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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Invariant Theory for Dispersed Transverse Isotropy: An Efficient Means for Modeling Fiber Splay

Most soft tissues possess an oriented architecture of collagen fiber bundles, conferring both anisotropy and nonlinearity to their elastic behavior. Transverse isotropy has often been assumed for a subset of these tissues that have a single macroscopically-identifiable preferred fiber direction. Micro-structural studies, however, suggest that, in some tissues, collagen fibers are approximately normally distributed about a mean preferred fiber direction. Structural constitutive equations that account for this dispersion of fibers have been shown to capture the mechanical complexity of these tissues quite well. Such descriptions, however, are computationally cumbersome for two-dimensional (2D) fiber distributions, let alone for fully three-dimensional (3D) fiber populations. In this paper, we develop a new constitutive law for such tissues, based on a novel invariant theory for dispersed transverse isotropy. The invariant theory is based on a novel closed-form splay invariant that can easily handle 3D fiber populations, and that only requires a single parameter in the 2D case. The model is polyconvex and fits biaxial data for aortic valve tissue as accurately as the standard structural model. Modification of the fiber stress-strain law requires no re-formulation of the constitutive tangent matrix, making the model flexible for different types of soft tissues. Most importantly, the model is computationally expedient in a finite-element analysis.

Freed, alan D.↗
NASA NTRS1988

A geometrically nonlinear theory of shear deformable laminated composite plates and its use in the postbuckling analysis

This paper is devoted to the formulation of a higher-order, geometrically nonlinear theory of anisotropic symmetrically-laminated composite plates and to the analysis, in this context, of their postbuckling behavior. Special attention is given to the postbuckling analysis of plates made of transversely isotropic layers for which case, the influence played by the degree of transversal-isotropy of the layers as well as by the goemetrical parameters of the panel is investigated. Finally, the results obtained within the present higher-order theory are compared with their first order transverse shear deformation as well as with their classical (Kirchhoff) counterparts and a number of conclusions concerning their range of applicability and the influence of various parameters are presented.

Librescu, L.↗
NASA NTRS1990

Creep and creep rupture of strongly reinforced metallic composites

A creep and creep damage theory is presented for metallic composites with strong fibers. Application is to reinforced structures in which the fiber orientation may vary throughout but a distinct fiber direction can be identified locally (local transverse isotropy). The creep deformation model follows earlier work and is based on a flow potential function that depends on invariants reflecting stress and the material symmetry. As the focus is on the interaction of creep and damage, primary creep is ignored. The creep rupture model is an extension of continuum damage mechanics and includes an isochronous damage function that depends on invariants specifying the local maximum transverse tension and the maximum longitudinal shear stress. It is posited that at high temperature and low stress, appropriate to engineering practice, these stress components damage the fiber/matrix interface through diffusion controlled void growth, eventually causing creep rupture. Experiments are outlined for characterizing a composite through creep rupture tests under transverse tension and longitudinal shear. Application is made to a thin-walled pressure vessel with reinforcing fibers at an arbitrary helical angle. The results illustrate the usefulness of the model as a means of achieving optimal designs of composite structures where creep and creep rupture are life limiting.

Robinson, D. N.↗
NASA NTRS1983

Uppermantle anisotropy and the oceanic lithosphere

Published Rayleigh and Love wave phase and group velocity data have been inverted taking into account sphericity, anelastic dispersion, and transverse isotropy. For a PREM-type modular parameterization, the thickness of the high velocity mantle seismic lithosphere (LID) varies in thickness from about 30 km for young ocean to about 50 km for old ocean, much less than previous estimates based on isotropic inversion of similar data. This LID thickness is comparable to the elastic or flexural thickness found from studies of seamount loading and flexure at trenches, suggesting that the thickness of the lithosphere may be controlled by mineralogy, composition, or crystal orientation rather than by temperature alone.

Anderson, D. L.↗
NASA NTRS1986

A viscoplastic constitutive theory for metal matrix composites at high temperature

A viscoplastic constitutive theory is presented for representing the high-temperature deformation behavior of metal matrix composites. The point of view taken is a continuum one where the composite is considered a material in its own right, with its own properties that can be determined for the composite as a whole. It is assumed that a single preferential (fiber) direction is identifiable at each material point (continuum element) admitting the idealization of local transverse isotropy. A key ingredient in this work is the specification of an experimental program for the complete determination of the material functions and parameters for characterizing a particular metal matrix composite. The parameters relating to the strength of anisotropy can be determined through tension/torsion tests on longitudinally and circumferentially reinforced thin-walled tubes. Fundamental aspects of the theory are explored through a geometric interpretation of some basic features analogous to those of the classical theory of plasticity.

Robinson, D. N.↗
NASA NTRS1988

A viscoplastic constitutive theory for metal matrix composites at high temperature

A viscoplastic constitutive theory is presented for representing the high temperature deformation behavior of metal matrix composites. The point of view taken is a continuum one where the composite is considered a material in its own right, with its own properties that can be determined for the composite as a whole. It is assumed that a single preferential (fiber) direction is identifiable at each material point (continuum element) admitting the idealization of local transverse isotropy. A key ingredient is the specification of an experimental program for the complete determination of the material functions and parameters for characterizing a particular metal matrix composite. The parameters relating to the strength of anisotropy can be determined through tension/torsion tests on longitudinally and circumferentially reinforced thin walled tubes. Fundamental aspects of the theory are explored through a geometric interpretation of some basic features analogous to those of the classical theory of plasticity.

Robinson, David N.↗
NASA NTRS1988

Unified constitutive model development for metal matrix composites at high temperature

Structural alloys used in high temperature applications exhibit complex thermomechanical behavior that is time dependent and hereditary. Recent attention is being focused on metal matrix composite materials for high temperature applications where they exhibit all the complexities of conventional alloys and their strong anisotropy adds further complexities. Here, a proven constitutive model for isotropic materials in which the inelastic strain rate and internal state are expressible as gradients of a dissipation potential is taken to depend on invariants that reflect local transverse isotropy. Applications illustrate the capability of the theory of representing the time dependent, hereditary, anisotropic behavior typical of these materials at high temperature.

Robinson, D. N.↗
NASA NTRS1987

A viscoplastic constitutive theory for metal matrix composites at high temperature

A viscoplastic theory is presented for representing the high-temperature deformation behavior of metal matrix composites. The point of view taken is a continuum one where the composite is considered a material in its own right, with its own properties that can be determined for the composite as a whole. It is presumed that a single preferential (fiber) direction is identifiable at each material point (continuum element) admitting the idealization of local transverse isotropy. A key ingredient in this work is the specification of an experimental program for the complete determination of the material functions and parameters for characterizing a particular metal matrix composite. The parameters relating to the strength of anisotropy can be determined through tension/torsion tests on longitudinally and circumferentially reinforced thin-walled tubes. Fundamental aspects of the theory are explored through a geometric interpretation of some basic features analogous to those of the classical theory of plasticity.

Robinson, D. N.↗
NASA NTRS1991

Simplified computational methods for elastic and elastic-plastic fracture problems

This paper presents an overview of some of the recent (1984-1991) developments in computational/analytical methods in the mechanics of fracture: (i) analytical solutions for elliptical or circular cracks embedded in isotropic or transversely isotropic solids (the crack-plane being at an arbitrary angle to the axis of transverse isotropy), with crack-faces being subjected to arbitrary tractions; (ii) finite-element or boundary-element alternating methods for two- and three-dimensional crack problems; (iii) a "direct-stiffness" method for stiffened panels with flexible fasteners and with multiple cracks, using the alternating method; (iv) multiplesite-damage near a row of fastener holes; (v) analysis of cracks with bonded repair patches; (vi) methods for generation of weight-functions for 2- and 3-D crack problems, and (vii) domain-integral methods for elastic-plastic or inelastic crack mechanics.

Aging Aircraft↗
NASA NTRS1994

An anisotropic extension of Bodner's model of viscoplasticity: Model development

An anisotropic viscoplasticity model is developed as an extension of the well known Bodner model. The extension is made by replacing the effective stress of the isotropic Bodner model by one involving invariants for transverse isotropy. The resulting model retains the simplicity of Bodner's in the ease with which the material constants are determined experimentally. It allows a representation of strong initial anisotropy yet is based on the scalar state variable under the assertion that induced anisotropy is negligible relative to the strong initial anisotropy. Temperature dependence is taken as in the original Bodner theory. Account is made of fiber volume fraction through nonlinear rules of mixture applied to the stress history and anisotropy parameters. Focus is on the theoretical development of the model, however, application to a W/Cu composite is in progress and will be reported as a sequel to this report.

Robinson, David N.↗
NASA NTRS1989

A thermoelastic transversely isotropic thick walled cylinder/disk application: An analytical solution and study

A continuum theory is utilized to represent the thermoelastic behavior of a thick walled composite cylinder that can be idealized as transversely isotropic. A multiaxial statement of the constitutive theory employed is presented, as well as the out of the plane of isotropy, plane stress, and plane strain reductions. The derived analytical solution presented is valid for a cylindrical tube or thin disk with a concentric hole, subjected to internal and/or external pressure and a general radial temperature distribution. A specific problem examined is that of a thick walled cylinder subjected to an internal and external pressure loading and a linear radial temperature distribution. The results are expressed in nondimensional form and the effects on the response behavior are examined for various material properties, fiber orientation and types of loadings.

Arnold, S. M.↗
NASA NTRS1950

Spectrums and Diffusion in a Round Turbulent Jet

In a round turbulent jet at room temperature, measurement of the shear correlation coefficient as a function of frequency (through bandpass filters) has given a rather direct verification of Kolmogoroff's local-isotropy hypothesis. One-dimensional power spectrums of velocity and temperature fluctuations, measured in unheated and heated jets, respectively, have been contrasted. Under the same conditions, the two corresponding transverse correlation functions have been measured and compared. Finally, measurements have been made of the mean thermal wakes behind local (line) heat sources in the unheated turbulent jet, and the order of magnitude of the temperature fluctuations has been determined. (author)

Corrsin, Stanley↗
NASA NTRS1951

Spectra and Diffusion in a Round Turbulent Jet

In a round turbulent jet at room temperature, measurement of the shear correlation coefficient as a function of frequency (through band-pass filters) has given a rather direct verification of Kolmogoroff's local-isotropy hypothesis. One-dimensional power spectra of velocity and temperature fluctuations, measured in unheated and heated jets, respectively, have been contrasted. Under the same conditions, the two corresponding transverse correlation functions have been measured and compared. Finally, measurements have been made of the mean thermal wakes behind local (line) heat sources in the unheated turbulent jet, and the order of magnitude of the temperature fluctuations has been determined.

Corrsin, Stanley↗
NASA NTRS1987

Test of spatial isotropy using a cryogenic torsion pendulum

Motion of the earth through the cosmic neutrino background, or through certain kinds of vacuum states, produces a term of the form g(sigma) x v in the energy of an electron. To search for such a term, a cryogenic torsion pendulum carrying a transversely polarized magnet was used. Superconducting shields reduced magnetic torques. A sigma x v term would produce a sinusoidal oscillation of the pendulum with a period of one sidereal day. Such an oscillation was not detected, and a new limit of 8.5 x 10 to the -18th eV has been set for the splitting of the spin states of an electron at rest on the earth.

Phillips, Peter R.↗
NASA NTRS1989

Recent results concerning the stability of viscoelastic shear deformable plates under compressive edge loading

Some recent results obtained by the authors are summarized concerning the stability of transversely isotropic flat panels whose materials exhibit a viscoelastic behavior and whose edges are subjected to in-plane biaxial compressive loads. Two transversely isotropic type materials, largely used in advanced technology, are considered: (1) the pyrolytic-graphite type, used in the thermal protection of aerospace vehicles, and (2) the type corresponding to unidirectional fiber-reinforced composites. In the former case, the planes of isotropy are parallel at each point to the midplane of the plate. In the latter case, they are normal to the fiber directions. The micromechanical relations developed by Aboudi (1984, 1986, 1987) are considered in conjunction with the correspondence principle of linear viscoelastic theory in order to predict the macroscopic viscoelastic properties of a material composed of uniaxial elastic fibers embedded in a linear viscoelastic matrix.

Librescu, L.↗
NASA NTRS1981

An improved transverse shear deformation theory for laminated antisotropic plates

An improved transverse shear deformation theory for laminated anisotropic plates under bending is presented. The theory eliminates the need for an arbitrarily chosen shear correction factor. For a general laminate with coupled bending and stretching, the constitutive equations connecting resultants with average displacements and rotations are derived. Simplified forms of these relations are also obtained for the special case of a symmetric laminate with uncoupled bending. The governing equation for this special case is obtained as a sixth-order equation for the normal displacement requiring prescription of the three physically natural bounday conditions along each edge. For the limiting case of isotropy, the present theory reduces to an improved version of Mindlin's theory. Numerical results are obtained from the present theory for an example of a laminated plate under cylindrical bending. Comparison with results from exact three-dimensional analysis shows that the present theory is more accurate than other theories of equivalent order.

Murthy, M. V. V.↗
NASA NTRS1983

Pulsations in magnetic field and ion flux observed at L = 4.5 on August 5, 1972

Observations made from space (Explorer 45) near L = 4.5 and from magnetic observatories on the ground of the large-amplitude ULF pulsations that followed the unusually strong compression of the earth's magnetosphere associated with the geomagnetic storm of August 1972 are analyzed. A spectral analysis of Explorer 45 magnetometer data indicates a compressional mode oscillation coupled to a transverse mode oscillation. Enhancements in amplitude of a 300-s period wave near 0040 UT August 5 are found to coincide with an intensification of 100- to 1000-Hz magnetic and electric field oscillations and with the appearance of fluxes of energetic ions. It is noted that during this period the ion pitch angle distribution in each available energy channel (24-300 keV) followed a periodic sequence, apparently synchronized with the magnetic pulsations, from normal trapping (highest fluxes near 90 deg and lowest near 0 deg and 180 deg) to a nearly isotropic particle distribution. It is found that during the transitions the particle flux near 90 deg pitch angle was alternately large earthward of the satellite (before isotropy) and larger radially outward from the satellite (after isotropy).

Engebretson, M. J.↗