Non-normality and bifurcation in a compressible pressure-sensitive circular cylinder under axisymmetric tesion and compression

This paper examines bifurcations, including diffuse bifurcation modes of deformation, such as necking, bulging and surface rumpling, and localized bifurcation modes, corresponding to the formation of shear bands, for a compressible pressure-sensitive circular cylinder under axisymmetric deformations. The analysis emphasizes the effects of non-normality, transverse anisotropy, and confining stress on the appearance of diffuse modes and their relationship to the onset of localization. In particular, introduction of transverse anisotropy and non-normality promotes not only localization but also geometric diffuse modes under compression. In addition, constant compressive confining stress promotes diffuse modes under compression but hinders them under tension. For the surface rumpling mode (short wavelength limit of diffuse mode), both anisotropy and compressive lateral stress favor pre-peak bifurcations; in-plane compressibility promotes prepeak bifurcations under compression but retards them under tension. Numerical solutions of the eigenvalue equation for the elliptic complex regime demonstrate that the earliest bifurcation available is the diffuse necking mode under tension. However, unexpectedly, some geometric diffuse modes with finite wave number, instead of the bulging mode, become the first possible bifurcation under compression. The possible angle of localization that may be triggered by such diffuse modes is about the same as those predicted by shear band analysis. Consequently, such diffuse eigenmodes may trigger localization in the vicinity of peak applied stress.