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

A modified fractional order thermo-viscoelastic theory with fractional order strain and its... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mechanics of Time-Dependent Materials Springer Journals

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

Mechanics of Time-Dependent Materials , Volume OnlineFirst – Jan 19, 2022

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer Nature B.V. 2022
ISSN
1385-2000
eISSN
1573-2738
DOI
10.1007/s11043-021-09518-9
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Mechanics of Time-Dependent MaterialsSpringer Journals

Published: Jan 19, 2022

Keywords: Fractional order derivative; Fractional order strain; Generalized thermo-viscoelasticity; Thermal-mechanical shock; Spherical cavity

References