A methodology to derive fractional derivative constitutive models for finite deformation of viscoelastic materials is proposed in a continuum mechanics treatment. Fractional derivative models are generalizations of the models given by the objective rates. The method of generalization is applied to the case in which the objective rate of the Cauchy stress is given by the Truesdell rate. Then, a fractional derivative model is obtained in terms of the second Piola–Kirchhoff stress tensor and the right Cauchy-Green strain tensor. Under the assumption that the dynamical behavior of the viscoelastic materials comes from a complex combination of elastic and viscous elements, it is shown that the strain energy of the elastic elements plays a fundamental role in determining the fractional derivative constitutive equation. As another example of the methodology, a fractional constitutive model is derived in terms of the Biot stress tensor. The constitutive models derived in this paper are compared and discussed with already existing models. From the above studies, it has been proved that the methodology proposed in this paper is fully applicable and effective.
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Onahama, Iwaki,
Fukushima 971-8135,
e-mail: nshim@motionlabo.com
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November 2015
Research-Article
Fractional Derivative Constitutive Models for Finite Deformation of Viscoelastic Materials
Masataka Fukunaga,
Masataka Fukunaga
1
P.T. Lecturer
College of Engineering,
e-mail: fukunaga@apple.ifnet.or.jp
College of Engineering,
Nihon University
,Koriyama, Fukushima 963-8642
, Japan
e-mail: fukunaga@apple.ifnet.or.jp
1Corresponding author.
Search for other works by this author on:
Nobuyuki Shimizu
Onahama, Iwaki,
Fukushima 971-8135,
e-mail: nshim@motionlabo.com
Nobuyuki Shimizu
MotionLabo Inc.
,TSK Boulevard 302, 9-1, Kanari-Sunada
,Onahama, Iwaki,
Fukushima 971-8135,
Japan
e-mail: nshim@motionlabo.com
Search for other works by this author on:
Masataka Fukunaga
P.T. Lecturer
College of Engineering,
e-mail: fukunaga@apple.ifnet.or.jp
College of Engineering,
Nihon University
,Koriyama, Fukushima 963-8642
, Japan
e-mail: fukunaga@apple.ifnet.or.jp
Nobuyuki Shimizu
MotionLabo Inc.
,TSK Boulevard 302, 9-1, Kanari-Sunada
,Onahama, Iwaki,
Fukushima 971-8135,
Japan
e-mail: nshim@motionlabo.com
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 23, 2014; final manuscript received August 25, 2014; published online April 9, 2015. Assoc. Editor: J. A. Tenreiro Machado.
J. Comput. Nonlinear Dynam. Nov 2015, 10(6): 061002 (8 pages)
Published Online: November 1, 2015
Article history
Received:
March 23, 2014
Revision Received:
August 25, 2014
Online:
April 9, 2015
Citation
Fukunaga, M., and Shimizu, N. (November 1, 2015). "Fractional Derivative Constitutive Models for Finite Deformation of Viscoelastic Materials." ASME. J. Comput. Nonlinear Dynam. November 2015; 10(6): 061002. https://doi.org/10.1115/1.4028438
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