MATHEMATICAL ANALYSIS OF THE THERMAL RESPONSE OF COCOON POROUS HIERARCHICAL STRUCTURE CAUSED BY A SUDDEN THERMAL SHOCK

Some extreme properties of cocoons are first revealed, which are extremely helpful for practical applications in the textile field (e.g., spacesuits and firefighters' clothing) and architectural engineering (e.g., thermal insulation coatings of buildings). The aim of this work is to study the cocoons' thermal response to a sudden thermal shock and explain it physically from the direction ofmathematical analysis. The cocoon is considered a fractal space, and a fractal variational theory is established to present its excellent advantages regarding thermal shock. The two-scale fractal dimension of the cocoon's hierarchical structure plays an important role in its biomechanism, and its value is close to 1.618, the golden mean, implying an optimal porous structure for pupa to survive in an extreme environment.