Fractional-order rate-dependent porous-thermo-elasticity model based on new fractional derivatives with non-singular kernels and 1D transient dynamic response analysis of magnesium-based porous half-space with voids

Abstract

Nowadays, the extensive applications of the ultrafast heating technologies (e.g., laser burst, induction heating, etc.) in the fabricating and manufacturing of the porous elastic solids (e.g., cellular material, mesoporous material, macroporous material, etc.) have aroused great interests on investigating the constitutive modeling and transient dynamic responses analysis of the porous-thermo-elastic coupling. Although the fractional temperature rate-dependent porous-thermo-elasticity theories have been historically proposed, the theoretical formulations still adopt the classical fractional derivatives with singular kernels, and the inherent strain relaxation effect and the associated memory dependency are not considered yet in the ultrafast heating condition. To compensate for such deficiency, the present work aims to establish a fractional-order rate-dependent porous-thermo-elasticity model based on the new fractional derivatives with the non-singular kernels (i.e., Caputo–Fabrizio, Atangana–Baleanu, and tempered Caputo fractional derivatives). With the aids of the extended thermodynamic principles, the new constitutive and governing equations are obtained. The proposed theoretical model is applied to investigate the 1D transient dynamic response analysis of magnesium-based porous half-space with voids by applying the Laplace transformation approach. The influences of the new fractional derivatives on the wave propagations and structural transient dynamic responses are evaluated and discussed.