¹Financial University under the Government of the Russian Federation, Moscow, Russia
²K.G.Razumovsky Moscow State University of Technologies and Management, Moscow, Russia
³Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow, Russia
⁴Moscow Polytechnic University, Moscow, Russia
⁵Institute of Contemporary Art, Moscow, Russia

Abstract. The work is devoted to the use of methods of applied mathematics and statistics for the formalization and mathematical modeling of the structure of shark skin as a prototype of new polymer materials for shipbuilding purposes. A technique for mathematical modeling of biological objects is described, and a method for using a biomimetic approach for the design of planar composite polymer materials with improved lyophilic adhesion properties is proposed. Because of studying images of shark skin obtained using high-resolution optical (HRO) and scanning electron (SEM) microscopy, we found that its texture is anisotropic. Quantitative analysis of BOM and SEM images made it possible to rationalize the choice of synthetic digital models intended for simulation prototyping of maximally and minimally texturally isotropic polymer samples using 3D printing and gas-phase surface modification.

Key words: digital models, creation of materials, scanning electron microscopy, nature similarity, biomimetics, image analysis, two-dimensional Fourier series, tribological properties.