ABSTRACT
When a body is subjected to external forces (body forces and surface tractions), its particles are in general subjected to components of stress as a result of which they deform. When the values of the external forces are small, the body and its particles assume their undeformed configuration upon removal of the external forces. That is, the deformation of the body is reversible. No energy is lost during the process of loading and unloading. In this case we say that the deformation of the body and its particles is elastic. For sufficiently high magnitudes of the external forces, the components of strain of some particles of the body may include an irreversible part. We say that at these particles
ijplastic deformation or yielding has occurred. The components of strain e of these
particles are equal to the sum of an elastic part and a plastic part . That is,
In this section we focus our attention to two models of idealized time-independent material behavior under general three-dimensional states of stress. These models are the isotropic, rigid-ideally plastic and the isotropic, linearly elastic-ideally plastic. In the special case of a uniaxial state of stress, these models reduce to the corresponding models described in Section 3.6 (see Fig. 3.14c and e, respectively). For these models of idealized time-independent material behavior, we present criteria for defining the limiting combinations of values of the components of stress acting on a particle of a body, for which its deformation is elastic.
