Fractal Models for Investigating Self-Similar Structures in Medical Engineering

In this work, two-dimensional fractional-differential rheological models were developed, taking into account the anisotropy of mechanical properties, which can be used to investigate the self-similar structure of biomedical materials. To account for non-local interaction and the “memory” effect of viscoelastic properties of the media, an integral form of the two-dimensional models’ representation was obtained. Based on the Maxwell model, a numerical implementation algorithm was introduced, utilizing the finite difference method. Numerical studies were conducted, and a series of regularities regarding the influence of the fractal structure and density of the material in different directions of anisotropy on the deformation process were obtained.