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  • 11
    Electronic Resource
    Electronic Resource
    A fiber matrix model for fluid flow and streaming potentials in the canaliculi of an osteon (1994)
    Springer
    Annals of biomedical engineering 22 (1994), S. 280-292 
    Details
    ISSN: 1573-9686
    Keywords: Osteon ; Canalieuli ; Streaming potentials ; Fiber matrix ; Osteocytes ; Fluid shear stress
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine , Technology
    Notes: Abstract A theoretical model is developed to predict the fluid shear stress and streaming potential at the surface of osteocytic processes in the lacunar-canalicular porosity of an osteon when the osteon is subject to mechanical loads that are parallel or perpendicular to its axis. The theory developed in Weinbaumet al. (31) for the flow through a proteoglycan matrix in a canaliculus is employed in a poroelastic model for the osteon. Our formulation is a generalization of that of Petrovet al. (17). Our model predicts that, in order to satisfy the measured frequency dependence of the phase and magnitude of the SGP in macroscopic bone samples, the fiber spacing in the fluid annulus must lie in the narrow range 6–7 nm typical of the spacing of GAG sidechains along a protein monomer. The model predictions for the local SGP profiles in the osteon agree with the experimental observations of Starkebaumet al. (24). The theory predicts that the pore pressure relaxation time, τd, for a 150–300 μm diameter osteon with the foregoing matrix structure is approximately 0.03–0.13 sec, and that the amplitude of the mean fluid shear stress on the membrane of the osteocytic process at the mean areal radius of the osteon has a maximum at 28 Hz if τd = 0.06 sec. This maximum, which is independent of the magnitude of the loading, could be importantin vivo since the recent experiments of Turneret al. (28) and McLeodet al. (15) have a peak in the strain frequency spectrum between 20 and 30 Hz that also appears to be independent of the type (magnitude) of loading. Numerical predictions for the amplitude of the average fluid shear stress on the osteocytic membrane at the mean areal radius of the osteon show that the fluid shear stress associated with the low amplitude 20–30 Hz spectral strain component is at least as large as the average fluid shear stress associated with the high amplitude 1 Hz stride component, although the latter loading is an order of magnitude larger, and has a magnitude that lies within the middle of the range, 6–30 dynes/cm2, where fluid shear stresses in tissue culture studies with osteoblast monolayers have elicited an intracellular Ca++ response (31). The implications of these results for intracellular electrical communication are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02368235
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  • 12
    Electronic Resource
    Electronic Resource
    Steady flow of a polar fluid in a rotating pipe (1972)
    Springer
    Rheologica acta 11 (1972), S. 330-332 
    Details
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Notes: Summary It is shown that the axial motion and rotational motion in the steady flow of a polar fluid in a rotating cylinder are coupled, and that the rotational motion is not a rigid body rotation. For the same problem in traditional viscous fluid theory the axial motion and rotational motion are uncoupled, and the rotational motion is a rigid body rotation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01974776
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  • 13
    Electronic Resource
    Electronic Resource
    On the steady rotational motion of polar fluids (1970)
    Springer
    Rheologica acta 9 (1970), S. 307-312 
    Details
    ISSN: 1435-1528
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Physics
    Description / Table of Contents: Zusammenfassung Es wird gezeigt, daß für alle physikalisch realisierbaren Grenzbedingungen, die in der Theorie der polaren Flüssigkeiten benutzt werden, diese Theorie das klassische Ergebnis liefert: die Flüssigkeit vollführt eine reine Rotation wie ein starrer Körper, wenn sie sich in einem stationär rotierenden zylindrischen Gefäß befindet.
    Notes: Summary It is shown that for all physically reasonable boundary conditions employed in the theory of polar fluids the theory predicts the traditional result that a fluid will undergo a pure rigid body rotation when subjected to a steady rotational motion in a cylindrical vessel.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01975395
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  • 14
    Electronic Resource
    Electronic Resource
    Unified complete solutions for the theories of thermoelasticity and poroelasticity (1989)
    Springer
    Journal of elasticity 21 (1989), S. 121-126 
    Details
    ISSN: 1573-2681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Complete solutions for the basic system of equations governing linear elastic materials with pores are extended to complete solutions for the basic system of equations for thermoelasticity and poroelasticity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00040938
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  • 15
    Electronic Resource
    Electronic Resource
    Strain energy density bounds for linear anisotropic elastic materials (1993)
    Springer
    Journal of elasticity 30 (1993), S. 191-196 
    Details
    ISSN: 1573-2681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Upper and lower bounds are presented for the magnitude of the strain energy density in linear anisotropic elastic materials. One set of bounds is given in terms of the magnitude of the stress field, another in terms of the magnitude of the strain field. Explicit algebraic formulas are given for the bounds in the case of cubic, transversely isotropic, hexagonal and tetragonal symmetry. In the case of orthotropic symmetry the explicit bounds depend upon the solution of a cubic equation, and in the case of the monoclinic and triclinic symmetries, on the solution of sixth order equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00041853
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  • 16
    Electronic Resource
    Electronic Resource
    The classical pressure vessel problems for linear elastic materials with voids (1983)
    Springer
    Journal of elasticity 13 (1983), S. 157-163 
    Details
    ISSN: 1573-2681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The traditional problems of the thick walled spherical and circular cylindrical shells under internal and external pressure are solved in the context of the theory of linear elastic materials with voids. The solutions are quasi-static. The stress distributions are those predicted by isotropic linear elasticity. The displacement and solid volume fraction charge fields exhibit a volumetric viscoelasticity induced by a rate dependence of the volume fraction change.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00041232
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  • 17
    Electronic Resource
    Electronic Resource
    A note on the problem of pure bending for linear elastic materials with voids (1984)
    Springer
    Journal of elasticity 14 (1984), S. 227-233 
    Details
    ISSN: 1573-2681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract This note concerns the problem of quasi-static pure bending of a beam in the context of the complete theory of linear elastic materials with voids presented in [1]. It is shown here that the solution in the context of the complete theory of [1] is coincident with the pure bending solution of classical elasticity for small time, and that the solution for large time is the bending solution given in [1], a solution which neglected the rate effect in the complete theory of [1]. In between these two limit solutions the rate effect moderates a monotonic transition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00041670
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  • 18
    Electronic Resource
    Electronic Resource
    Bone remodeling III: uniqueness and stability in adaptive elasticity theory (1978)
    Springer
    Journal of elasticity 8 (1978), S. 285-295 
    Details
    ISSN: 1573-2681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Zusammenfassung Ein Eingigkeitsatz für unendich klein adaptives Elastizitätstheoric ist gebeweisen, Zwei Sätze aussagen hinreichende Bedingingen für Stabilität werden demonstrieren.
    Notes: Abstract A uniqueness theorem for infinitesimal adaptive elasticity is proved. Two theorems establishing sufficient conditions for stability are demonstrated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00130467
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  • 19
    Electronic Resource
    Electronic Resource
    Material symmetry optimization by Kelvin modes (2000)
    Springer
    Journal of engineering mathematics 37 (2000), S. 27-43 
    Details
    ISSN: 1573-2703
    Keywords: anisotropic elasticity ; Kelvin modes ; optimization ; strain energy.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Abstract Pointwise optimization of the material symmetry of an anisotropic elastic material with respect to fixed and specified stress (or strain) states is accomplished. The conceptual variables in this problem are the type of material symmetry and the orientation of the canonical symmetry axis for the material at a point in the material. The actual variables are the coefficients of the elasticity (or compliance) matrix. The results are presented in the form of the elasticity (or compliance) matrices that minimize the strain energy with respect to specified, but arbitrary, stress (or strain) states.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004749203449
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  • 20
    Electronic Resource
    Electronic Resource
    Bone remodeling I: theory of adaptive elasticity (1976)
    Springer
    Journal of elasticity 6 (1976), S. 313-326 
    Details
    ISSN: 1573-2681
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Description / Table of Contents: Zusammenfassung Eine Thermo-mechanische kontinuum Theorie als Modell für die Knochenrekonstrucktion wird entwickelt, die eine chemische Reaktion und einen Massentransport zwischen zwei Komponenten behandelt. Knochenrekonstruktion ist ein Sammelbegriff für die kontinuierlichen Prozesse des Wachsens, der Verstärkung und des Abbaus wie sie im lebenden Knochen auftreten. Die Theorie beschreibt ein elastisches Material, das sich in der Form der Belastung anpasst.
    Notes: Abstract A thermomechanical continuum theory involving a chemical reaction and mass transfer between two constituents is developed here as a model for bone remodeling. Bone remodeling is a collective term for the continual processes of growth, reinforcement and resorbtion which occur in living bone. The resulting theory describes an elastic material which adapts its structure to applied loading.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00041724
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