Final answer:
Violet-le-Duc was an advocate of cast iron, a material that gained widespread use during the Industrial Revolution thanks to the innovation in building techniques and structural engineering.
Step-by-step explanation:
The material that Violet-le-Duc was an advocate of is cast iron. During the Industrial Revolution, there was an increasing availability of new building materials such as iron, steel, and sheet glass, which drove the invention of new building techniques. Notably, Charles Bage's "fireproof" mill design which relied on cast iron and brick and Eaton Hodgkinson's introduction of the section beam led to the widespread use of iron construction. Violet-le-Duc, well-known for his work in the restoration of medieval buildings, recognized the structural and aesthetic potential of cast iron and was a prominent proponent of its use in architecture.