Discuss the interplay between material properties and structural design in civil engineering, considering factors such as stress, strain, and deformation. Explore how advancements in materials science have influenced the evolution of structural engineering practices, and evaluate the challenges and opportunities presented by emerging materials such as carbon fiber composites and self$-$healing concrete. Illustrate your arguments with relevant case studies and propose innovative approaches to address the complexities of material selection and structural integrity in modern civil engineering projects.