Two-field variational formulations for the problem of the beam on a continuous elastic support

Localization and dissipation in a nonlocal strain softening bar are investigated analytically. A nonlocal elastic-plastic model consistent with thermodynamic theory is proposed. The flow rules of nonlocal associated plasticity are derived by invoking a generalized form of the principle of maximum dissipation in classical plasticity. Analytical solutions are derived for a linearly strain softening material. The relationship between nonlocal characteristic length and width of localized zone is elucidated. A comparison with results obtained from corresponding gradient approach is presented. 0 1997 Elsevier Science Ltd