hardening type of nonlinearity in the case of flat plates and straight beams and the softening type of nonlinearity in the case of shells and rings can, in general, be traced to the amount of curvature present in the underformed median surface of the structure concerned.

Pandalia, K. A. V.↗
NASA NTRS1979

Determination of the technical constants of laminates in oblique directions

An off-axis tensile test theory based on Hooke's Law is applied to glass fiber reinforced laminates. A corrective parameter dependent on the characteristics of the strain gauge used is introduced by testing machines set up for isotropic materials. Theoretical results for a variety of strain gauges are compared with those obtained by a finite element method and with experimental results obtained on laminates reinforced with glass.

Vidouse, F.↗
NASA NTRS1992

An investigation of the isotropy of epoxy polymers

Measurements of the engineering constants E, G, and nu are routinely made for polymeric materials. If these materials are isotropic, these measurements should satisfy the relationship G = E/2(1 nu). However, many past measurements have indicated that this relationship is not satisfied. This raises questions about the assumptions of material isotropy and the applicability of Hooke's law. The methods used to measure these engineering constants for a number of different polymers are first described. Then, new results obtained in the current investigation are presented, indicating that the elastic constants do in fact satisfy the isotropic relationship for strains up to 0.5 percent. However, it is shown that at strain levels above this level, the relationship between stress and strain is nonlinear.

Odom, Edwin M.↗
NASA NTRS1993

Ratchetting behavior in viscoplasticity - A technical note

Viscoplastic models that use the Armstrong and Frederick (1966) kinematic hardening relationship are known to generally overpredict the observed accumulation of ratchet strains. The reason for this behavior is a consequence of the mathematics used to describe Hooke's law and the evolution equations for plastic strain and back stress. Conditions for ratchetting exist whenever there is a cycle-averaged mean stress present over a cyclic loading path. Two types of controlled loading paths are often studied: cyclic relaxation is the ratchet mechanism associated with displacement (strain) control, while cyclic creep is the ratchet mechanism associated with load (stress) control. Overcoming the possible adverse trends in predicted ratchetting behavior is a difficult task, and how one ought to go about doing this is not yet completely clear. We therefore choose to discuss the mathematical cause of ratchetting and how it has been dealt with to date, but make no attempt to correct this flaw.

Freed, Alan D.↗
NASA NTRS1993

A new constitutive equation for elastomers

A new mathematical approach for quantifying the mechanical properties of elastomeric materials under biaxial loads is presented. Specific equations relating principal strains and principal true stresses for a homogeneous, isotropic, and elastic material are proposed that resemble the conventional Hooke's law of linear elasticity. The predicted stresses are compared to those from three different sets of experimental data and to stresses from three different theories based on Rivlin's work-of-deformation approach. The proposed approach is considered to be of benefit to design engineers involved in a broad range of rubber products.

Erickson, Larry↗
NASA NTRS1936

The stress criterion of a tension member with graded flexural stiffness : contribution to the problem of "clamping effect" outside of the elastic range

The approximate size of the stress criterion of a bar on two supports stressed beyond the elastic range is assessed by an approximation. The calculation proceeds from the premise of "substitute flexural stiffness" so defined that the part stressed beyond the elastic range may be considered as following Hooke's law when determining the flexural deformation quantities. For the determination of the substitute flexural stiffness, it is presumed that the material is already stressed so much beyond the yield point as to be strain-hardened. The data are directly applicable to materials having no definite yield point. For the rest, von Karman's method for compressed and subsequently deflected bars serves as basis for the calculation.

Kaul, Hans W↗