Rational Bézier triangles for the analysis of isogeometric higher-order gradient damage models
The computational approach of modeling smeared damage with quadrilateral elements in isogeometric analysis (e.g., using NURBS and T-splines) has limitations in scenarios where complicated geometries are involved. In particular, the higher-order smoothness that emerges due to the inclusion of higher-order terms in the nonlocal formulation is not always easy to preserve with multiple NURBS patches or unstructured T-splines where reduced continuity is observed at extraordinary points. This
... oints. This drawback can be bypassed by the use of Bézier triangles for domain triangulation, which significantly increases the flexibility in discretizing arbitrary spaces and eases the difficulty in handling singular points resulting from sharp changes in curvature. Moreover, the process of mesh generation can be completely automated and does not require any user intervention. We also adopt in this research an implicit higher-order gradient damage model in order to fix the non-physical mesh dependency exhibited in continuum damage analysis. For the solution of the fourth-order and sixth-order gradient damage models, Lagrange multipliers are adopted to elevate the global smoothness to a desired order in an explicit fashion. The solution algorithm initializes with the cylindrical arc-length method and switches to a dissipation-based arc-length control for better numerical stability as the damage evolves. A number of numerical examples with singularities demonstrated improved results in terms of efficiency and accuracy, as compared to the damage models represented by Powell-Sabin triangles.