Transient thermal stress waves in microvoided cylindrical semiconductor metamaterials with bi-fractional heat conduction

Abstract

This paper presents a theoretical investigation of transient thermal stress wave propagation in microvoided cylindrical semiconductor metamaterials governed by a bi-fractional heat conduction model. The formulation is developed within the framework of generalized thermoelasticity with voids, where microvoids introduce additional microstructural interactions that significantly influence the material’s thermo-mechanical response. To capture the complex thermal memory effects occurring under rapid thermal loading, the classical heat conduction equation is extended through two fractional time derivatives, forming a bi-fractional heat transport model. The governing coupled equations for displacement, temperature, stress fields, and void volume fraction are derived in cylindrical coordinates and transformed into a solvable form using the Laplace transform. Analytical expressions for the thermoelastic fields are obtained in the transform domain and subsequently inverted numerically to evaluate their transient spatial behavior. Numerical simulations are performed on semiconductor metamaterial parameters to illustrate the influence of fractional orders and microvoid characteristics on the propagation of thermal stress waves. The results demonstrate that the presence of microvoids significantly modifies the amplitude, attenuation, and propagation speed of thermal stress waves, while the bi-fractional heat conduction mechanism introduces pronounced thermal memory effects that alter the stress distribution within the medium. These findings provide new insight into the thermo-mechanical behavior of microstructured semiconductor metamaterials subjected to transient thermal excitations and may contribute to the design of advanced microelectronic devices, photothermal systems, and thermal stress management technologies.