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

  • Manuela CariniEmail author
  • Vittorio Zampoli
Original Paper


This work aims to highlight, by a series of simulations, the effect of the presence of pores in the material matrix on the transmission depth of a thermomechanical signal: two linear thermoelastic models are considered, for which the thermal response obeys a time-differential constitutive equation with two relaxation times, derived from the dual-phase lag theory. A porous material matrix, modeled on the basis of the Cowin–Nunziato theory, is compared with its counterpart without voids: this is done under hypotheses of linearity, compatible with the assumption to deal with very small spatial scales, in the order of the micrometer or nanometer. The results of such simulations are graphically presented and are completely unexpected; in the opinion of the authors, they can represent an interesting starting point for further discussions and insights.

Mathematics Subject Classification

74A15 74F10 74G55 



Vittorio Zampoli acknowledges the Italian National Group of Mathematical Physics (GNFM-INdAM) for supporting the research projects Progetto Giovani 2018 Heat-pulse propagation in FGMs and Progetto Giovani 2019 On a thermodynamically consistent reformulation of the Becker and Döring model for two-phase materials.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dipartimento di Ingegneria per l’Ambiente e il Territorio e Ingegneria ChimicaUniversità della CalabriaArcavacata di RendeItaly
  2. 2.Dipartimento di Ingegneria dell’Informazione ed Elettrica e Matematica ApplicataUniversità di SalernoFiscianoItaly

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