Effective thermo-electro-mechanical properties of Menger sponge-like fractal structures: a finite element study

Menger sponges are hierarchical structures with tunable mechanical and electrical properties. In this work, different orders (0th, 1st, 2nd and 3rd) of hierarchical structures were studied for their effective properties by square, circular and hexagonal-shaped cavities. The elastic modulus, Poisson’s ratio, thermal and electrical conductivities were investigated as a functions of the density. The variation of normalized parameters with normalized density for square, cylindrical, and hexagonal-shaped cavities was used to obtain the empirical relations. The normalized specific modulus and Poisson’s ratio were validated using available analytical models for all cavities. The normalized Poisson’s ratio, thermal conductivity and electrical conductivity decreased with a reduction in the effective density. The effect of a different cavity (square, cylindrical and hexagonal) on the Menger sponge’s mechanical and electrical behaviour shows variation after the effective density falls below 0.8. Menger sponge with a square cavity shows the maximum decrement in thermal and electrical conductivity among other cavities with increasing order of structure. Menger sponge with hexagonal cavity consists of least reduced normalized thermal and electrical conductivity with decreasing effective density. An increment in the order of fractals leads to a near-zero value for Poisson’s ratio. These structures can be used for medical, aerospace, and industrial applications according to the properties required in different applications.