Constitutive bifurcation and shear band initiation of rate independent brittle damage materials

Continuum damage mechanics (CDM) has been widely used to model the mechanical behavior of brittle damage materials for the last two decades. In this dissertation, the stability issues of the CDM models are studied. The stress-strain relations derived from CDM theory are shown to possess bifurcation points associated with the loss of uniqueness of the constitutive configurations. The study focuses on damage models which are restricted to elastic-brittle response with distributed microcracks causing the reduction of stiffness of the material. It is shown that this nonlinear degradation of the material, despite restriction to infinitesimal strain, leads to the presence of multiple constitutive paths. The stability of the constitutive paths is analyzed by considering augmented dynamical systems. Asymptotic post-bifurcation analyses are also presented demonstrating the sensitivity of the material strength to imperfections in the form of deviations from initial isotropy.;The effects of material degradation on failure modes of a brittle damage material are also investigated. Bifurcations from the homogeneous deformation mode in the form of shear bands are captured for loading conditions of plane strain compression and uniaxial compression. The inclination angle and critical strain for shear band initiation are calculated based on the well-founded mathematical theory. In contrast with the previous research on shear band initiation that all rely on plasticity and flow theory formulation, the present study finds it sufficient for the shear band to emerge in the regime of infinitesimal strain for brittle damage materials. A finite element simulation of shear band initiation for a rectangular mesh deformed in plane strain compression is also presented.;Applications are then directed to boundary value problems involving ice and structure indentation. The ice medium is idealized as a bar of polycrystalline ice and a three dimensional continuum damage model is used to define the constitutive response. Constitutive bifurcation points are captured on the rate dependent stress-strain curves and the phenomenon of brittle to ductile transition is successfully explained using the constitutive bifurcation theory.