Analysis of a heterogeneous functionally graded material with a spherical void exposed to time-dependent ramp-type heating according to the TPL heat conduction model.

Functionally graded materials (FGMs) are sophisticated composites distinguished by a progressive alteration in composition and characteristics, facilitating customized performance for particular applications. Their distinctive architecture facilitates improved mechanical characteristics, thermal resilience, and operational efficacy in domains such as aerospace, biomedical, and automotive engineering. This study presents a novel three-phase-lag (TPL) thermal conductivity model and examines the thermoelastic behavior of a functionally graded medium featuring a spherical void. The paper examines the coupled thermo-mechanical behavior under time-dependent slope-type heating given to the sphere's traction-free inner surface, addressing complex linkages often overlooked in previous research. This research meticulously investigates the influence of critical factors, relaxation times, and ramping time on the dynamic physical response. A rigorous Laplace transform methodology is used to resolve the governing equations, which yields extensive quantitative insights. The findings indicate that the dynamic behavior of functionally graded materials under complex mechanical and thermal loading situations can be more comprehensively understood. This study makes a significant contribution to the field by integrating the TPL model with functionally graded analysis. This represents a substantial progression in thermoelastic functionally graded analysis, with prospective applications in the design of advanced materials, optimization of thermal management systems, and smart material technologies.