Fluid-pressure eigenstates and bifurcation in tension specimens under lateral pressure

An analysis is presented of an eigenstate that may be significant in deformation processes where part of the surface of a body is subjected to loading by uniform fluid pressure. The ‘fluid-pressure eigenstate’ is a configuration in which quasi-static incremental deformation is possible under surface traction-rates that are related to the instantaneous velocity field in a certain way, the fluid pressure being momentarily stationary. Deformation processes exist such that, given certain rate boundary-conditions, uniqueness of the incremental deformation is guaranteed at every instant up to a fluid-pressure eigenstate. For a cylindrical specimen, of arbitrary cross-section, of elastic/plastic or incompressible, finite elastic material it is shown that the first fluid-pressure eigenstate to be reached on a path of uniform stretching corresponds to the instant at which the ‘effective load’ reaches a maximum. No fluid-pressure eigenstates are reached in isotropic Cauchy-elastic solids under all-round fluid pressure loading provided the physically reasonable conditions that the instantaneous bulk and shear moduli remain positive are satisfied.