A modified fractional order thermo-viscoelastic theory with fractional order strain and its application in a thermo-viscoelastic problem containing a spherical cavity

The applicability of stress–strain relation in classical viscoelasticity models is increasingly questionable in solving transient problems of viscoelastic materials. It is found that the fractional order viscoelastic models fit well with the experimental data from relaxation tests. Meanwhile, althou...

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Bibliographic Details
Published in:Mechanics of time-dependent materials 2022-12, Vol.26 (4), p.891-907
Main Authors: Peng, Wei, Chen, Like, He, Tianhu
Format: Article
Language:English
Subjects:
Characterization and Evaluation of Materials
Classical Mechanics
Dynamic response
Engineering
Hoop stress
Laplace transforms
Mathematical models
Mechanical shock
Order parameters
Polymer Sciences
Solid Mechanics
Strain rate
Stress relaxation tests
Stress-strain relationships
Thermal shock
Viscoelastic materials
Viscoelasticity
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Summary:The applicability of stress–strain relation in classical viscoelasticity models is increasingly questionable in solving transient problems of viscoelastic materials. It is found that the fractional order viscoelastic models fit well with the experimental data from relaxation tests. Meanwhile, although the strain rate is small, which is often neglected in thermo-viscoelasticity models, it is not reasonable to neglect the strain rate in the case of ultrafast heating. In this work, a new generalized fractional order thermo-viscoelastic theory with fractional order strain is formulated by extending the existing thermo-viscoelastic theory. Then, this new theory is applied to investigating the dynamic response of an infinite thermo-viscoelastic medium containing a spherical cavity. The infinite medium is subjected to a thermal shock and a mechanical shock simultaneously at the inner surface of the cavity. The corresponding governing equations are formulated and then solved by the Laplace transform together with its numerical inversion. The distributions of the non-dimensional temperature, displacement, radial stress, and hoop stress are obtained and illustrated graphically. In calculation, the effects of the fractional order parameter, fractional order strain parameter, and mechanical relaxation parameter on the variations of the considered variables are presented and discussed in detail.
ISSN:1385-2000
1573-2738
DOI:10.1007/s11043-021-09518-9