Example 19: Nonlocal plasticity in softening bar.

A bar is clamped at the left edge and is subjected at the right edge to a prescribed deformation. A plasticity model is used to limit the possible tensile stress in the bar. This limit of the tensile stress is softened to zero with the effective plastic strain $\kappa$. Due to softening, unlimited localization would be possible. This is prevented, however, by applying a viscoplastic power law in combination with a nonlocal yield rule, see options_nonlocal. A nonlocal radius of $0.2$ is used in the determination of the nonlocal yield rule.

At the right side of the bar we introduce a relatively weak spot, so that plasticity occurs first there. In the plots below the results for the velocity field $v_x$, the effective plastic strain $\kappa$ and the nonlocal yield rule $fn$ respectively are shown. Please notice that the softening zone is of a limited, non mesh dependent, size.