Longitudinal shearing of elastic-plastic fibrous composite with frictional fibre-matrix interface

The problem of macroscopic behaviour of a periodic, elastic-plastic, fibrous composite material with frictional fibre-matrix interface is considered. Anti-plane shear of the material is analysed. The problem is formulated with the help of variational inequalities using the two approaches: displacement-based and stress-based ones. The variational inequalities are solved using the finite element method. In the case of stress-based approach, the Prandtl stress function is utilized. The obtained effective constitutive model of the composite can be used directly in analysis of the problem of torsion of a composite bar with a fine, periodic structure.