Advanced Mathematical Models & Applications

This paper presents mathematical models for predicting the durability of materials intended for use in the manufacturing of nanosatellites, considering both simple and complex stress states. The material damage process is examined in two phases. In the first phase, analytical formulas for the incubation period (latent damage) are derived using a criterion-based approach, considering fixed, exponential, and Abel kernels for the damage operator. In the second phase, an integral equation of the Volterra type, characterizing the failure process, is derived and solved based on the classical strength criterion, accounting for hereditary-type damaged materials. Time dependence graphs of the damage process were constructed using the obtained results and comparisons were made. The research determined that for the exponential case of the damage operator kernel, the incubation period constitutes 12.5% and 5.6% of the total failure time for mechanical memory coefficients of 0.3 and 0.2, respectively.