Two types of models are proposed for describing nonlinear fractional derivative dynamical behavior of viscoelastic materials subject to impulse forces. The models are derived based on the thermodynamic elasticity in terms of entropy and on the “scale-free response of the material” under the basic assumption that the viscoelastic materials consist of stable coils of polymers, which we refer to as blobs. The blobs, which may be connected to each other by chemical bonds or physical bonds, are considered here as the elementary constituent of viscoelastic materials from which the nonlinear fractional derivative models are derived. Responses of individual blobs can determine the net collective response of the viscoelastic material to impulse forces. From the above consideration, two types of models are proposed in which the force elements or the stress elements are connected by the generalized Maxwell law.
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e-mail: fukunaga@apple.ifnet.or.jp
e-mail: nshim@iwakimu.ac.jp
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April 2011
Research Papers
Nonlinear Fractional Derivative Models of Viscoelastic Impact Dynamics Based on Entropy Elasticity and Generalized Maxwell Law
Masataka Fukunaga,
Masataka Fukunaga
P. T. Lecturer
College of Engineering,
e-mail: fukunaga@apple.ifnet.or.jp
Nihon University
, Koriyama, Fukushima 963-8642, Japan
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Nobuyuki Shimizu
Nobuyuki Shimizu
Department of Mechanical Systems and Design Engineering,
e-mail: nshim@iwakimu.ac.jp
Iwaki Meisei University
, Iwaki 970-8551, Japan
Search for other works by this author on:
Masataka Fukunaga
P. T. Lecturer
College of Engineering,
Nihon University
, Koriyama, Fukushima 963-8642, Japane-mail: fukunaga@apple.ifnet.or.jp
Nobuyuki Shimizu
Department of Mechanical Systems and Design Engineering,
Iwaki Meisei University
, Iwaki 970-8551, Japane-mail: nshim@iwakimu.ac.jp
J. Comput. Nonlinear Dynam. Apr 2011, 6(2): 021005 (6 pages)
Published Online: October 21, 2010
Article history
Received:
August 20, 2009
Revised:
March 26, 2010
Online:
October 21, 2010
Published:
October 21, 2010
Citation
Fukunaga, M., and Shimizu, N. (October 21, 2010). "Nonlinear Fractional Derivative Models of Viscoelastic Impact Dynamics Based on Entropy Elasticity and Generalized Maxwell Law." ASME. J. Comput. Nonlinear Dynam. April 2011; 6(2): 021005. https://doi.org/10.1115/1.4002383
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