Dual Adaptivity in Nonlocal Macro-meso-scale Consistent Damage model: SFVEM Discretization and Nonlocal Damage Quadrature
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A dual-adaptive framework for nonlocal macro-meso-scale consistent damage (NMMD) modeling is presented. The proposed approach introduces adaptivity at two distinct levels. The first level concerns spatial discretization and is realized by a stabilization-free virtual element method (SFVEM). The second level is intrinsic to NMMD and governs nonlocal damage interactions through adaptive damage quadrature. The two adaptive mechanisms act on different modeling layers and are independent in nature. At the discretization level, a hierarchical damage-triggered adaptive mesh refinement strategy is adopted. Mesh refinement is driven by the evolution of the damage field and is organized into two stages. In the first stage, refinement is activated at the onset of damage. This stage enhances the resolution near crack nucleation and stabilizes the representation of the crack tip. In the second stage, further refinement is applied when damage becomes strongly localized. This stage enables accurate tracking of crack propagation paths. In both stages, the target mesh size is linked to the intrinsic nonlocal length scale of the damage model, which ensures a physically consistent spatial resolution. At the modeling level, a nonlocal damage quadrature strategy with adaptive activation of virtual family points is introduced. Nonlocal interactions are initially evaluated using a reduced set of virtual point pairs to limit computational cost. When the stretch of any outer family point pair exceeds a prescribed fraction of the critical stretch, the full virtual family is activated. This binary activation mechanism enriches the damage quadrature only in regions where strong deformation and damage localization occur, while keeping the computational effort low in the remaining parts of the domain. Numerical results demonstrate that the proposed approach preserves the accuracy of crack initiation and crack propagation predictions. At the same time, a significant reduction in computational cost is achieved when compared with conventional phase-field and original strategies.
