On the influence of voids on the depth of an external signal in thermoelasticity with two relaxation times

Carini, Manuela; Zampoli, Vittorio

doi:10.1007/s00707-019-02547-z

Cited by 2 publications

(3 citation statements)

References 33 publications

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“…The issue appears particularly relevant also in light of the unexpected indications obtained through the numerical simulations in [27] and, in our opinion, it can actively contribute to the comprehension of the thermal exchange mechanisms involving materials with a porous skeleton at micro-and nanoscales in very fast transients. As for the hypothesis of thermal effects small enough to allow the activation of linearity assumptions, we believe that it is consistent with the evolution of a phenomenon that occurs in an extremely rapid transient; coherently, any involvement of thermal deformations of greater magnitude would probably entail a real behavior of the material gradually less superimposable to that predicted by the current model.…”

Section: Introductionmentioning

confidence: 92%

“…We premise that our reference will be the work of Ieşan [30] in order to take into account the presence of pores into the thermoelastic matrix (similarly to [26,27]). Our study is framed into a fixed Cartesian system of axes Ox 1 x 2 x 3 , and the common summation and differentiation conventions are used.…”

Section: Mathematical Formulation: Identification Of the Proposed Thementioning

confidence: 99%

“…The present work has to be considered as the natural continuation of the path recently traced in [26,27], where porous material matrices were investigated when coupled with heat transfer phenomena modeled through time-differential constitutive laws with two relaxation times. This was done not only in terms of well-posedness of the theory, but also obtaining interesting information about the influence of the voids on the model's response to certain external stimulations.…”

Section: Introductionmentioning

confidence: 99%

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On Porous Matrices with Three Delay Times: A Study in Linear Thermoelasticity

Carini

Zampoli

2020

Mathematics

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Through the present work, we want to lay the foundation of the well-posedness question for a linear model of thermoelasticity here proposed, in which the presence of voids into the elastic matrix is taken into account following the Cowin-Nunziato theory, and whose thermal response obeys a three-phase lag time-differential heat transfer law. By virtue of the linearity of the model investigated, the basic initial-boundary value problem is conveniently modified into an auxiliary one; attention is paid to the uniqueness question, which is addressed through two alternative paths, i.e., the Lagrange identity and the logarithmic convexity methods, as well as to the continuous dependence issue. The results are achieved under very weak assumptions involving constitutive coefficients and delay times, at most coincident with those able to guarantee the thermodynamic consistency of the model.

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Section: Introductionmentioning

confidence: 92%