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

doi:10.1007/s11043-021-09518-9

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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
	Peng, Wei 1; Chen, Like 2; He, Tianhu 1,3
刊名	MECHANICS OF TIME-DEPENDENT MATERIALS
	2022
关键词	Fractional order derivative Fractional order strain Generalized thermo-viscoelasticity Thermal-mechanical shock Spherical cavity
ISSN号	1385-2000
DOI	10.1007/s11043-021-09518-9
英文摘要	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.
WOS研究方向	Mechanics ; Materials Science
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000744402200001
内容类型	期刊论文
源URL	[http://ir.lut.edu.cn/handle/2XXMBERH/154840]
专题	研究生院
作者单位	1.Lanzhou Univ Technol, Key Lab Disaster Prevent & Mitigat Civil Engn Gan, Lanzhou 730050, Peoples R China; 2.Lanzhou Univ, Sch Civil Engn & Mech, Lanzhou 730000, Peoples R China; 3.Lanzhou Univ Technol, Sch Sci, Lanzhou 730050, Peoples R China
推荐引用方式 GB/T 7714	Peng, Wei,Chen, Like,He, Tianhu. A modified fractional order thermo-viscoelastic theory with fractional order strain and its application in a thermo-viscoelastic problem containing a spherical cavity[J]. MECHANICS OF TIME-DEPENDENT MATERIALS,2022.
APA	Peng, Wei,Chen, Like,&He, Tianhu.(2022).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.
MLA	Peng, Wei,et al."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 (2022).