Localization properties of three-invariant plasticity models at finite strain

Strain localization refers to the formation of zones of relatively high strains. When the predominant mode is shear, one speaks of shear bands. Deformation bands (shear, compaction, dilation) are of great importance in geomechanics due to the negative impact they may have on properties such as strength, stiffness, permeability, etc. While strain localization is characterized by a strong directional feature, instabilities of the diffuse type (e.g. liquefaction), which do not display preferred orientations, also occur.; Capture of both localized and diffuse instabilities within the realm of elastoplasticity rely on the spectral properties of the continuum tangent operator. This operator is strongly affected by the adopted mechanics (geometrically linear or nonlinear) and constitutive law. In recent years, experimental observations have indicated that proper modeling of isotropic geomaterials, under multidimensional loading, requires the use of three-invariant models.; The purpose of this dissertation is to investigate the effect of the third invariant on the stability of geomaterials undergoing finite deformations.; Firstly, local sufficient conditions for the onset of both localized and diffuse instabilities are derived within the framework of isotropic hyperelastoplasticity at large strains. Localization is related to bifurcation in the material response while diffuse instability is associated with a nonpositive second order work. Secondly, a family of three-invariant models along with a principal stress space integration scheme are presented. Finally, numerical simulations are performed to assess stability characteristics.; It is shown that inclusion of the third stress invariant may lead to an increased susceptibility to both localized and diffuse instability in dilatant geomaterials. This is particularly true for stress paths with rotating principal directions. It is also demonstrated that geometric nonlinearities lead to stability predictions, which deviate from those obtained with the infinitesimal theory, when the applied deformation is large.; The use of three-invariant constitutive laws should be accompanied by an awareness of the implications for localized and diffuse instabilities. Along with material nonlinearities, three-invariant models are expected to not only lead to better capture of inelastic load-deformation behavior, but also to improve stability predictions.