Fractional-order rate-dependent thermoelastic diffusion theory based on new definitions of fractional derivatives with non-singular kernels and the associated structural transient dynamic responses analysis of sandwich-like composite laminates

Abstract

Nowadays, the ultrafast heating technologies (e.g., laser-aided material processing, etc.) have been extensively applied in the manufacturing and micro-machining of microelectronic and semiconductor devices (e.g., field-effect transistor, etc.). In recent years, there have been a large number of literatures contributed on constitutive modeling and transient dynamic responses analysis of the coupled thermoelastic diffusion to provide a comprehensive understanding on multi-field coupling behavior on this topic and avoid the unwanted vibration response in intelligent active vibration control. Although the rate-dependent thermoelastic diffusion theories have been historically proposed, the memory-dependence characteristics of strain relaxation as well as heat conduction and mass diffusion are still not considered in ultrafast heating condition. To compensate for such deficiency, a fractional-order rate-dependent thermoelastic diffusion theory is established in this work by introducing the new fractional derivatives with non-singular kernels (i.e., the Atangana-Baleanu and the Tempered-Caputo definitions) into the strain rate dependent constitutive equation as well as classical Fourier heat conduction and Fick mass diffusion laws. With the aids of the extended thermodynamic principles, the new constitutive and governing equations are obtained. The proposed theory is applied to investigate the structural dynamic responses of sandwich-like composite laminates subjected to axisymmetric transient thermal and chemical shock loadings by using Laplace transformation approach. The influences of the different fractional derivatives and material constants ratios on wave propagations and structural dynamic responses are evaluated and discussed.