Numerical realization of asymptotic homogenization method for thermoelastic multidirectional composites

摘要

In this study, a zero approximation of thehomogenization technique [1] is applied to investigate thestructural stresses in structures made of composite materials,which are subjected to mechanical loading and high-temperatureheating. A carbon-carbon composite material reinforced withanisotropic fibers in three mutually orthogonal directions in theratio 1:1:1 is considered. According to the method ofhomogenization, the local functions, namely the components ofthe tensor of elastic moduli and of the thermoelasticity tensor in azero approximation must be determined by solving a set ofproblems for a periodicity cell. The effective thermoelasticconstants of the composite are found by averaging the obtainedlocal functions over the periodicity cell. To found the structuralstresses in constructions, the periodic local functions and the fieldof macrostrains must be known, which are obtained from thesolution of the homogenized boundary value problem. Theproblems posed for the periodicity cell are solved by the method offinite elements. The average values of the local functions and themeasures of deviation from them are examined for varioustemperatures and volume fractions of fibers of two different cross-sectional shapes.