Generalized thermoviscoelastic analysis with fractional order strain in a thick viscoelastic plate of infinite extent

Abstract

Viscoelastic materials (e.g. rubber, resin, concrete skeleton, etc.) serve as one of the most promising candidate for new multifunctional materials due to their excellent rheological properties, as they are widely used in biology, petroleum industry, chemical and civil engineering, and other areas. The interaction of high-heat-flux loads (e.g. ultrafast pulsed lasers) with viscoelastic materials is a hot topic of numerous theoretical and experimental studies. Nevertheless, classical and extended generalized thermoviscoelasticity models available in literatures cannot characterize the strain relaxation behavior for viscoelastic materials. In this work, the time-based fractional thermoviscoelasticity model is further extended with a new consideration of fractional order strain. The governing equations involving strain and thermal relaxation times as well as fractional order parameters of strain and heat flux are formulated and are also applied to investigate thermal shock problem of a transient heated thick viscoelastic plate of infinite extent. With the aids of Laplace transformation methods, the transient solutions are also obtained. Finally, the effects of fractional order parameters of strain and heat flux on the transient thermoviscoelastic responses are studied and discussed.

Keywords:

• Fractional calculus
• generalized thermoviscoelasticity
• strain relaxation time
• thermal relaxation time
• transient thermal shock

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This study was funded by National Natural Science Foundation of China (11372123).