Antisymmetric Bifurcations in a Compressible Pressure-Sensitive Circular Cylinder Under Axisymmetric Tension and Compression

Abstract

This paper examines antisymmetric bifurcations of geometric diffuse modes, including buckling and surface rumpling modes, for a compressible pressure-sensitive circular cylinder of finite length under axisymmetric loadings. The analysis includes the effects of nonnormality, transverse isotropy, and confining stress on the appearance of antisymmetric geometric diffuse modes and their relationship to the onset of localization. The long wavelength limit of the eigenvalue equation is found corresponding to the Euler’s buckling load; the short wavelength limit corresponds to the eigenstress for the surface rumpling mode if the cylinder is incompressible and satisfies plastic normality. If the lateral stress is nonzero, a finite solution exists for the antisymmetric long wavelength limit; for the cases that the in-plane bulk modulus becomes unbounded, this finite eigenstress equals to the plane-strain results obtained by Chau and Rudnicki (1990). The lowest possible bifurcation stresses are plotted for various constitutive parameters by combining the results of the bifurcation analyses for both the axisymmetric (Chau, 1992) and the antisymmetric modes. This eigenvalue surface also provides a condition that determines whether buckling (antisymmetric) or bulging (axisymmetric) appears first for a fixed specimen geometry under compression. For typical specimen size (length/radius ratio from 4 to 6), the numerical results suggest that the first possible bifurcation is always the antisymmetric buckling mode under compression; however, for specimen sizes with length/radius ratio approximately less than π/2, bulging mode becomes the first possible bifurcation. The hypothesis that the prepeak and antisymmetric bifurcation triggers the subsequent localization of deformation is further discussed.