Bifurcations of thick-walled hollow cylinders of geomaterials under axisymmetric compression

This paper derives analytically the condition for the onset of diffuse mode bifurcations in thick-walled hollow cylinders with internal radius a, external radius b and length L under axial compression and confining pressure. The thick-walled cylindrical specimens are made of geometrical characterized by Rudnicki's constitutive model, and the method of solution for the governing equations is the velocity potential approach employed by Chau. Numerical results show that thick-walled cylinders are stronger than thin-walled cylinders against diffuse mode bifurcations, including both buckling, axisymmetric and non-axisymmetric deformations. In contrast to the conclusion for solid cylinders (Chau), no buckling solution is found for γ=mπa/L smaller than about 0.7 under compression for a fixed and finite value of a/b (i.e. no buckling for long and slender hollow cylinders with small a/L and fixed b/a). When 0.7 <γ<0.9, buckling is the expected first bifurcation; whereas, when γ>0.9, bulging or barrelling is anticipated. The exact value of ↔ that excludes buckling and separates the buckling and barrelling phenomena depends on the current values of the constitutive parameters of the solid. Hollow cylinders with higher degree of anisotropy, disobeying normality flow rule, and subjected to confining pressure are more conducive to bifurcations than cylinders made of materials with isotropy, obeying normality, and subjected to no confining pressure. In addition, diffuse mode bifurcations are found possible in the pre-peak regime of the stress-strain curve.