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Abstract: We explore a variationally based nonlocal damage model, based on a combination of a nonlocal variable and a local damage variable. The model is physically motivated by the concept of “nonlocal” effective stress. The energy functional which depends on the displacement and the damage fields is given for a one-dimensional bar problem. The higher-order boundary conditions at the boundary of the elasto-damaged zone are rigorously derived. We show that the gradient damage models can be obtained as particular cases of such a formulation (as an asymptotic case). Some new analytical solutions will be presented for a simplified formulation where the stress–strain damage law is only expressed in a local way. These Continuum Damage Mechanics models are well suited for the tension behaviour of quasi-brittle materials, such as rock or concrete materials. It is theoretically shown that the damage zone evolves with the load level. This dependence of the localization zone to the loading parameter is a basic feature, which is generally well accepted, from an experimental point of view. The computation of the nonlocal inelastic problem is based on a numerical solution obtained from a nonlinear boundary value problem. The numerical treatment of the nonlinear nonlocal damage problem is investigated, with some specific attention devoted to the damageable interface tracking. A bending cantilever beam is also studied from the new variationally based nonlocal damage model. Wood’s paradox is solved with such a nonlocal damage formulation. Finally, an anisotropic nonlocal tensorial damage model with unilateral effect is also introduced from variational arguments, and numerically characterized in simple loading situations. [ABSTRACT FROM AUTHOR]

Abstract: Through a mixed local and nonlocal formulation, a continuous transition from a local to a nonlocal behavior is obtained. Initially driven by the local action, the damage driving quantity at a material point in non-damaged materials is later influenced by the nonlocal effect only if the occurrence of damage is effectively found in the surroundings. Qualitative resemblance is hence expected in the prediction of damage initiation by the non-regularized and regularized damage models. Numerical simulations with simple tests and comparisons with existing nonlocal damage models show the qualitative improvement of the mixed formulation in the prediction of damage initiation for 1D and 2D damaged structures. [Copyright &y& Elsevier]