# Serial deformation maps and elasto-plastic continua

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## Abstract

This paper deals with the kinematics of finite plastic deformation. The starting point is E.H. Lee’s *multiplicative* decomposition of the deformation gradient into its elastic and plastic parts. We *diverge from Lee’s (and others’) derivation of the deformation rate and spin tensors* and prove that the elastic and plastic deformation rate and spin tensors *are additive*. It is then shown that the elastic and plastic strains are also additive and equal to the total strain. A central result, and a major deviation from continuum mechanics, is that not one, but two deformation maps are necessary for the constitutive response in elasto-plasticity. The two-map decomposition is then extended to the n-th order, and additivity is shown there as well. Elastoplastic constitutive equations in large deformation are presented and discussed in the context of path-dependent (endochronic) plasticity.

## Notes

## References

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