The unit cell method in predictions of thermal expansion properties of textile reinforced composites

Thermal expansion properties of textile reinforced composites with certain structure symmetries can be efficiently calculated by a size-limited unit cell. In this paper, a general approach is developed for the establishment of such a unit cell model. For the derivation of unit cell boundary conditions, three rules are summarized according to the displacement fields in translational, reflectional and 180° rotational symmetric structures under a uniform temperature change loading. The application scope of present unit cell method is clarified from the thermal and mechanical point of views. Three typical composites, i.e., unidirectional fiber reinforced composite, plain woven composite and multi-harness (4HS, 5HS, 6HS, 7HS and 8HS) satin woven composites are then studied, and four, three and two size-reducing unit cells are formulated, respectively. The thermal expansion behaviors of each composite are analyzed, and the effective thermal expansion coefficients are predicted. The influence of structure symmetries on the deformation pattern of unit cell models is clarified. The numerical models are validated by the identical results obtained from unit cells of different sizes and also by the results available in literatures. The approach developed in this paper can be applied to thermal expansion studies of any other composites with relevant structure symmetries.