6 Finite Strain Elastoplasticity

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Finite strain plasticity implies the existence of large strains or rotations. Therefore, the

concept of objectivity (Section 1.6) plays a major role in the development of a finite strain

elastoplasticity theory. There are two major classes of models. The first class extends the

additive strain concept of the infinitesimal theory to the deformation rate tensor d, that

is, d = de + dp. This, however, leads to a hypoelastic formulation, which means that the

elastic stress–strain relations cannot be derived from a stored energy function. For a discussion

of this type of models the reader is referred to (Simo and Hughes 1997). The

second class of models involves a multiplicative decomposition of the deformation gradient

into a plastic and an elastic part and goes back to the work by Lee and Liu (Lee

and Liu 1967), (Lee 1969), see also (Simo 1988a), (Simo 1988b) and (Simo and Miehe

1992). Thereby, the elastoplastic motion is viewed as a composition of stress-free plastic

flow and stress-inducing elastic deformation. Because of its physical relevance and hyperelastic

description of the elastic deformation, this type of model has grown very popular.

The theory has been extended to anisotropic viscoplasticity (Miehe 1996a), (Miehe 1996b),

(Reese and Svendsen 2003) and nonlocal gradient-enhanced elastoplasticity (Geers et al.

2003). The multiplicative concept is also applicable to the inelastic deformation of nonmetallic

materials such as rubber (Lubliner 1985), (Reese 2003b) and is micromechanically

motivated (Reese 2001).

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