Abstract
The change in the stress-strain state over time in structures and their elements from polymeric materials can be quite substantial. This is due to the pronounced rheology of the polymers. One of the most accurate laws of stress-strain bond is generalized nonlinear Maxwell-Gurevich equation, which takes into account three rheological parameters: the modulus of elasticity, the velocity modulus and the coefficient of initial relaxation viscosity. A significant influence on the physico-mechanical parameters of the polymer is also exerted by various factors: the presence of a temperature field and ionizing radiation, the presence of additives in the polymer and so on. The paper presents the results of mathematical modeling of a disc made of high-density polyethylene (HDPE) in an axisymmetric setting under the influence of mechanical axial pressure. This model is chosen because of the most frequent use of HDPE irradiated and with additives in medicine, including for the manufacture of orthopedic prostheses. Different compositions of HDPE are considered: under the influence of ionizing radiation, with additives of hydroxyapatite and with their combined effect. All physico-mechanical parameters of HDPE (dose of ionizing radiation and the fraction of hydroxyapatite injected) are described by mathematical expressions obtained in the scientific school of Professor B.M. Yazyev on the basis of an analysis of the corresponding polymer relaxation curves. The results of the solution of the problem have shown that the basic stresses (radial, circumferential and axial) vary in the course of time in different ways. The growth of the value of the primary basic stresses can be 2-2.5 times. If the analysis is carried out on the main stresses, then their value increases by approximately 1.5 times. Also, the change in the principal stresses is observed even when it is not observed for the basic stresses.
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