Thermoelastic behavior of temperature-dependent materials using conformable fractional derivative and multi-temperature theory

Abstract

This paper presents a comprehensive study of the thermoelastic behavior of a two-dimensional generalized thermoelastic material characterized by a single relaxation time. The study incorporates the effects of various factors, including conformable fractional order, multi-temperature theory, and temperature-dependence for the material properties. We employ wave analysis to solve the governing equations and boundary conditions for the system, providing insights into the thermal and mechanical responses of the material under dynamic loading. The conformable fractional parameter is introduced to capture the material's memory effects and long-range interactions, while the multi-temperature theory accounts for the influence of different temperature fields within the system. Additionally, temperature-dependent material properties are modeled to assess how variations in temperature affect the system's behavior. These factors are studied graphically to evaluate their impact on stress, displacement, and temperature distribution, offering a deeper understanding of the material's performance under various thermal and mechanical conditions. The results contribute to the design and optimization of advanced composite materials, providing more accurate predictions of their behavior in complex environments.