DOE OSTI2014
Mechanical testing of porous materials generates physical data that contain contributions from more than one underlying physical phenomenon. All that is measurable is the "ensemble" hardening modulus. This thesis is concerned with the phenomenon of dilatation in triaxial compression of porous media, which has been modeled very accurately in the literature for monotonic loading using models that predict dilatation under triaxial compression (TXC) by presuming that dilatation causes the cap to move outwards. These existing models, however, predict a counter-intuitive (and never validated) increase in hydrostatic compression strength. This work explores an alternative approach for modeling TXC dilatation based on allowing induced elastic anisotropy (which makes the material both less stiff and less strong in the lateral direction) with no increase in hydrostatic strength. Induced elastic anisotropy is introduced through the use of a distortion operator. This operator is a fourth-order tensor consisting of a combination of the undeformed stiffness and deformed compliance and has the same eigenprojectors as the elastic compliance. In the undeformed state, the distortion operator is equal to the fourth-order identity. Through the use of the distortion operator, an evolved stress tensor is introduced. When the evolved stress tensor is substituted into an isotropic yield function, a new anisotropic yield function results. In the case of the von Mises isotropic yield function (which contains only deviatoric components), it is shown that the distortion operator introduces a dilatational contribution without requiring an increase in hydrostatic strength. In the thesis, an introduction and literature review of the cap function is given. A transversely isotropic compliance is presented, based on a linear combination of natural bases constructed about a transverse-symmetry axis. Using a probabilistic distribution of cracks constructed for the case of transverse isotropy, a compliance expression is presented that demonstrated a decrease in lateral stiffness, but leaves axial stiffness unchanged. A demonstration of how the distortion operator could be used in the elastic/plastic analysis of a von Mises surface loaded in TXC is also presented.