Bio-thermo-mechanics behavior in living viscoelastic tissue under the fractional dual-phase-lag theory

Ezzat, Magdy A.

doi:10.1007/s00419-021-01984-4

Cited by 33 publications

(10 citation statements)

References 42 publications

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“…Combining with equation ( 6) and Taylor series expansion of the Caputo fractional derivative yields 34,41…”

Section: Fdpl Heat Conduction Modelmentioning

confidence: 99%

“…To describe the memory-dependence caused by the heat transfer at time microscale, the generalized thermoelastic theories were further extended into fractional-order ones. [32][33][34] In follow-up studies, the transient response analyses of microstructures under the fractional-order thermoelasticity were further studied. 35,36 Subsequently, the fractional order dual-phase-lag (FDPL) thermoelasticity about dynamic response has made remarkable progress.…”

Section: Introductionmentioning

confidence: 99%

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Fractional dual-phase-lag thermal-mechanical response of an functionally graded spherical microshell with size-dependent effect

Peng,

Pan

2024

The Journal of Strain Analysis for Engineering Design

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Functionally graded materials (FGM) have attracted much attention due to their superior thermal shock resistance in extreme thermal environment. In addition, the memory-dependent feature of transient heat transfer progress can’t be reflected in the frame of integer-order heat conduction model due to the inability of depicting the effect of the past states on the current state. It is noticed that the size-dependent effect of elastic deformation has become significant due to the development of micro-devices. To describe the memory-dependent effect and the size-dependent effect in the functionally graded microstructures, the work aims a thermoelastic model by incorporating the fractional dual-phase-lag heat conduction model and the Eringen’s nonlocal model. To illustrate its application values, the modified model is used to investigate the dynamic performance of an functionally graded spherical microshell subjected to a thermal-mechanical loading. Governing equations including the modified parameters are derived and solved by Laplace transformation. The achieved results show that considering the influences of nonlocal effect and ceramic composition will reduce the thermal deformation under ultrafast heating condition.

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“…Combining with equation ( 6) and Taylor series expansion of the Caputo fractional derivative yields 34,41…”

Section: Fdpl Heat Conduction Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Fractional dual-phase-lag thermal-mechanical response of an functionally graded spherical microshell with size-dependent effect

Peng,

Pan

2024

The Journal of Strain Analysis for Engineering Design

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“…Several papers relating to generalized thermoelasticity theories have been presented in Refs. [10–24].…”

Section: Introductionmentioning

confidence: 99%

“…Several papers relating to generalized thermoelasticity theories have been presented in Refs. [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Effect of gravity and initial stress on a nonlocal thermo‐viscoelastic medium with two‐temperature and fractional derivative heat transfer

2022

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The basic equations for a nonlocal thermoelastic–viscoelastic medium are formulated based on the multi‐phase‐lag model with a fractional derivative heat transfer. Using suitable nondimensional variables, the problem is solved using the Fourier series and Laplace transforms to solve the problem of a thermal shock problem to obtain the exact expressions of physical fields. The numerical results obtained have been illustrated graphically to illustrate the effect of the initial stress, gravity, nonlocal parameter, two‐temperature parameter, and time‐fractional derivative parameter on the physical variables.

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“…The fractional derivative or integral does not reflect merely the nature or quantity of a local area or a single point, but a way of comprehensive consideration, which is more appropriate to describe these problems than an integer order model. Therefore, fractional calculus has been widely used in dynamic systems such as vibration control, [13][14][15][16] viscoelastic material [17][18][19] modeling and so on. So far, the solution of fractional order dynamic system and the analysis of dynamic characteristics become very important.…”

Section: Introductionmentioning

confidence: 99%

Analysis of resonance and bifurcation in a fractional order nonlinear Duffing system

Bai

Yang

Xie

et al. 2022

Math Methods in App Sciences

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In this paper, resonance and bifurcation of a nonlinear damped fractional‐order Duffing system are studied. The amplitude and phase of the steady‐state response of system are obtained by means of the average method, the stability is analyzed, and then the amplitude‐frequency characteristic curves of the system with different parameters are drawn based on the implicit function equation of amplitude. Grunwald–Letnikov fractional derivative is used to discretize the system numerically, the response curve and phase trajectory of the system under different parameters are obtained; meanwhile, the dynamic behavior is analyzed. The bifurcation and saddle bifurcation behavior of the system is studied through numerical simulation with different parameters.

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Bio-thermo-mechanics behavior in living viscoelastic tissue under the fractional dual-phase-lag theory

Cited by 33 publications

References 42 publications

Fractional dual-phase-lag thermal-mechanical response of an functionally graded spherical microshell with size-dependent effect

Fractional dual-phase-lag thermal-mechanical response of an functionally graded spherical microshell with size-dependent effect

Effect of gravity and initial stress on a nonlocal thermo‐viscoelastic medium with two‐temperature and fractional derivative heat transfer

Analysis of resonance and bifurcation in a fractional order nonlinear Duffing system

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