Second gradient Green–Naghdi type thermo-elasticity and viscoelasticity

Fabrizio, Mauro; Franchi, Franca; Nibbi, Roberta

doi:10.1016/j.mechrescom.2022.104014

Cited by 7 publications

(2 citation statements)

References 22 publications

(40 reference statements)

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“…We assume that all the relevant functions are sufficiently smooth on the real line such that the Fourier transform of these functions exists. According to the homogeneous initial conditions (39), upon applying the Laplace transform on both sides of Equations ( 32) and (33), we arrive at…”

Section: Solutions In the Integral-transform Domainmentioning

confidence: 99%

“…When τ ε → 0 , the Hookean response is recovered, i.e., σ = Eε. The Kelvin-Voigt thermoelasticity has been considered in a variety of viscoelastic applications, e.g., unbounded thermoviscoelastic domain with spherical cavity [35], vibration of an Euler Bernoulli beam [36,37], and micropolar thermoelasticity [38], and has been extended to the second-gradient media [39].…”

Section: Introductionmentioning

confidence: 99%

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Anomalous Thermally Induced Deformation in Kelvin–Voigt Plate with Ultrafast Double-Strip Surface Heating

et al. 2023

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The Jeffreys-type heat conduction equation with flux precedence describes the temperature of diffusive hot electrons during the electron–phonon interaction process in metals. In this paper, the deformation resulting from ultrafast surface heating on a “nanoscale” plate is considered. The focus is on the anomalous heat transfer mechanisms that result from anomalous diffusion of hot electrons and are characterized by retarded thermal conduction, accelerated thermal conduction, or transition from super-thermal conductivity in the short-time response to sub-thermal conductivity in the long-time response and described by the fractional Jeffreys equation with three fractional parameters. The recent double-strip problem, Awad et al., Eur. Phy. J. Plus 2022, allowing the overlap between two propagating thermal waves, is generalized from the semi-infinite heat conductor case to thermoelastic case in the finite domain. The elastic response in the material is not simultaneous (i.e., not Hookean), rather it is assumed to be of the Kelvin–Voigt type, i.e., σ=Eε+τεε˙, where σ refers to the stress, ε is the strain, E is the Young modulus, and τε refers to the strain relaxation time. The delayed strain response of the Kelvin–Voigt model eliminates the discontinuity of stresses, a hallmark of the Hookean solid. The immobilization of thermal conduction described by the ordinary Jeffreys equation of heat conduction is salient in metals when the heat flux precedence is considered. The absence of the finite speed thermal waves in the Kelvin–Voigt model results in a smooth stress surface during the heating process. The temperature contours and the displacement vector chart show that the anomalous heat transfer characterized by retardation or crossover from super- to sub-thermal conduction may disrupt the ultrafast laser heating of metals.

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Section: Solutions In the Integral-transform Domainmentioning

confidence: 99%