ABSTRACT
Plasticity was originally developed for modeling the behavior of a wide variety of metals, which are pressure-insensitive and incompressible. Figure 5.1 shows some idealizations of these material responses, including both elastic and plastic materials: (a) nonlinearly elastic; (b) linearly elastic; (c) inelastic or plastic; (d) rigid, perfectly plastic; (e) elastic, perfectly plastic; (f) rigid, work-hardening; and (g) elastic, work-hardening. The traditional plastic materials were assumed to satisfy associated flow rule or normality law during plastic deformation. This, however, is not true for geomaterials, such as soil and rocks. For geomaterials, terms like non-associated flow rule or non-normality rule emerge naturally due to their constitutive properties, including pressure-sensitivity (i.e., frictional effect), compressibility, and plastic dilatancy. The application of plasticity to soil mechanics starts probably with Drucker and Prager (1952), who extended the classical form of Coulomb criteria to three-dimensional cases (Pietruszczak, 2010), and its application to rock-like materials is more recent (Rudnicki and Rice, 1975). In this chapter, we will present a generalized constitutive form which is applicable to both soils and rocks.
