Modeling Conformable Fractional Order Theory and Temperature–dependent Properties on a Non-local Thermoelastic Material with Multi-temperatures

This paper presents a comprehensive study on the thermoelastic and visco-elastic behavior of fiber-reinforced materials, incorporating the effects of various parameters such as conformable fractional order, multi-temperature theory, non-local interactions, and temperature-dependent material properties. Normal-mode analysis is used to solve the system's governing equations, offering detailed insights into the material's thermal and mechanical behavior under dynamic loading. Conformable fractional parameter is introduced to capture the material's memory effects and long-range interactions. At the same time, the multi-temperature theory accounts for the influence of different temperature fields within the system. The non-local parameter is also incorporated to account for the impact of microstructural effects and long-range interactions. The temperature-dependent effect is modeled to reflect how variations in material properties with temperature affect the system's overall behavior. These factors are studied graphically to evaluate their impact on stress, strain, and temperature distribution, offering a deeper understanding of the material's performance under various thermal and mechanical conditions. The results contribute to designing and optimizing advanced composite materials, providing a more accurate prediction of their behavior in complex environments.