Global existence for finite strain plasticity based on the plastic metric tensor.

Diego Grandi (Università di Vienna)

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Global existence for finite strain plasticity based on the plastic metric tensor.

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Abstract
A finite-strain plasticity model based on the symmetric plastic strain $\mathbf
C_p=\mathbf P^\top \mathbf P $ (where $\mathbf P$ is the usual plastic deformation
tensor) is discussed.  Such assumption reflects the invariance of the model with respect to frame
transformations of the intermediate configuration. A quasi-static setting is assumed for
elastic response, while the plastic flow rule is expressed in a variational form in terms
of free-energy and dissipation potentials, corresponding to a rate-independent evolution.
The resulting variational model is lower-dimensional, symmetric,
and based solely on the reference configuration. We discuss the existence of energetic
solutions for the quasistatic boundary-value problem.
These solutions are constructed as limits of time discretizations.