Plasticity theory for concrete is based on the observation that concrete fails along planes. These planes slide against and/or separate from each other during failure. If it isassumed that concrete is a ductile material, capable of redistributing stresses along the failure plane, then plasticity theory can be applied to it. The question, naturally, is whether this assumption is valid.
Before embarking on that question, it is necessary to know a few of the less controversial assumptions. These are that the Modified Mohr-Coulomb Failure Criterion with a tension cut-off is used. All blocks between zones of discontinuity (or yield-lines) are assumed to be rigid. Plane stress or plane strain conditions can occur across the failure plane, the choice of which is up to the user.
Concrete is a brittle material. Is it a valid argument to use the theory of plasticity for analysing such a material? Plasticity theory relies on infinite ductility.
Ductile failure in reinforced concrete can easily be demonstrated in bending of beams or slabs, where the ultimate moment capacity and yield-line theories have been accepted as good representations of the behaviour of reinforced concrete structures.
It is in shear that the theory of plasticity applied to concrete is more questionable.
Plain concrete is a wholly brittle material. Reinforced concrete, on the other hand is not necessarily brittle. Indeed, shear failures of beams containing 'reasonable' quantities of longitudinal and stirrup steel are generally not as brittle as might be expected. Beyond the ultimate load, gradual softening of the structure occurs, with much internal energy being dissipated over a reasonable displacement variation in the structure. In such cases, plasticity theory may well be a viable choice of analysis method. However, in cases which fall outside the 'reasonable' reinforcement arrangement, it is more debatable whether to rely on plasticity or not. For instance, either extremely under- or over-reinforced sections would be inappropriate for plasticity analysis, due to the possible brittleness of failure. In addition, the absence of stirrups would suggest that ductility was severely limited in such a structure.
Therefore, it is imperative that one knows when the theory is applicable or not.
Having said that, the following statement is of relevance. If it can be shown that plasticity theory predicts reasonable results even outside the obvious areas of applicability, then the method should be considered in some way. The only way to show this is by experiments. Such testing was carried out.
The models I worked on cover the following.
The 2-D model looks at a beam with arbitrary cross-section, loaded in any way. The beam fails in shear along a line of discontinuity, which is piece-wise linear. This allows optimisation of the shape of the line, with respect to the kinematic variables being applied to the rigid portions of the beam (rotations and displacements).
This model was formulated and compared with several hundred test results to calibrate the theory. Such calibration is necessary, as the so-called 'effectiveness' of the concrete is important in plasticity. Because the concrete cannot attain its maximum strength all along the line of discontinuity at the same time, an 'effectiveness factor' is used to reduce the strength of the concrete correspondingly and produce the correct result during calibration. Following calibration, this model was compared with several dozen more tests and a favourable correlation between test and theory was obtained.
The goal of this research, however, was the determination of shear strength of concrete beam-and-slab bridges, rather than individual beams. Therefore a 3-D model was developed, based on the failure mechanisms observed during testing of such structures. This model consisted of beam shear failure, coupled with adjacent slab failure to create an overall mechanism of failure.
While plasticity theory has been used in this research, it is not implied in any way that plasticity theory is always applicable to concrete structures. On the contrary, as a by-product, we hope to determine just when we should or shouldn't be using this theory.