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H. Youssef, Eman Al-Lehaibi (2010)
Fractional order generalized thermoelastic half-space subjected to ramp-type heatingMechanics Research Communications, 37
S.S. Sherbakov (2019)
207Devices Methods Meas., 10
S. Mashayekhi, P. Miles, M. Hussaini, W. Oates (2018)
Fractional viscoelasticity in fractal and non-fractal media: Theory, experimental validation, and uncertainty analysisJournal of The Mechanics and Physics of Solids, 111
M. Biot (1956)
Thermoelasticity and Irreversible ThermodynamicsJournal of Applied Physics, 27
H. Lord, Y. Shulman (1967)
A GENERALIZED DYNAMICAL THEORY OF THERMOELASTICITYJournal of The Mechanics and Physics of Solids, 15
Q. Xiong, X. Tian (2012)
Thermoelastic Study of an Infinite Functionally Graded Body with a Cylindrical Cavity Using the Green-Naghdi ModelJournal of Thermal Stresses, 35
M. Ezzat (2011)
Magneto-thermoelasticity with thermoelectric properties and fractional derivative heat transferPhysica B-condensed Matter, 406
Yongbin Ma, Tianhu He (2017)
The transient response of a functionally graded piezoelectric rod subjected to a moving heat source under fractional order theory of thermoelasticityMechanics of Advanced Materials and Structures, 24
H. Youssef (2010)
Theory of Fractional Order Generalized ThermoelasticityJournal of Heat Transfer-transactions of The Asme, 132
I. Abbas, H. Youssef (2015)
Two-Dimensional Fractional Order Generalized Thermoelastic Porous MaterialLatin American Journal of Solids and Structures, 12
PROGRAMS FOR FAST NUMERICAL INVERSION OF LAPLACE TRANSFORMS IN MATLAB LANGUAGE ENVIRONMENT
R. Bagley, P. Torvik (1983)
A Theoretical Basis for the Application of Fractional Calculus to ViscoelasticityJournal of Rheology, 27
V. Peshkov (1944)
381J. Phys., 8
M. Ghosh, M. Kanoria (2008)
Generalized thermoelastic functionally graded spherically isotropic solid containing a spherical cavity under thermal shockApplied Mathematics and Mechanics, 29
M. Caputo, F. Mainardi (1971)
Linear models of dissipation in anelastic solidsLa Rivista del Nuovo Cimento (1971-1977), 1
M. Ezzat, A. El-Karamany, A. El-Bary (2014)
Generalized thermo-viscoelasticity with memory-dependent derivativesInternational Journal of Mechanical Sciences, 89
I.A. Abbas (2016)
84J. Assoc. Arab Univ. Basic Appl. Sci., 20
Stefano Aime, L. Cipelletti, L. Ramos (2018)
Power law viscoelasticity of a fractal colloidal gelJournal of Rheology
M. Caputo (1974)
Vibrations of an infinite viscoelastic layer with a dissipative memoryJournal of the Acoustical Society of America, 56
F. Meral, T. Royston, R. Magin (2010)
Fractional calculus in viscoelasticity: An experimental studyCommunications in Nonlinear Science and Numerical Simulation, 15
H. Sherief, A. El-Sayed, A. El-Latief (2010)
Fractional order theory of thermoelasticityInternational Journal of Solids and Structures, 47
A. Bahdanovich (2019)
292Mater. Sci., 25
S. Shcherbakov (2013)
State of Volumetric Damage of Tribo-Fatigue SystemStrength of Materials, 45
H. Sherief, A. El-Latief (2015)
A one-dimensional fractional order thermoelastic problem for a spherical cavityMathematics and Mechanics of Solids, 20
(1958)
A form of heat conduction equation which eliminates the paradox of instantaneous propagation
T.H. He (2002)
1081Int. J. Eng. Sci., 40
H. Sherief, A. Elmisiery, M. Elhagary (2004)
GENERALIZED THERMOELASTIC PROBLEM FOR AN INFINITELY LONG HOLLOW CYLINDER FOR SHORT TIMESJournal of Thermal Stresses, 27
S. Shcherbakov (2012)
Modeling of the damaged state by the finite-element method on simultaneous action of contact and noncontact loadsJournal of Engineering Physics and Thermophysics, 85
A. Bahdanovich, R. Bendikiene, R. Česnavičius, A. Ciuplys, V. Grigas, A. Jutas, D. Marmysh, Aleh Mazaleuski, A. Nasan, Liudmila Shemet, S. Sherbakov, Kestutis Spakauskas, L. Sosnovskiy (2019)
Research on Tensile Behaviour of New Structural Material MoNiCaMaterials Science
I. Abbas (2016)
Eigenvalue approach to fractional order thermoelasticity for an infinite body with a spherical cavityJournal of the Association of Arab Universities for Basic and Applied Sciences, 20
M. Caputo, F. Mainardi (1971)
A new dissipation model based on memory mechanismpure and applied geophysics, 91
R. Bendikiene, A. Bahdanovich, R. Česnavičius, A. Ciuplys, V. Grigas, A. Jutas, D. Marmysh, A. Nasan, Liudmila Shemet, S. Sherbakov, L. Sosnovskiy (2020)
Tribo-fatigue Behavior of Austempered Ductile Iron MoNiCa as New Structural Material for Rail-wheel SystemMaterials Science, 26
Y. Yu, Zhangna Xue, X. Tian (2018)
A modified Green–Lindsay thermoelasticity with strain rate to eliminate the discontinuityMeccanica, 53
J. Maxwell (1868)
IV. On the dynamical theory of gasesPhilosophical Transactions of the Royal Society of London
(2002)
State space approach to one-dimensional thermal shock problem for a semiinfinite piezoelectric rod
C. Cattaneo (1958)
431Cr. Phys., 247
E. Bassiouny, H. Youssef (2018)
Sandwich structure panel subjected to thermal loading using fractional order equation of motion and moving heat sourceCanadian Journal of Physics, 96
L. Sosnovskii, V. Komissarov, S. Shcherbakov (2012)
A method of experimental study of friction in a active systemJournal of Friction and Wear, 33
(2010)
Peshkov, V.: Second sound in helium II
A. El-Karamany, M. Ezzat (2017)
Fractional phase-lag Green–Naghdi thermoelasticity theoriesJournal of Thermal Stresses, 40
M. Zhuravkov, N Romanova (2016)
Review of methods and approaches for mechanical problem solutions based on fractional calculusMathematics and Mechanics of Solids, 21
A. Green, K. Lindsay (1972)
ThermoelasticityJournal of Elasticity, 2
M. Paola, A. Pirrotta, A. Valenza (2011)
Visco-elastic behavior through fractional calculus: An easier method for best fitting experimental resultsMechanics of Materials, 43
Xiaoya Li, Zhangna Xue, X. Tian (2018)
A modified fractional order generalized bio-thermoelastic theory with temperature-dependent thermal material propertiesInternational Journal of Thermal Sciences
V. Peshkov (1944)
Second sound in helium IIJ. Phys., 8
L. Brancik (1999)
27
H. Youssef, Eman Al-Lehaibi (2019)
State-space approach to three-dimensional generalized thermoelasticity with fractional order strainMechanics of Advanced Materials and Structures, 26
A. Green, P. Naghdi (1993)
Thermoelasticity without energy dissipationJournal of Elasticity, 31
S. Warbhe, J. Tripathi, K. Deshmukh, J. Verma (2018)
Fractional heat conduction in a thin hollow circular disk and associated thermal deflectionJournal of Thermal Stresses, 41
H. Sherief, H. Saleh (2005)
A half-space problem in the theory of generalized thermoelastic diffusionInternational Journal of Solids and Structures, 42
Yongbin Ma, W. Peng (2018)
Dynamic response of an infinite medium with a spherical cavity on temperature-dependent properties subjected to a thermal shock under fractional-order theory of thermoelasticityJournal of Thermal Stresses, 41
S. Sherbakov (2019)
Measurement and Real Time Analysis of Local Damage in Wear-and-Fatigue TestsDevices and Methods of Measurements
(1958)
Paradoxes in the continuous theory of the heat equation
P.M. Vernotte (1958)
3154C. R. Acad. Sci. Paris, 246
H. Youssef, Eman Al-Lehaibi (2010)
Variational principle of fractional order generalized thermoelasticityAppl. Math. Lett., 23
H. Youssef (2016)
Theory of generalized thermoelasticity with fractional order strainJournal of Vibration and Control, 22
R. Bendikiene (2020)
432Mater. Sci., 26
S. Shcherbakov (2013)
Spatial stress-strain state of tribofatigue system in roll–shaft contact zoneStrength of Materials, 45
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.
Mechanics of Time-Dependent Materials – Springer Journals
Published: Dec 1, 2022
Keywords: Fractional order derivative; Fractional order strain; Generalized thermo-viscoelasticity; Thermal-mechanical shock; Spherical cavity
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