Biological processes as factor of variability of c/c composites with a damaged pyrolytic carbon matrix

C/C composites are promising for use in the field of implantology. The technology for obtaining C/C composites allows one to adjust the physical and mechanical properties over a wide range and change the material's scope. A distinctive feature of the C/C composite as a functional material, in comparison with traditional materials, is the characteristic range of properties, which is due to the structure of the pyrolytic carbon matrix. The pyrolytic carbon matrix has a stochastic structure, which determines its mechanical behavior at the crystallite dimensional level. Stress fluctuations in the matrix grains lead to damage to the grains and a change in the mechanical state, and the accumulation of damage to a certain extent results in an increase in the load-bearing capacity of the implant made from the C/C composite. The damage occurs in specific areas of the C/C composite implant. The accumulation of damage in localized areas leads to a granular appearance of the matrix. In areas where the matrix is damaged, the bone tissue that forms during osteogenesis is also likely to be damaged. In the subsequent stages of osseointegration and bone remodeling, the biological environment penetrates into areas of increased permeability. The penetration of cells and growth factors occurs in a percolation-type manner. The result of these processes is a change in the elastic characteristics of the material in the damaged area. The aim of this work is to obtain asymptotic formulas based on percolation theory and probability theory, which allow the calculation of the altered elastic properties of a damaged pyrocarbon matrix as a result of the processes of osseointegration and bone remodeling. This study aims to expand the understanding of the C/C composite structure in order to improve the properties of the C/C composite and further enhance the effectiveness of endoprosthetics with C/C composite implants. The analytical results of the formulas obtained based on percolation theory demonstrate an increase in the volume compression modulus of the damaged pyrocarbon matrix by 16,1 %, and the shear modulus by 28,1%. The results obtained fit within the strict boundaries of elastic modules according to the Hashina – Shtrikman and Voigt – Reuss models.