| Abstract: |
| Engineering materials such as metals exhibit elastic deformation under small loads, but may develop permanent (plastic) deformation once the load exceeds a threshold. In a variational framework, elastoplasticity can be formulated through a stress constraint of variational inequality type. Under repeated loading and unloading, the yield surface evolves due to strain hardening; one common modeling choice is kinematic hardening, where the admissible stress set translates in stress space as plastic deformation accumulates.
We study an elastoplastic model with kinematic hardening in a variational inequality setting, coupled with an equation of motion including Kelvin--Voigt viscosity. A key analytical and computational difficulty is to construct solutions while respecting the stress constraint at all times.
We propose a projection-based time discretization. At each time step we first compute an unconstrained trial stress and then project it onto the translated admissible set. This trial-projection strategy preserves the constraint while avoiding a nonlinear fully implicit problem, leading to a simple implementation.
We prove stability of the resulting discrete solutions under appropriate norms. Moreover, these stability estimates yield existence of a solution to the original continuous coupled problem. |
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