Area-preserving azimuthal shear deformation of an incompressible tube reinforced by radial fibres

The principal problem of interest in this paper is that of the area-preserving azimuthal shear strain of an incompressible transversely isotropic hyper-elastic circular cylindrical tube subjected to homogeneous radial tractions on both its inner and outer boundaries. A considerable part of the solution to this problem is achieved numerically. A comparison is made between the stress distributions obtained here when fibres are very strong and their counterparts obtained in the limiting case of an ideal fibre-reinforced material [Soldatos, J Eng Math 68(1):99-127, 2010]. Pure azimuthal shear strain may be considered as a particular case of the present deformation. However, in the present case, equilibrium requires a change of the inner and outer tube boundaries which, due to the incompressibility constraint, may take place only in a manner which preserves the area of the tube cross section. Another particular case is the isotropic material counterpart of the present problem, which was considered previously.