OICC Press Journal of Solid Mechanics 2008-7683 17 3 2025 11 24 Kelvin-Voigt and Elastic Load-deflection Models under Special Relativity 270 279 10.60664/jsm.2025.1202747 EN Arezu Jahanshir Buein Zahra Technical University (BZT) Ekwevugbe Omugbe Department of Physics, University of Agriculture and Environmental Sciences Umuagwo, Imo State, Nigeria Journal Article 2025 11 24 The classical Kelvin-Voigt and elastic load-deflection models in describing the mechanical response of materials under applied forces in this fundamental research are described. When materials experience high-velocity deformations under supersonic motion, classical mechanics fails to account for essential relativistic effects such as time dilation and length contraction. This study extends these models by incorporating special relativity to improve the accuracy of stress-strain predictions in supersonic conditions. By relativistic behavior of motion, a theoretical framework for analyzing hypervelocity mechanism, structural-mechanical behavior of materials in aerospace applications, and the dynamic stability of supersonic velocities are provided. Our approach is particularly relevant for the development of smart materials, adaptive structural systems, and defensive shielding technologies used in space exploration and supersonic velocities. Furthermore, we explore the oscillatory behavior and energy dissipation mechanisms in relativistic regimes, offering insights into the stability and damping characteristics of high-velocity mechanical systems. The findings bridge the gap between classical continuum mechanics and relativistic physics, presenting a novel methodology for studying the deformation and load-bearing behavior of materials under extreme accelerations. These results have significant implications for advanced engineering applications, including spacecraft shielding, high-speed transportation, and next-generation aerospace structures.