ABSTRACT
The existence of an equation of state for u and the requirement of a nonnegative energy dissipation are the consequences of the general principles
of thermodynamics. It is therefore necessary to introduce an energy dissipation function that fully describes the dissipative process. Within the simplifying assumption of a time independent process, we may replace this notion by the notion of inelastic criteria. These inelastic criteria
characterize the limit behavior between an elastic and an inelastic state under arbitrary loading conditions. These inelastic criteria are represented by a scalar mapping of the form
where S:={t|t=tT} represents the space of arbitrary second order symmetric tensors, k is a scalar. The domain in the (t, q) space encompasses the set of all physically admissible states (t, q) and is defined by
hardening/softening rule, respectively. and are nonnegative parameters, is a scalar function that characterizes how the damage evolves and is an equivalent strain measure which will be specified in section 3.2. The model is completed with the introduction of the loading/unloading conditions in the Kuhn-Tucker form along with the consistency condition
3.1 The plastic model: Cap model The adopted cap model can be characterized with the following key words: isotropic, rate-independent, associative with respect to the flow rule and nonassociative with respect to the hardening rule (in the framework of a consistent linearisation), composed of three yield surfaces with nonsmooth transition and described by two stress tensor invariants (I1, J2). In Figure 1 the cap model is represented in the (I1, J2) plane. The functions for the description of the model follow the work of Hofstetter et al. [1] and are shown in Table 1(the notation was adopted from [1]). The yield surfaces are represented by eq. (h) in Table 1. The reader is also refered to the original development of the cap model, see DiMaggio and Sandler [3].
