Discuss the theory and applications of materials science and engineering in mechanical design. Begin by explaining the structure$-$property relationships of materials, including crystalline structure, defects, and phase transformations. Explore the mechanical properties of materials, such as strength, stiffness, toughness, and ductility, and their implications in design considerations. Delve into the classification and selection of engineering materials based on their mechanical, thermal, and chemical properties for specific applications. Analyze the principles of failure analysis and fracture mechanics, including stress concentration, fatigue, and creep, and their significance in ensuring the reliability and safety of mechanical components. Furthermore, discuss emerging trends in materials science, such as nanomaterials, composites, and additive manufacturing, and their potential impact on future mechanical design paradigms.