Stressed state of isotropic medium with spherical inclusions under omnidirectional pressure - Nikolay N. Fedonyuk (Труды Крыловского государственного научного центра, 2020)
Object and purpose of research. This study investigates polymeric composite material syntactic foam consisting of a polymeric matrix filled with glass microspheres. The main purpose of this study is to develop mathematical apparatus for calculation of stress concentrations generated in the medium by these spherical inclusions, thus paving the way to developing, at the next stage, a structured model for straining and failure of these materials due to hydrostatic compression. Materials and methods. The inputs for these studies were composition and structure of polymeric composites, as well as the properties of their components, i.e. polymeric matrix and glass microspheres. This task was accomplished as per linear elasticity theory methods. Main results. This work solved the problems of elasticity theory about stress concentration in the infinite medium with two spherical inclusions consisting of two layers with different geometry and physical & mechanical properties, and with one spherical inclusion (also double-layered) near the boundary of the medium. The mathematical apparatus developed in this study made it possible to create a calculation algorithm written in C++ language. Calculation results for stress concentration in the matrix with microspheres have been compared with FE calculation data and turned out to be in practically perfect correlation with them. Conclusion. These theoretical studies have shown that the mathematical apparatus suggested in this paper is a very powerful calculation tool that can be used to develop a structured model of straining and failure for heterogeneous materials (syntactic foam) under hydrostatic pressure.