8.1 INTRODUCTION

The use of an elastic work-hardening-plastic model to describe the stress-strain behavior of concrete materials is attractive in view of the many apparent similarities between the behavior of concrete materials in compression and of an idealized elastoplastic material with work hardening. This can be seen from the stress-strain relation as symbolized by the uniaxial stress-strain curve for plain concrete in simple compression (Fig. 6.1). The nonlinear deformations from point A to D are basically inelastic, since upon unloading only a portion ? ^e can be recovered from the total deformations ? = ? ^e + ? ^p. It is clear that the latter phenomenon corresponds exactly to the behavior of a work- or strain-hardening elastoplastic solid.

Figure 8.1: Bauschinger effect, i.e., an unequal raising of the yield value or actual lowering when the yield stress is reversed.

In developing suitable constitutive equations for plastic materials, two basic approaches have been used. The first is the so-called total-strain or deformation type. Deformation theories of plasticity for work-hardening materials postulate that the state of stress determines the state of strain uniquely as long as plastic deformation continues. They are identical with nonlinear-elastic stress-strain relations of Chap. 4, as unloading does not occur. For example, if isotropy is assumed, the most general form of deformation theory can be written as

where ? ^p _ij = ? _ij ? ? ^e _ij is the plastic component of strain; the elastic component is assumed...