Feature-preserving rational Bézier triangles for isogeometric analysis of higher-order gradient damage models

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The computational approach of modeling smeared damage with quadrilateral elements in isogeometric analysis (e.g., using NURBS or 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 often easy to preserve with multiple NURBS patches or unstructured T-splines where reduced continuity is observed at patch interfaces and extraordinary points. This defect can be circumvented by the use of rational Bézier triangles for domain triangulation. In particular, rational Bézier triangles increase the flexibility in the discretization of arbitrary spaces and facilitate the handling of singular points that result from sharp changes in curvature. Moreover, the process of mesh generation can be completely automated and does not require any user intervention. A Delaunay-based feature-preserving discretization coupled with a local refinement technique is implemented to capture small geometric features and locally resolve areas of damage propagation. Additionally, we adopt an implicit higher-order gradient damage model in order to amend the non-physical mesh dependency issue exhibited in continuum damage analysis. For the solution of the fourth- and sixth-order gradient damage models, Lagrange multipliers are leveraged to elevate the global smoothness to any desired order in an explicit manner. The solution algorithm is initialized with the cylindrical arc-length control and switches to a dissipation-based arc-length control for better numerical stability as the damage evolves. Numerical examples with singularities demonstrate improvements in terms of efficiency and accuracy, as compared to the damage models represented by Powell–Sabin B-splines.