Chapter 2 Plasticity Review 2.1 Stress Invariants

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The creation of the concrete model in this thesis required extensive use of current plasticity theory. In order for the reader to understand the model, a brief review of relevant plasticity theory is presented here. First, Section 2.1 defines the stress invariants used for the definition of this model and discusses their physical significance. Second, the definition and requirements of a failure surface are reviewed in Section 2.2. Third, the definitions for plastic flow and effective plastic strain are discussed in Section 2.3. Finally, the consistency condition, used for determining the tangent material matrix, is outlined in Section 2.4. For a complete discussion of plasticity theory and its application to concrete, see Chen (1982). For a concrete model to be most useful, the model itself should be defined independent of the coordinate system attached to the material. Thus, it is necessary to define the model in terms of stress invariants which are, by definition, independent of the coordinate system selected. The three-dimensional stress state of the material is traditionally defined by the stress tensor, which can be represented relative to a


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