For many practical applications, a material may be idealized and assumed to have a negligible strain-hardening effect, i.e., its uniaxial stress-strain diagram beyond the yield point can be approximated by a horizontal straight line, with the constant stress level ? 0 (Fig. 4.1a). Thus, plastic deformation is assumed to occur under a constant flow stress. This behavior is called perfectly or ideally plastic behavior.
Perfectly plastic idealization can lead to a drastic simplification of the analysis of a complex structural problem. In particular, for a perfectly plastic material, the powerful upper- and tower-bound theorems of limit analysis can be established, from which simple, direct, and realistic methods for estimating the load-carrying capacity of structures in a direct manner can be developed. These bounding theorems and their applications to structural engineering problems will be given in Chapters 8 and 9. This chapter deals only with the stress-strain relations of a perfectly plastic material.
The stress-strain relation in the uniaxial case as shown in Fig. 4.1a is rather simple. However, the general behavior of the material under a complex stress state is not so straightforward, because it involves six stress and six strain components. The question therefore arises as to how the simple stress-strain relationships observed from a...
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