Under the effect of an inner pressure, a thick hyperelastic shell cylinder is susceptible to developing mechanical instabilities, leading to a bifurcated shape that no longer has the initial cylindrical symmetry. The considered problem has a strong resonance in a biomedical context, considering pathologies encountered for arteries, such as aneurysm. In this contribution, the mechanical behavior of thick elastic shells has been analyzed, considering a thick-walled cylindrical hyperelastic model material obeying a transversely isotropic behavior, first in a large-displacement situation and then in a large-deformation case. The response of the material is assumed to be instantaneous, so that time-dependent effects shall not be considered in this paper. The case of a Saint-Venant–Kirchhoff material is considered with special emphasis to exemplify a large-displacement small-strain situation; the neo-Hookean behavior is next considered to enlarge the constitutive law toward consideration of large strains. The stability conditions of the shell are studied and bifurcation conditions formulated in terms of the applied pressure and of the geometrical and mechanical parameters that characterize the shell. Analytical solutions of some bifurcation points are evidenced and calculated when the direction of the fibers coincide with the cylinder axis.
