5.1 Introduction

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The materials treated so far had no memory. The instantaneous deformation for such materials

is a function of the instantaneous loading only. The previous loading history is of no

importance. However, for a lot of practical materials this assumption does not hold. A piece

of metal that has been forged into a car component will react differently on loading because

of the forging process: the component remembers it has been forged. Furthermore, the activation

of memory allows for the simulation of another new phenomenon: irreversibility

of deformation. Without this feature, it would be impossible to deform a body into a new

form without continuously applying loads: on releasing pressure, a car would return into

ore!

Memory and irreversibility of deformation are two important characteristics of plasticity.

Although the term is most often applied to metals, it is also used to describe irreversible

behavior in soils, biological tissue, and so on. Here, we treat metals only. Furthermore,

attention is focused on the infinitesimal theory, that is, strains and rotations are assumed

to be so small that material and spatial quantities coincide. First, the general framework

is derived using the one-dimensional example as a guide. Then, the isotropic viscoplastic

theory is deduced. Finally, a detailed analysis is presented of single-crystal viscoplasticity

and von Mises plasticity of elastically anisotropic materials. The treatment of other viscoplastic

formulations, such as Drucker–Prager or Gurson, runs along the same lines. For

fundamental reference works on plasticity, see ((Kachanov 1971); (Lemaitre and Chaboche

1990); and (Save and Massonnet 1972)).

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