0The main objective of this dissertation is to develop a nonlinear constitutive model for plain concrete under uniaxial stress. In addition to providing a good stress-strain curve, the model can predict both the stress at which failure occurs and the mode of failure for concrete under both uniaxial tension and uniaxial compression. Here the failure is defined as the point at which material stability is lost, or a discontinuous bifurcation exists. The partial differential equation governing equilibrium ceases to provide stable solutions when ellipticity is lost. This criterion turns out to be the same as the existence of a discontinuous bifurcation. In particular, such a failure criterion provides the stress state at which failure occurs as well as the mode of failure. The mode of failure is given by two vectors; one gives the normal to the failure plane and the second gives the direction of relative motion of material points on the two sides of the failure plane. If the two vectors are parallel, the mode is simply called Mode I fracture. If the two vectors are perpendicular, the failure is said to be of Mode II fracture. In general, any angle between the two vectors is possible, which is mixed mode fracture. The opening mode under uniaxial tension and the vertical splitting under uniaxial compression for concrete are the Mode I failures. Here, an anisotropic damage model is developed to provide the opening failure mode under uniaxial tension; and a combined plasticity and damage model is also shown to predict the vertical splitting failure mode under uniaxial compression.
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