On the concept of an intermediate configuration and its application to a representation of viscoelastic-plastic material behavior

Abstract

The term intermediate configuration denotes a general concept, which can be applied to represent some types of inelastic material behavior. Basically, the 'idea of an intermediate configuration leads to a decomposition of the constitutive functional: It implies a rather simple constitutive equation of elastic or viscoelastic type, but this constitutive equation is related to a varying configuration, which depends on the history of the mechanical process in a more complicated way. The concept of an intermediate configuration is related to the question of a decomposition of the total strain into components corresponding to different physical qualities. These different components are called elastic and plastic parts or, more generally, recovered and unrecovered parts of the total strain. There are situations where the solution of engineering problems requires a consistent analysis of finite deformations. In these cases the question of decomposition together with the associated problem of a convenient formulation of constitutive assumptions has to be carefully considered. The history of the discussion about the decomposition problem and its main arguments within a rational foundation of the idea of an intermediate state will not be described here. The reader might be referred to papers of GREEN & NAGI-,IDI [1965, 1966, 1971], BESSELING [1966], LEE [1969, 1981], KLEIBER [1975], LEHMANN [1982] etc.; of course, this list should not be regarded as complete. In this paper some arguments are reviewed to understand the phenomenological description of finite plastic deformations within the constitutive theory of simple materials with memory in the sense of TRUESDELL ~ Note [1965]. Essentially, the intermediate state represents an accumulation of permanent memory effects, whereas the relation between the actual and the intermediate state is characterized by fading memory properties (see also HAUPT [1977]). In the following the intermediate configuration is understood as a noncompatible strain field, which arises as a result of a local unloading process. In other words, this intermediate state of strain is the asymptotic limit of the response of the material element to a given mechanical process, which is followed by a state of zero stress. Essentially, this is the idea of a natural state, which has been discussed by HOLSAPPLE [1973a, b, c] in the context o f the functional theory of simple materials with memory. In general, the local unloading process is an abstract idea, that means: it does not take place in reality. Therefore, as an alternative, it could be governed by a fictitious elasticity law: This version might be useful in view of a more general incorporation of