Dynamic Stability Analysis with Nonlocal Damage

The classic localization instability analysis for strain-softening materials is expanded to dynamic solutions. The nonlocal continuum with local strain, which ensures proper convergence of finite element calculations and physically realistic solutions, is adopted in its simplified form, the nonlocal damage model. The dynamic response of a one-dimensional bar initially in a uniform strain-softening equilibrium state is calculated by finite elements. The stability limit of the bar subjected to a small initial disturbance is computed from the time evolution of the energy dissipation due to damage. The limits found for various lengths of bar are very close to static analytic calculations and exhibit the correct size effect when bars of increasing length are considered.