Abstract
The theory of plasticity as a special field of continuum mechanics deals with the irreversible, i.e. permanent, deformation of solids. Under the action of given loads or deformations, the state of the stresses and strains or the strain rates in these bodies is described. In this way, it complements the theory of elasticity for the reversible behavior of solids. In practice, it has been observed that many materials behave elastically up to a certain load (yield point), beyond that load, however, increasingly plastic or liquid-like. The combination of these two material properties is known as elastoplasticity. The classical elastoplastic material behavior is assumed to be time-independent or rate-independent. In contrast, we call a time- or rate-dependent behavior visco-elastoplastic and visco-plastic—if the elastic part of the deformation is neglected. In plasticity theory, because of the given loads the states of the state variables stress, strain and temperature as well as their changes are described. For this purpose, the observed phenomena are introduced and put into mathematical relationships. The constitutive relations describing the specific material behavior are finally embedded in the fundamental relations of continuum theory and physics. Historically, the theory of plasticity was introduced in order to better estimate the strength of constructions. An analysis based purely on elastic codes is not in a position to do this, and can occasionally even lead to incorrect interpretations. On the other hand, the entire field of forming techniques requires a theory for the description of plastic behavior. Starting from the classical description of plastic behavior with small deformations, the present review is intended to provide an insight into the state of the art when taking into account finite deformations.
Highlights
Since people have learned to melt and process metals, they know that these can be deformed under the influence of heat and large forces and that their properties can change as well
It is obvious that Eq (1) is valid only for plastic deformation
Representing a special case of the more general Prandtl-Reuss model for vanishing elastic deformations or for those cases where the latter can be neglected compared with the plastic deformations
Summary
Since people have learned to melt and process metals, they know that these can be deformed under the influence of heat and large forces and that their properties can change as well. Under loading condition beyond the yield limit and with Eq (2) during unloading and purely elastic processes, and (iii) the Prandtl-Reuss equations: ε. The two models of Prandtl-Reuss and Hencky, were a matter of discussion whether they could adequately reproduce experimental observations With this respect, Hill [7] stated that the Hencky equations were unsuitable to describe a complete plastic behavior of a metal, and further: “None the less, in situations where the loading is continuous, the Hencky equations may lead to results in approximate agreement with observations. It turned out that applying the Hencky equations could be associated with great inaccuracies, especially in those cases where the loads are prescribed in the form of non-radial processes This model, which is referred to as deformation theory, is no longer used today.
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