Compressive failure of microcracked and brittle damaged materials and structures.

When brittle elastic solids are subjected to compressive stress states, microcracks nucleate and grow as the stresses are increased. The microcracks generally grow from pre-existing flaws, pores, or other discontinuities within the solid. The presence of microcavities and microcracks affects the effective or volume average elastic properties of the material. The formation and evolution of the microcrack damage cause a progressive loss of stiffness of the constitutive response of the material. Clearly, the structural response of microdamaged materials involves the interaction of material and structural behavior on the microscale and on the macroscale. The dependence of the macroscale response on the microscale behavior generates many issues that need investigation before this dependence can be adequately understood. The first issue is the combination of fracture mechanics and micromechanics to form a highly nonlinear constitutive relation. This relation incorporates the effects of the initial microscale flaws and the developing microcrack growth in a constitutive relation that describes the macroscale behavior of the material. Another issue deals with predicting the complex modes of failure and failure strength, using various bifurcation and localization theories. These theories are used to investigate the stability of the constitutive and equilibrium paths, to determine bifurcations of those paths, and to determine if localization or global buckling occurs. The last issue is addressed by the incorporation of the micromechanics based constitutive relations into finite element analysis to determine the interaction between the global failure modes and the local instabilities. A structural analysis is also performed on a beam under axial compressions. The global buckling mode dominates when a beam is long. For short beams, the local instabilities strongly influence the global bucking mode and the critical buckling load. For cases of tensile lateral confinement on short beams, the dominant failure mode is localization in the form of fault zones, while compressive lateral confinement reduces the effects of localization.PhDApplied SciencesMechanicsOcean engineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/131131/2/9825378.pd