Localization of deformation and inelastic deformation of pressure-sensitive dilatant materials

This dissertation investigates localization of deformation (Part I) and inelastic of deformation (Part II) for pressure-sensitive dilatant materials.;Part II of the dissertation presents a variation of Costin's (1986) microcrack model and its prediction of the yield vertex effect on the effective shear moduli. The response of shearing deformation is found to be highly nonlinear at a yield or damage surface corner. This model provides a preliminary study to incorporating the reduced shear moduli into the constitutive parameters needed for the prediction of the onset of localization.;In Part I, bifurcations, including shear band and diffuse geometric modes, are analyzed for rectangular slabs under plane strain deformation and circular cylinders under axisymmetric deformations. For the plane strain analysis, Chapter 2 shows that when the lateral confining stress is zero, the picture of bifurcations is qualitatively similar to that investigated by Needleman (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. 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. For a circular cylinder under axisymmetric deformation, Chapter 3 shows that introduction of transverse anisotropy and non-normality promotes not only localization but also geometric diffuse modes under compression. Numerical solutions of the eigenvalue equation for the elliptic complex regime demonstrate that some geometric diffuse modes with finite wave number, instead of bulging mode, become the first possible bifurcation under compression. The possible angle of localization that may be triggered by such diffuse modes is about the same as those predicted by shear band analysis. Consequently, such diffuse eigenmodes may trigger localization in the vicinity of peak stress.