Under investigation is the effective response of a helical strand (helix) made of a viscoelastic material governed by a constitutive relation with fractional-order (i.e., not integer-order) derivatives. The relation involves a 5-parameter model, which is well known to represent a real response much better than the conventional, integer-order models with the same number of parameters. We employ the correspondence principle of viscoelasticity to pass from the level of the strand’s material to that of an effective, coupled axial-torsional response of the helix. The resulting fractional-order differential equation is more complex (i.e., it involves higher derivatives) than the constitutive equation governing the material per se. Also, the use of a fractional-order model results in more complexity of the helix’ effective viscoelastic response than does an integer-order model with the same number of parameters. It is shown that shear deformations are more important than dilatational deformations. Lastly, a standard relaxation test is studied and an analytic solution is derived.
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January 2008
Research Papers
Response of a Helix Made of a Fractional Viscoelastic Material
M. Ostoja-Starzewski,
M. Ostoja-Starzewski
Fellow ASME
Department of Mechanical Science and Engineering,
University of Illinois at Urbana-Champaign
, Urbana, IL 61801
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H. Shahsavari
H. Shahsavari
Department of Mechanical Engineering,
Massachusetts Institute of Technology
, Cambridge, MA 02139
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M. Ostoja-Starzewski
Fellow ASME
Department of Mechanical Science and Engineering,
University of Illinois at Urbana-Champaign
, Urbana, IL 61801
H. Shahsavari
Department of Mechanical Engineering,
Massachusetts Institute of Technology
, Cambridge, MA 02139J. Appl. Mech. Jan 2008, 75(1): 011012 (4 pages)
Published Online: January 14, 2008
Article history
Received:
November 18, 2006
Revised:
February 26, 2007
Published:
January 14, 2008
Citation
Ostoja-Starzewski, M., and Shahsavari, H. (January 14, 2008). "Response of a Helix Made of a Fractional Viscoelastic Material." ASME. J. Appl. Mech. January 2008; 75(1): 011012. https://doi.org/10.1115/1.2745401
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