On the relationship between young's modulus, shear modulus and Poisson's ratio

Young's modulus measures stretching or compression resistance, shear modulus characterizes shearing resistance, and Poisson's ratio describes lateral deformation when subjected to axial loads. This work establishes a mathematical framework to elucidate the connections between these properties, providing insights into their interdependence and practical significance. It includes equations, graphs, and examples to visually depict the relationships and emphasizes the importance of these properties in material science and engineering. The study enhances understanding and inform material selection, structural design, and failure analysis.