Summary
A theory of finite deformation plasticity is developed which involves a multiplicative decomposition of the deformation gradient through the assumption that there exists a stress-free configuration which can be used to separate the elastic and plastic components of the response. By using the polar decomposition on the usual indeterminate elastic and plastic deformation tensors, two uniquely defined stress-free configurations can be identified. The structure of this theory is compared with that of a spatial theory involving the polar decomposition of the total deformation gradient. It is shown that for the special case of linear response between the stress and the elastic strain, the two theories are indistinguishable in terms of their stress responses.
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Bammann, D.J., Johnson, G.C. On the kinematics of finite-deformation plasticity. Acta Mechanica 70, 1–13 (1987). https://doi.org/10.1007/BF01174643
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DOI: https://doi.org/10.1007/BF01174643