| Abstract: |
| Quasi-variational inequality for elastoplasticity with nonlinear kinematic hardening
Abstract: We study the mathematical formulation of elastoplasticity problems with strain hardening, focusing on nonlinear kinematic hardening. The problem is formulated as a coupled system consisting of an evolution inclusion for the stress field, described by the subdifferential operator of the indicator function associated with a constraint set, and an equation of motion for the displacement field.
Our model extends the Duvaut-Lions type formulation for perfect plasticity. The hardening behavior is characterized by the translation of the constraint
set depending on the strain through the back-stress tensor, which represents the movement of the yield surface in the stress space. This leads to a quasivariational inequality structure where the constraint set depends on the unknown function.
To prove the well-posedness, we employ a fixed-point argument. We introduce solution operators for the variational inequality and the equation of motion, respectively, and consider their composition as a mapping on a suitable function space. By establishing that this mapping is a contraction on a sufficiently small time interval, we obtain the existence and uniqueness of solutions via the Banach fixed-point theorem. The key a priori estimates then enable us to extend the local solution to the entire time interval. |
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