The homogenization of multimodular composites at their longitudinal deformation - Grebenyuk, Sergii; Smoliankova, Tetiana; Klymenko, Mykhailo; Kudin, Oleksii (Eastern-European Journal of Enterprise Technologies, 2020)
A model has been proposed of the homogenization of a transversally-isotropic composite material, whose mechanical characteristics differ at the longitudinal stretching and compression. On its basis, the longitudinal elasticity module of the first kind has been derived, as well as a Poisson coefficient for a multimodular composite. These indicators are necessary to design structural elements made from composites. The object of the study is a unidirectional fibrous composite consisting of the isotropic elastic matrix and fibers. To determine the effective elastic constants, an approach has been suggested, which is based on the use of conditions for the alignment of the displacements of points in the homogenized composite, matrix, and fiber. First, the displacements and stresses are determined for the matrix and fiber points at their joint axisymmetric stretching. An equation from the multimodular theory of elasticity was preliminarily obtained for solving this problem. Similar components of the stressed-strained state are determined at the same deformation of the cylindrical cell made from a homogeneous transversally-isotropic composite. The conditions for the displacement alignment, derived in solving the specified problems, are the equality of axial displacements in an arbitrary cross-section of the composite by a plane, parallel to the isotropy plane, and the radial displacements at the surface of the composite cell. The result of applying these conditions is the derived formulae for effective constants – the longitudinal module of elasticity of the first kind and a Poisson coefficient, which express these indicators through the mechanical characteristics of the matrix and fiber, as well as the proportion of fibers in the composite cell volume. Similar formulae have been obtained for the longitudinal compression. The derived effective elastic characteristics of a transversally-isotropic composite could be used when calculating the stressed-strained state of the structural elements made from it. In this case, one takes into consideration differences in the values of stresses and deformations under axial stretching and compression