Plasticity, localization, and friction in porous materials
Badders, Daniel Christopher
Carroll, Michael M.
Doctor of Philosophy
Original variations of two-invariant rate-independent plasticity models capture many features of the homogeneous behavior of porous materials. All of the variations proposed are based on a simple 7 parameter critical state plasticity model proposed by Carroll (1991). The models utilize an associative flow rule along with a yield surface dependent on Terzaghi effective pressure and shear stress with plastic volume strain as the only hardening variable. In Carroll's original model, a parabolic yield surface accommodates hardening by translating along the pressure axis while the top of the yield surface moves along a critical state line. The base of the parabolic yield surface is of constant width, and hardening is linear in plastic volume strain. Even in this simple form with only 5 plastic constants the model can predict dilation, shear enhanced compaction, critical state behavior, hardening, softening, and yielding during unloading. To test Carroll's simplifying assumptions and to extend the constitutive formulation for more complex behavior, variations of the model are compared to test data published by Terra Tek. The large groups of test data for sandstone and diatomite include varied stress paths for axisymmetric loading, unloading and reloading. Modifications proposed to Carroll's model address nonlinear hardening, initial elastic transverse isotropy, variation of the shape of the yield surface, variation of the elastic moduli due to pore closure, anisotropic hardening, and pore fluid pressure interaction with matrix compressibility. Evaluation of these modifications indicates they are secondary effects and points to the strength of Carroll's original model, while providing refinements for treating these aspects of poro-behavior. Plastic softening creates potential for localization and subsequent frictional behavior. While this behavior is not represented in the constitutive model or test data, a framework is outlined for treating formation and growth of localization bands based on a bifurcation analysis of the plasticity model. The most practical application of this would be using finite elements modified to include an embedded localization. Extreme localization leading to fracture can switch the dominant form of inelastic deformation from plasticity to frictional slip. It should be possible to accommodate this behavior within an embedded localization finite element.
Mechanical engineering; Applied sciences; diatomite sandstone