Soil is a nonlinear material that experiences a significant amount of inelastic deformation under applied loads. For many geotechnical problems, an understanding of such behavior requires the development of necessary theoretical models which are then used in the numerical evaluation of the soil response. The classical plasticity theory provides a suitable framework for the development of a constitutive model (stress-strain relationship), which reproduces such a soil behavior under monotonic loading. These models employ a plastic potential and a yield surface, the latter being allowed to expand or contract depending on whether the material hardens or softens during the course of loading. However in these models, soil remains elastic within the yield surface where no plastic deformation can develop. As a consequence, these models fail to reproduce the phenomena occurring during cyclic loading, such as the progressive generation of the pore fluid pressure or the densification behavior.

In this chapter, the fundamentals of the Theory of Plasticity is presented, which provides a framework for the development of a constitutive model for the nonlinear static behavior of soils. A number of useful MATLAB programs simulating the elasto-plastic behavior under various stress-states are also included.