Bifurcations of compressible pressure-sensitive materials in plane strain tension and compression

Bifurcations, including shear band and diffuse geometric modes, are analysed for plane strain deformation of a rectangular slab subject to a constant lateral confining stress. The response of the slab material is characterized by an incrementally linear constitutive relation that allows for the possibility of volume change accompanying shear deformation, pressure dependence and deviations from plastic "normality". When the lateral confining stress is zero, the picture of bifurcations is qualitatively similar to that investigated by Needleman (J. Mech. Phys. Solids 27, 231, 1979) for incompressible materials. For example,. when normality is satisfied, localization is excluded by a positive uniaxial tangent modulus (to within terms of order stress divided by elastic modulus), deviations from normality promote localization, and the occurrence of a long wavelength symmetric, diffuse bifurcation coincides with the attainment of maximum load in tension. However, increasing the compressibility decreases the value of the uniaxial tangent modulus at which localization modes become possible. When lateral confining stress is non-zero, differences from the analysis of Needleman (1979) are more dramatic. For example, a finite stress difference is required for the onset of an anti-symmetric, long wavelength bifurcation and, when the lateral stress is compressive, shear band modes become possible prior to the maximum load in tension.