PROGRESSIVE DAMAGE AND CONSTITUTIVE BEHAVIOR OF GEOMATERIALS INCLUDING ANALYSIS AND IMPLEMENTATION.

Abstract

In this dissertation, first the experimental and theoretical observations on the deformational characteristics of brittle geomaterials are reviewed and discussed. A basic conclusion is that special features such as strain softening can not be considered as true material (continuum) properties. These conclusions created a renewed emphasis on the constitutive modelling of such materials. A model that accounts for structural changes is developed. Such changes are incorporated in the theory through a tensor form of a damage variable. It is shown subsequently that formation of damage is responsible for the degradation in strength (softening) observed in experiments, for the degradation of the elastic shear modulus and for mechanical, damage induced anisotropy. A generalized plasticity model is incorporated for the so-called topical or continuum part of the behavior, whereas the damage part is represented by the so-called stress-relieved behavior. The question of uniqueness in the strain-softening regime is examined. It is shown that the constitutive equations lead to a unique solution for the case of rate dependent as well as rate independent formulation. Its implementation in finite element analysis shows mesh size insensitivity in the hardening and softening regimes. The general order of bifurcation of differential equations is employed in order to study the effect of damage accumulation on formation of narrow, so-called shear bands. It is shown that as the damage accumulates, the material approaches localization of deformation. The theory of mixtures is employed for further theoretical establishment of the proposed model. Energy considerations show the equivalence of the two-component damage body to an elastoplastic body containing cracks; the equivalence is considered in the Griffith sense. The mechanisms of failure are considered and discussed with respect to multiaxial stress pads. An explanation of failure, at the micro level, is given. The material constants involved in the theory are identified and determined from available experimental data. The model is then verified by back-predicting the observed behavior.