Symmetry in a problem of transverse shear of unidirectional composites

Unidirectional fibre-reinforced composites with symmetrical structure, loaded by transverse shear, are investigated. The focus of the paper is on mathematical models for different representative cells. Transverse shear of symmetrical composites, unlike other types of loads, does not allow application of Curie’s principle for detection of possible symmetry of mechanical fields. The existence of such symmetry is shown by employing the theorem proven earlier by the author. Respective boundary value problems can be formulated for the minimal representative cell. In contrast to the existing approach, which contains inaccuracy of Saint–Venant’s principle, the proposed formulations are exact. It is shown that employing the symmetry cell in numerical solutions can reduce computational cost by 2–3 orders. With the use of Lagrange’s and Castigliano’s variational principles in generalised form, it is proven that solutions for the “infinite” cell give lower and upper bounds for the transverse shear modulus. It is proven, as well, that these bounds lie within the Voigt and Reuss bounds.